Journal articles: 'Geometry and topology in quantum mechanics and condensed matter'

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GU, B. Y., and CHAITALI BASU. "A NUMERICAL STUDY OF THE QUANTUM OSCILLATIONS IN MULTIPLE DANGLING RINGS." International Journal of Modern Physics B 09, no. 23 (October 20, 1995): 3085–97. http://dx.doi.org/10.1142/s0217979295001178.

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We present the quantum mechanical calculations on the conductance of the quantum waveguide topology containing multiply connected dangling mesoscopic rings with the transfer matrix approach. The profiles of the conductance as functions of the Fermi wave number of electrons depend on the number of rings and also on the geometric configuration of the system. The conductance spectrum of this system for disordered lengths in the ring circumferences, dangling links, ballistic leads connecting consecutive dangling rings is examined in detail. We find that there exist two kinds of mini-bands, one originating from the eigenstates of the rings, i.e. the intrinsic mini-bands, and the extra mini-bands. Some of these extra minibands are associated with the dangling links connecting the rings to the main quantum wire, while others are from the standing wave modes associated with the ballistic leads connecting adjacent dangling rings. These different kinds of mini-bands have completely different properties and respond differently to the geometric parameter fluctuations. Unlike the system of potential scatterers, this system of geometric scatterers shows complete band formations at all energies even for finite number of scatterers present. There is a preferential decay of the energy states, depending upon the type of disorder introduced. By controling the geometric parameters, the conductance band structure of such a model can be artificially tailored.

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Yu, Min, Pengcheng Yang, Musang Gong, Qingyun Cao, Qiuyu Lu, Haibin Liu, Shaoliang Zhang, et al. "Experimental measurement of the quantum geometric tensor using coupled qubits in diamond." National Science Review 7, no. 2 (November 27, 2019): 254–60. http://dx.doi.org/10.1093/nsr/nwz193.

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Abstract Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.

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Canessa, Enrique. "Possible connection between probability, spacetime geometry and quantum mechanics." Physica A: Statistical Mechanics and its Applications 385, no. 1 (November 2007): 185–90. http://dx.doi.org/10.1016/j.physa.2007.06.006.

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Stachurski, Zbigniew H., and T. Richard Welberry. "Geometry and Topology of Structure in Amorphous Solids." Metallurgical and Materials Transactions A 42, no. 1 (July 23, 2010): 14–22. http://dx.doi.org/10.1007/s11661-010-0270-y.

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Ochoa, Hector, and Yaroslav Tserkovnyak. "Quantum skyrmionics." International Journal of Modern Physics B 33, no. 21 (August 20, 2019): 1930005. http://dx.doi.org/10.1142/s0217979219300056.

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Skyrmions are topological solitons that emerge in many physical contexts. In magnetism, they appear as textures of the spin-density field stabilized by different competing interactions and characterized by a topological charge that counts the number of times the order parameter wraps the sphere. They behave as classical objects when the spin texture varies slowly on the scale of the microscopic lattice of the magnet. However, the fast development of experimental tools to create and stabilize skyrmions in thin magnetic films has led to a rich variety of textures, sometimes of atomistic sizes. In this paper, we discuss, in a pedagogical manner, how to introduce quantum interference in the translational dynamics of skyrmion textures, starting from the micromagnetic equations of motion for a classical soliton. We study how the nontrivial topology of the spin texture manifests in the semiclassical regime, when the microscopic lattice potential is treated quantum-mechanically, but the external driving forces are taken as smooth classical perturbations. We highlight close relations to the fields of noncommutative quantum mechanics, Chern–Simons theories, and the quantum Hall effect.

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PACHOS, JIANNIS K., and MICHAEL STONE. "AN INDEX THEOREM FOR GRAPHENE." International Journal of Modern Physics B 21, no. 30 (December 10, 2007): 5113–20. http://dx.doi.org/10.1142/s0217979207038228.

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We consider a graphene sheet folded in an arbitrary geometry, compact or with nanotube-like open boundaries. In the continuous limit, the Hamiltonian takes the form of the Dirac operator, which provides a good description of the low energy spectrum of the lattice system. We derive an index theorem that relates the zero energy modes of the graphene sheet with the topology of the lattice. The result coincides with analytical and numerical studies for the known cases of fullerene molecules and carbon nanotubes, and it extends to more complicated molecules. Potential applications to topological quantum computation are discussed.

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Tscheuschner, Ralf D., Sascha Hoch, Eva Leschinsky, Cedrik Meier, Sabine Theis, and Andreas D. Wieck. "Robustness of the Quantum Hall Effect, Sample Size Versus Sample Topology, and Quality Control Management of III–V Molecular Beam Epitaxy." International Journal of Modern Physics B 12, no. 11 (May 10, 1998): 1147–70. http://dx.doi.org/10.1142/s0217979298000636.

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We measure the IQHE on macroscopic (1.5 cm × 1.5 cm) "quick and dirty" prepared III–V heterostructure samples with van der Pauw and modified Corbino geometries at 1.3 K. We compare our results with (i) data taken on smaller specimens, among them samples with a standard Hall bar geometry, (ii) results of our numerical analysis taking inhomogenities of the 2DEG into account. Our main finding is a confirmation of the expected robustness of the IQHE which favors the development of wide plateaux for small filling factors and very large samples sizes (here with areas 10 000 times larger than in standard arrangements).

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MISTRANGELO, C. "Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 1. Hydrodynamic flow." Journal of Fluid Mechanics 674 (March 23, 2011): 120–31. http://dx.doi.org/10.1017/s0022112010006439.

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Numerical simulations are performed to study three-dimensional hydrodynamic flows in a sudden expansion of rectangular ducts. Separation phenomena are investigated through the analysis of flow topology and streamline patterns. Scaling laws describing the evolution of the reattachment length of the vortical areas that appear behind the cross-section enlargement are derived. The results discussed in this paper are required as a starting point to investigate the effects of an applied homogeneous magnetic field on separation phenomena in a geometry with a sudden expansion.

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MOSTAFAZADEH, ALI. "PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS." International Journal of Geometric Methods in Modern Physics 07, no. 07 (November 2010): 1191–306. http://dx.doi.org/10.1142/s0219887810004816.

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A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study. We then offer a survey of the necessary mathematical tools, present their utility in establishing a lucid and precise formulation of a unitary quantum theory based on a non-Hermitian Hamiltonian, and elaborate on a number of relevant issues of fundamental importance. In particular, we discuss the role of the antilinear symmetries such as [Formula: see text], the true meaning and significance of the so-called charge operators [Formula: see text] and the [Formula: see text]-inner products, the nature of the physical observables, the equivalent description of such models using ordinary Hermitian quantum mechanics, the pertaining duality between local-non-Hermitian versus nonlocal-Hermitian descriptions of their dynamics, the corresponding classical systems, the pseudo-Hermitian canonical quantization scheme, various methods of calculating the (pseudo-) metric operators, subtleties of dealing with time-dependent quasi-Hermitian Hamiltonians and the path-integral formulation of the theory, and the structure of the state space and its ramifications for the quantum Brachistochrone problem. We also explore some concrete physical applications and manifestations of the abstract concepts and tools that have been developed in the course of this investigation. These include applications in nuclear physics, condensed matter physics, relativistic quantum mechanics and quantum field theory, quantum cosmology, electromagnetic wave propagation, open quantum systems, magnetohydrodynamics, quantum chaos and biophysics.

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Descamps, Benoît, and Rajan Filomeno Coelho. "The nominal force method for truss geometry and topology optimization incorporating stability considerations." International Journal of Solids and Structures 51, no. 13 (June 2014): 2390–99. http://dx.doi.org/10.1016/j.ijsolstr.2014.03.003.

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Selvam, A. Mary. "Deterministic chaos, fractals, and quantumlike mechanics in atmospheric flows." Canadian Journal of Physics 68, no. 9 (September 1, 1990): 831–41. http://dx.doi.org/10.1139/p90-121.

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The complex spatiotemporal patterns of atmospheric flows that result from the cooperative existence of fluctuations ranging in size from millimetres to thousands of kilometres are found to exhibit long-range spatial and temporal correlations. These correlations are manifested as the self-similar fractal geometry of the global cloud cover pattern and the inverse power-law form for the atmospheric eddy energy spectrum. Such long-range spatiotemporal correlations are ubiquitous in extended natural dynamical systems and are signatures of deterministic chaos or self-organized criticality. In this paper, a cell dynamical system model for atmospheric flows is developed by consideration of microscopic domain eddy dynamical processes. This nondeterministic model enables formulation of a simple closed set of governing equations for the prediction and description of observed atmospheric flow structure characteristics as follows. The strange-attractor design of the field of deterministic chaos in atmospheric flows consists of a nested continuum of logarithmic spiral circulations that trace out the quasi-periodic Penrose tiling pattern, identified as the quasi-crystalline structure in condensed matter physics. The atmospheric eddy energy structure follows laws similar to quantum mechanical laws. The apparent waveparticle duality that characterizes quantum mechanical laws is attributed to the bimodal phenomenological form of energy display in the bidirectional energy flow that is intrinsic to eddy circulations, e.g., formation of clouds in updrafts and dissipation of clouds in downdrafts that result in the observed discrete cellular geometry of cloud structure.

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Filikhin, Igor, Sergei Matinyan, and Branislav Vlahovic. "Electron Localization, Tunneling and Energy Spectrum for Systems of Double Quantum Dots." MRS Proceedings 1551 (2013): 129–34. http://dx.doi.org/10.1557/opl.2013.961.

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ABSTRACTSemiconductor heterostructures as quantum dots demonstrate discrete atom-like energy level structure based on several hundred of electron confinement states. In the case of double QD (DQD) or double QR (DQR), there is a single electron spectrum composed of a set of quasi-doublets. We study these specific spectrum properties with their relation to the electron tunneling in DQD (DCQR) when the wave function of electron localized initially in one of the double quantum object is spread into whole system. The double InAs/GaAs quantum dots are considered within the effective approach. Tunneling in DQD is studied in connection with change of inter-dot distance and QD geometry. There are two types of such tunneling in DQD. The first is related to tunneling in the system of two identical QDs; the second one occurs in the system of non-identical QDs. The tunneling in the DQR is a tunneling in the system with non-identical quantum objects. The quasi-doublets of the DQD spectrum play an important role in the tunneling. We study effect of violation of symmetry of DQD geometry on the tunneling and show that the violation of symmetry makes difficulties for such tunneling.

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Kumar, Manish, Jeffrey S. Guasto, and Arezoo M. Ardekani. "Transport of complex and active fluids in porous media." Journal of Rheology 66, no. 2 (March 2022): 375–97. http://dx.doi.org/10.1122/8.0000389.

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Complex and active fluids find broad applications in flows through porous materials. Nontrivial rheology can couple to porous microstructure leading to surprising flow patterns and associated transport properties in geophysical, biological, and industrial systems. Viscoelastic instabilities are highly sensitive to pore geometry and can give rise to chaotic velocity fluctuations. A number of recent studies have begun to untangle how the pore-scale geometry influences the sample-scale flow topology and the resulting dispersive transport properties of these complex systems. Beyond classical rheological properties, active colloids and swimming cells exhibit a range of unique properties, including reduced effective viscosity, collective motion, and random walks, that present novel challenges to understanding their mechanics and transport in porous media flows. This review article aims to provide a brief overview of essential, fundamental concepts followed by an in-depth summary of recent developments in this rapidly evolving field. The chosen topics are motivated by applications, and new opportunities for discovery are highlighted.

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He, Xiaoliang, Sourabh V. Apte, Justin R. Finn, and Brian D. Wood. "Characteristics of turbulence in a face-centred cubic porous unit cell." Journal of Fluid Mechanics 873 (June 25, 2019): 608–45. http://dx.doi.org/10.1017/jfm.2019.403.

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Direct numerical simulations (DNS) are performed in a triply periodic unit cell of a face-centred cubic (FCC) lattice covering the unsteady inertial, to fully turbulent, flow regimes. The DNS data are used to quantify the flow topology, integral scales, turbulent kinetic energy (TKE) transport and anisotropy distribution in the tortuous geometry. Several unique flow features are observed within this low porosity configuration, where the mean flow undergoes strong acceleration and deceleration regions with presence of three-dimensional helical motions, weak wake-like structures behind spheres, stagnation and jet-impingement-like flows together with merging and spreading jets in the main pore space. The jet-impingement and weak wake-like flow structures give rise to regions with negative total TKE production. Unlike flows in complex shaped ducts, the turbulence intensity levels in the cross-stream directions are found to be larger than those in the streamwise direction. Furthermore, due to the compact nature and confined geometry of the FCC packing, the turbulent integral length scales are estimated to be less than 10 % of the bead diameter even for the lowest Reynolds number studied, indicating the absence of macroscale turbulence structures for this configuration. This finding suggests that even for the highly anisotropic flow within the pore, the upscaled flow statistics are captured well by the representative volumes defined by the unit cell.

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Hotaling, S. P. "Ultra-low density aerogel optical applications." Journal of Materials Research 8, no. 2 (February 1993): 352–55. http://dx.doi.org/10.1557/jmr.1993.0352.

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Despite the extremely low density and the hence low weight of aerogel materials, the applicability of these materials to reflective applications has had little attention due to the high porosities exhibited by the materials. This high porosity yields an intrinsically rough but uniform surface topology for aerogel of density in the low hundreds of milligrams per cubic centimeter and a fractal surface geometry for lower density aerogel (densities of the order of tens of milligrams per cubic centimeter). This paper presents new results of aerogel materials used as ultra-light substrates for reflective coatings by way of surface machining, polishing, and planarization prior to metallization, and the optical characterization thereof.

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Liu, A. C. Y., J. C. McCallum, and J. Wong-Leung. "Defect formation due to the crystallization of deep amorphous volumes formed in silicon by mega electron volt (MeV) ion implantation." Journal of Materials Research 16, no. 11 (November 2001): 3229–37. http://dx.doi.org/10.1557/jmr.2001.0445.

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Solid-phase epitaxy was examined in deep amorphous volumes formed in silicon wafers by multi-energy self-implantation through a mask. Crystallization was effected at elevated temperatures with the amorphous volume being transformed at both lateral and vertical interfaces. Sample topology was mapped using an atomic force microscope. Details of the process were clarified with both plan-view and cross-sectional transmission electron microscopy analyses. Crystallization of the amorphous volumes resulted in the incorporation of a surprisingly large number of dislocations. These arose from a variety of sources. Some of the secondary structures were identified to occur uniquely from the crystallization of volumes in this particular geometry.

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BARZ, DOMINIK P. J., HAMID FARANGIS ZADEH, and PETER EHRHARD. "Measurements and simulations of time-dependent flow fields within an electrokinetic micromixer." Journal of Fluid Mechanics 676 (April 14, 2011): 265–93. http://dx.doi.org/10.1017/jfm.2011.44.

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We investigate the flow field in an electrokinetic micromixer. The concept of the micromixer is based on the combination of an alternating electrical field applied to a pressure-driven base flow in a meander–channel geometry. The presence of the electrical field leads to an additional electro-osmotic velocity contribution, which results in a complex flow field within the meander bends. The velocity fields within the meander are measured by means of a microparticle-image velocimetry method. Furthermore, we introduce a mathematical model, describing the electrical and fluid-mechanical phenomena present within the device, and perform simulations comparable to the experiments. The comparison of simulations and experiments reveals good agreement, with minor discrepancies in flow topology, obviously caused by small but crucial differences between experimental and numerical geometries. In detail, simulations are performed for sharp corners of the bends, while in the experiments these corners are rounded due to the microfabrication process.

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Lodato, G., L. Vervisch, and P. Clavin. "Direct numerical simulation of shock wavy-wall interaction: analysis of cellular shock structures and flow patterns." Journal of Fluid Mechanics 789 (January 19, 2016): 221–58. http://dx.doi.org/10.1017/jfm.2015.731.

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The reflection on a wavy wall of a planar shock propagating at Mach number 1.5 in air is simulated in a two-dimensional geometry by solving the fully compressible Navier–Stokes equations. A high-order spectral difference numerical discretization is used over an unstructured mesh composed of quadrilateral elements. The shock discontinuity is handled numerically through a specific treatment, which is limited in space to a small portion of the computational cell through which the shock is travelling. In the conditions under investigation, the reflection on the wavy wall leads to a weak and smooth deformation of the shock front without singularities just after reflection. Long-living triple points (Mach stems) are spontaneously formed on the reflected shock at a finite distance from the wavy wall. They then propagate on the front in both directions and collide regularly, forming a periodic cellular pattern quite similar to that of a cellular detonation. Transverse waves, issued from the triple points, are generated in the shocked gas. As a result of their mutual interaction, a complex and strongly unsteady flow is produced in the shocked gas. The topology of the instantaneous streamline patterns is characterized by short-lived critical points that appear intermittently. Due to the compressible character of the unsteady two-dimensional flow, the topology of critical points which can be observed is more diverse than would be expected for incompressible two-dimensional flows. Some of them take the form of short-lived sources or sinks. The mechanism of formation and the dynamics of the triple points, as well as the instantaneous streamline patterns, are analysed in the present paper. The results are useful for deciphering the cellular structure of unstable detonations.

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Bedingfield, Kalun, Eoin Elliott, Nuttawut Kongsuwan, Jeremy J. Baumberg, and Angela Demetriadou. "Morphology dependence of nanoparticle-on-mirror geometries: A quasinormal mode analysis." EPJ Applied Metamaterials 9 (2022): 3. http://dx.doi.org/10.1051/epjam/2022002.

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Plasmonic nanoantennas are able to produce extreme enhancements by concentrating electromagnetic fields into sub-wavelength volumes. Recently, one of the most commonly used nanoantennas is the nanoparticle-on-mirror geometry, which allowed for the room temperature strong coupling of a single molecule. Very few studies offer analysis of near-field mode decompositions, and they mainly focus on spherical and/or cylindrically-faceted nanoparticle-on-mirror geometries. Perfectly spherical nanoparticles are not easy to fabricate, with recent publications revealing that a rhombicuboctahedron is a commonly occurring nanoparticle shape – due to the crystalline nature of metallic nanoparticles. In this paper, we perform a quasi-normal mode analysis for the rhombicuboctahedron-on-mirror nanoantenna and map the field distributions of each mode. We examine how the geometry of the cavity defines the near-field distribution and energies of the modes, and we show that in some cases the mode degeneracies break. This has a significant impact on the radiative emission and far-field profile of each mode, which are measured experimentally. Understanding how realistic nanoantenna geometries behave in the near-field and far-field helps us design antennas with specific properties for controlling and sensing quantum emitters in plasmonic systems.

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BONN, JAMES, and RICHARD M. McLAUGHLIN. "Sensitive enhanced diffusivities for flows with fluctuating mean winds: a two-parameter study." Journal of Fluid Mechanics 445 (October 16, 2001): 345–75. http://dx.doi.org/10.1017/s002211200100564x.

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Enhanced diffusion coefficients arising from the theory of periodic homogenized averaging for a passive scalar diffusing in the presence of a large-scale, fluctuating mean wind superimposed upon a small-scale, steady flow with non-trivial topology are studied. The purpose of the study is to assess how the extreme sensitivity of enhanced diffusion coefficients to small variations in large-scale flow parameters previously exhibited for steady flows in two spatial dimensions is modified by either the presence of temporal fluctuation, or the consideration of fully three-dimensional steady flow. We observe the various mixing parameters (Péclet, Strouhal and periodic Péclet numbers) and related non-dimensionalizations. We document non-monotonic Péclet number dependence in the enhanced diffusivities, and address how this behaviour is camouflaged with certain non-dimensional groups. For asymptotically large Strouhal number at fixed, bounded Péclet number, we establish that rapid wind fluctuations do not modify the steady theory, whereas for asymptotically small Strouhal number the enhanced diffusion coefficients are shown to be represented as an average over the steady geometry. The more difficult case of large Péclet number is considered numerically through the use of a conjugate gradient algorithm. We consider Péclet-number-dependent Strouhal numbers, S = QPe−(1+γ), and present numerical evidence documenting critical values of γ which distinguish the enhanced diffusivities as arising simply from steady theory (γ < −1) for which fluctuation provides no averaging, fully unsteady theory (γ ∈ (−1, 0)) with closure coefficients plagued by non-monotonic Péclet number dependence, and averaged steady theory (γ > 0). The transitional case with γ = 0 is examined in detail. Steady averaging is observed to agree well with the full simulations in this case for Q [les ] 1, but fails for larger Q. For non-sheared flow, with Q [les ] 1, weak temporal fluctuation in a large-scale wind is shown to reduce the sensitivity arising from the steady flow geometry; however, the degree of this reduction is itself strongly dependent upon the details of the imposed fluctuation. For more intense temporal fluctuation, strongly aligned orthogonal to the steady wind, time variation averages the sensitive scaling existing in the steady geometry, and the present study observes a Pe1 scaling behaviour in the enhanced diffusion coefficients at moderately large Péclet number. Finally, we conclude with the numerical documentation of sensitive scaling behaviour (similar to the two-dimensional steady case) in fully three dimensional ABC flow.

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TATSUMI, TOMOMASA. "Cross-independence closure for statistical mechanics of fluid turbulence." Journal of Fluid Mechanics 670 (January 26, 2011): 365–403. http://dx.doi.org/10.1017/s002211201000532x.

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The infinite set of the Lundgren-Monin equations for the multi-point velocity distributions of fluid turbulence is closed by making use of the cross-independence closure hypothesis proposed by Tatsumi (Geometry and Statistics of Turbulence, 2001, p. 3), and the minimum deterministic set of equations is obtained as the equations for the one-point velocity distribution f, the two-point velocity distribution f(2) and the two-point local velocity distribution f(2)*. In practice, the two-point distributions f(2) and f(2)* are more conveniently expressed in terms of the velocity-sum and -difference distributions g+, g− and g+*, g−*, respectively.As an outstanding result, the energy dissipation rate is expressed in terms of the distribution g− which is mainly contributed from small-scale turbulent fluctuations, making clear analogy with the ‘fluctuation-dissipation theorem’ in non-equilibrium statistical mechanics.It is to be remarked that the integral moments of the equations for the distributions f and f(2) give the equations for the mean flow and the mean velocity procducts of various orders, which are identical with the corresponding equations derived directly from the Navier--Stokes equation. This results clearly shows the exact consistency of the cross-independence closure and gives an overall solution for the classical closure problem concerning the mean velocity products since they are derived from the known distributions.Although the present work is confined to the two-point statistics of turbulence, the analysis can be extended to the higher-order statistics and even to turbulence in other fluids such as magneto and quantum fluids.

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Ke, Changhong, and Horacio D. Espinosa. "Numerical Analysis of Nanotube-Based NEMS Devices—Part I: Electrostatic Charge Distribution on Multiwalled Nanotubes." Journal of Applied Mechanics 72, no. 5 (September 1, 2005): 721–25. http://dx.doi.org/10.1115/1.1985434.

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The charge distribution on the surface of a biased conductive, finite-length, cylindrical nanotube, free standing above an infinite grounded plane, is investigated. The diameter range of the cylinder tube under study is 20–60 nm, which is much larger than the screening length, meaning the quantum and statistical effects on the charge distribution are negligible. The relationship between the charge distribution and the geometry of the nanotube is examined in detail by classical electrostatics using full three-dimensional numerical simulations based on the boundary element method. A model of the concentrated charge at the end of nanotubes is proposed. The charge distribution for a clamped cantilever nanotube is also computed and discussed. The findings here reported are of particular usefulness in the design and modeling of electrostatic actuated nanotube/nanowire based nano-electromechanical systems.

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Gusev, G. M., Z. D. Kvon, D. A. Kozlov, E. B. Olshanetsky, M. V. Entin, and N. N. Mikhailov. "Transport through the network of topological channels in HgTe based quantum well." 2D Materials 9, no. 1 (November 30, 2021): 015021. http://dx.doi.org/10.1088/2053-1583/ac351e.

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Abstract Topological insulators (TIs) represent a new quantum state of matter which is characterized by edge or surface states and an insulating band gap in the bulk. In a two-dimensional (2D) system based on the HgTe quantum well (QW) of critical width random deviations of the well width from its average value result in local crossovers from zero gap 2D Dirac fermion system to either the 2D TI or the ordinary insulator, forming a complicated in-plane network of helical channels along the zero-gap lines. We have studied experimentally the transport properties of the critical width HgTe QWs near the Dirac point, where the conductance is determined by a percolation along the zero-gap lines. The experimental results confirm the presence of percolating conducting channels of a finite width. Our work establishes the critical width HgTe QW as a promising platform for the study of the interplay between topology and localization.

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Tian, Na, Jun Sun, Wenbo Xu, and Choi-Hong Lai. "Quantum-Behaved Particle Swarm Optimization with Ring Topology and Its Application in Estimating Temperature-Dependent Thermal Conductivity." Numerical Heat Transfer, Part B: Fundamentals 60, no. 2 (August 2011): 73–95. http://dx.doi.org/10.1080/10407790.2011.594392.

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CAMASSA, ROBERTO, RICHARD M. McLAUGHLIN, and LONGHUA ZHAO. "Lagrangian blocking in highly viscous shear flows past a sphere." Journal of Fluid Mechanics 669 (February 16, 2011): 120–66. http://dx.doi.org/10.1017/s0022112010004933.

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An analytical and computational study of Lagrangian trajectories for linear shear flow past a sphere or spheroid at low Reynolds numbers is presented. Using the exact solutions available for the fluid flow in this geometry, we discover and analyse blocking phenomena, local bifurcation structures and their influence on dynamical effects arising in the fluid particle paths. In particular, building on the work by Chwang & Wu, who established an intriguing blocking phenomenon in two-dimensional flows, whereby a cylinder placed in a linear shear prevents an unbounded region of upstream fluid from passing the body, we show that a similar blocking exists in three-dimensional flows. For the special case when the sphere is centred on the zero-velocity plane of the background shear, the separatrix streamline surfaces which bound the blocked region are computable in closed form by quadrature. This allows estimation of the cross-sectional area of the blocked flow showing how the area transitions from finite to infinite values, depending on the cross-section location relative to the body. When the sphere is off-centre, the quadrature appears to be unavailable due to the broken up-down mirror symmetry. In this case, computations provide evidence for the persistence of the blocking region. Furthermore, we document a complex bifurcation structure in the particle trajectories as the sphere centre is moved from the zero-velocity plane of the background flow. We compute analytically the emergence of different fixed points in the flow and characterize the global streamline topology associated with these fixed points, which includes the emergence of a three-dimensional bounded eddy. Similar results for the case of spheroids are considered in Appendix B. Additionally, the broken symmetry offered by a tilted spheroid geometry induces new three-dimensional effects on streamline deflection, which can be viewed as effective positive or negative suction in the horizontal direction orthogonal to the background flow, depending on the tilt orientation. We conclude this study with results on the case of a sphere embedded at a generic position in a rotating background flow, with its own prescribed rotation including fixed and freely rotating. Exact closed-form solutions for fluid particle trajectories are derived.

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Friesen, C. A., and J. R. Hayes. "Nanoscale mechanical patterning for the selective deposition of nanostructures." Journal of Materials Research 15, no. 12 (December 2000): 2684–89. http://dx.doi.org/10.1557/jmr.2000.0386.

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In this paper, we describe a new method for creating nanostructures, and demonstrate its use by depositing Au, Ni, and Zn on a SiO2 passivated Si substrate. The method combined the spatial control of electron-beam lithography with the ease of fabrication of self-assembled arrays. The technique enabled the selective electrochemical deposition of nanostructures by creating specific nucleation sites by nanoindentation. This offered the possibility of accurately creating nanostructures ranging in size from one to hundreds of nanometers. We showed that it is possible to electrically isolate the nanostructures from the substrate and each other by a thermal oxidation process. In principle, this technique allowed fabrication of quantum devices of any geometry.

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Evecen, Meryem, and Hasan Tanak. "Quantum chemical studies on the molecular structure, spectroscopic and electronic properties of (6-Methoxy-2-oxo-2H-chromen-4-yl)-methyl pyrrolidine-1-carbodithioate." Materials Science-Poland 34, no. 4 (December 1, 2016): 886–904. http://dx.doi.org/10.1515/msp-2016-0115.

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AbstractIn this paper, the molecular geometry, vibrational frequencies and chemical shifts of (6-Methoxy-2-oxo-2H-chromen-4-yl)methyl pyrrolidine-1-carbodithioate in the ground state have been calculated using the Hartree-Fock and density functional methods with the 6-311++G(d,p) basis set. To investigate the nonlinear optical properties of the title compound, the polarizability and the first hyperpolarizability were calculated. The conformational properties of the molecule have been determined by analyzing molecular energy properties. Using the time dependent density functional theory, electronic absorption spectra have been calculated. Frontier molecular orbitals, natural bond orbitals, natural atomic charges and thermodynamical parameters were also investigated by using the density functional theory calculations.

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Schempp, Walter. "Quantum holography and neurocomputer architectures." Journal of Mathematical Imaging and Vision 2, no. 4 (December 1992): 279–326. http://dx.doi.org/10.1007/bf00121876.

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Gurin, V. S. "Towards a quantum-chemical simulation of the cadmium chalcogenide nanoclusters linked with biomolecules: An effect of terminating group upon the core geometry." Materials Science and Engineering: B 169, no. 1-3 (May 2010): 73–77. http://dx.doi.org/10.1016/j.mseb.2009.12.049.

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Matthews, P. C., M. R. E. Proctor, and N. O. Weiss. "Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour." Journal of Fluid Mechanics 305 (December 25, 1995): 281–305. http://dx.doi.org/10.1017/s0022112095004630.

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Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

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Camassa, Roberto, and H. Reed Ogrosky. "On viscous film flows coating the interior of a tube: thin-film and long-wave models." Journal of Fluid Mechanics 772 (May 7, 2015): 569–99. http://dx.doi.org/10.1017/jfm.2015.221.

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A theoretical and numerical investigation of two classes of models for pressure-driven core–annular flow is presented. Both classes, referred to as ‘long-wave’ and ‘thin-film’ models, may be derived from a unified perspective using long-wave asymptotics, but are distinct from one another in the role played by the curved tube geometry with respect to the planar (limiting) case. Analytical and numerical techniques are used to show and quantify the significant differences between the behaviour of solutions to both model types. Temporal linear stability analysis of the constant solution is carried out first to pinpoint with closed-form mathematical expressions the different dynamical regimes associated with absolute or convective instabilities. Numerical simulations for the models are then performed and qualitative differences in the evolution of the free surface are explored. Mathematically, different levels of asymptotic accuracy are found to result in different regularizing properties affecting the long-time behaviour of generic numerical solutions. Travelling wave solutions are also studied, and qualitative differences in the topology of streamline patterns describing the flow of the film in a moving reference frame are discussed. These topological differences allow for further classification of the models. In particular, a transition from a regime in which waves trap a fluid core to one where waves travel faster than any parcel of the underlying fluid is documented for a variant of the primary model. In the corresponding thin-film model, no such transition is found to occur. The source of these differences is examined, and a comparison of the results with those of related models in the literature is given. A brief discussion of the merits of each class of models concludes this study.

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Niewiadomska-Kaplar, Justyna. "New Approach to the Molecular Electronics of Graphene." Materials Science Forum 1058 (April 5, 2022): 63–78. http://dx.doi.org/10.4028/p-g8qm59.

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The structure of graphene has been described in this research work by introducing some innovative elementary theoretical concepts such as: - interpretation of the free electron pair not as a concentration of the electron cloud on one side of the nucleus (lone pair), but as a symmetrical distribution of the electron cloud on both sides, - hypothesis that in polar bonds and the vast majority of multiple bonds, one electron is shared, not an electron pair and distinction of intermolecular bonds in bi-electronic and mono-electronic, - interpretation of the transformation of the geometry of molecules in relation to the number of bonds as a result of changes in the spatial relationships between atoms, and not as a result of the hybridization of orbitals and prediction and calculation of the spatial parameters of molecules (topology, bond lengths and angles) by applying trigonometric equations and other geometric rules, - consideration that the formation of multiple bonds occurs thanks to the transformation of bi electronic bonds (sigma) into mono-electronic bonds. This transformation serves to increase the quantity of electrons available to form pi bonds which intensifies the cohesion between the atoms. According to the proposed model, it is a dense cross-linking of π bonds inside each graphene ring that allows exceptional cohesion, strength and stability to a thin "spiderweb" formed by a single layer of atoms.

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Sharma, Bajrang, Rishita Das, and Sharath S. Girimaji. "Local vortex line topology and geometry in turbulence." Journal of Fluid Mechanics 924 (August 5, 2021). http://dx.doi.org/10.1017/jfm.2021.613.

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Horváthy, Peter A. "Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics." Symmetry, Integrability and Geometry: Methods and Applications, December 14, 2006. http://dx.doi.org/10.3842/sigma.2006.090.

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Chan, Fan Kiat, Yashraj Bhosale, Tejaswin Parthasarathy, and Mattia Gazzola. "Three-dimensional geometry and topology effects in viscous streaming." Journal of Fluid Mechanics 933 (January 6, 2022). http://dx.doi.org/10.1017/jfm.2021.1106.

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Recent studies on viscous streaming flows in two dimensions have elucidated the impact of body curvature variations on resulting flow topology and dynamics, with opportunities for microfluidic applications. Following that, we present here a three-dimensional characterization of streaming flows as functions of changes in body geometry and topology, starting from the well-known case of a sphere to progressively arrive at toroidal shapes. We leverage direct numerical simulations and dynamical systems theory to systematically analyse the reorganization of streaming flows into a dynamically rich set of regimes, the origins of which are explained using bifurcation theory.

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Legner, Markus, and Titus Neupert. "Relating the entanglement spectrum of noninteracting band insulators to their quantum geometry and topology." Physical Review B 88, no. 11 (September 9, 2013). http://dx.doi.org/10.1103/physrevb.88.115114.

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Dmytruk, Olesia, and Marco Schirò. "Controlling topological phases of matter with quantum light." Communications Physics 5, no. 1 (November 4, 2022). http://dx.doi.org/10.1038/s42005-022-01049-0.

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AbstractControlling the topological properties of quantum matter is a major goal of condensed matter physics. A major effort in this direction has been devoted to using classical light in the form of Floquet drives to manipulate and induce states with non-trivial topology. A different route can be achieved with cavity photons. Here we consider a prototypical model for topological phase transition, the one-dimensional Su-Schrieffer-Heeger model, coupled to a single mode cavity. We show that quantum light can affect the topological properties of the system, including the finite-length energy spectrum hosting edge modes and the topological phase diagram. In particular we show that depending on the lattice geometry and the strength of light-matter coupling one can either turn a trivial phase into a topological one or viceversa using quantum cavity fields. Furthermore, we compute the polariton spectrum of the coupled electron-photon system, and we note that the lower polariton branch disappears at the topological transition point. This phenomenon can be used to probe the phase transition in the Su-Schrieffer-Heeger model.

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Ma, Qiong, Adolfo G. Grushin, and Kenneth S. Burch. "Topology and geometry under the nonlinear electromagnetic spotlight." Nature Materials, June 14, 2021. http://dx.doi.org/10.1038/s41563-021-00992-7.

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Culler, Michael, Keri A. Ledford, and Jason H. Nadler. "The Role of Topology and Tissue Mechanics in Remora Attachment." MRS Proceedings 1648 (2014). http://dx.doi.org/10.1557/opl.2014.229.

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ABSTRACTRemora fish are capable of fast, reversible and reliable adhesion to a wide variety of both natural and artificial marine hosts through a uniquely evolved dorsal pad. This adhesion is partially attributed to suction, which requires a robust seal between the pad interior and the ambient environment. Understanding the behavior of remora adhesion based on measurable surface parameters and material properties is a critical step when creating artificial, bio-inspired devices. In this work, structural and fluid finite element models (FEM) based on a simplified “unit cell” geometry were developed to predict the behavior of the seal with respect to host/remora surface topology and tissue material properties.

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Guo, Xu, Weisheng Zhang, and Wenliang Zhong. "Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework." Journal of Applied Mechanics 81, no. 8 (May 22, 2014). http://dx.doi.org/10.1115/1.4027609.

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In the present work, we intend to demonstrate how to do topology optimization in an explicit and geometrical way. To this end, a new computational framework for structural topology optimization based on the concept of moving morphable components is proposed. Compared with the traditional pixel or node point-based solution framework, the proposed solution paradigm can incorporate more geometry and mechanical information into topology optimization directly and therefore render the solution process more flexibility. It also has the great potential to reduce the computational burden associated with topology optimization substantially. Some representative examples are presented to illustrate the effectiveness of the proposed approach.

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Simmons, D. J., F. O. Thomas, T. C. Corke, and F. Hussain. "Experimental characterization of smooth body flow separation topography and topology on a two-dimensional geometry of finite span." Journal of Fluid Mechanics 944 (July 5, 2022). http://dx.doi.org/10.1017/jfm.2022.465.

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A smooth body, adverse pressure gradient (APG), turbulent boundary layer (TBL) separation is experimentally studied. The geometry features canonical TBL development prior to encountering a smooth, two-dimensional convex ramp geometry of finite span onto which a streamwise APG that is fully adjustable is imposed. Both large- and small-scale separations are studied, and all data are archived on the NASA Turbulence Modeling Resource website. This paper describes the large-scale separation case with focus on the surface topography and topology of both separation and reattachment. Despite the spanwise uniform approach TBL and ramp geometry, the separation is highly three-dimensional but the reattachment is spanwise uniform. The surface flow topology is characterized by the ‘owl-face pattern of the fourth kind’ – found to be highly repeatable over multiple experiments. This ubiquitous topology has been reported for a variety of flows including inclined bodies of revolution. It is demonstrated that the APG and the secondary flow associated with the sidewall–ramp juncture is responsible for the formation of the surface separation patterns.

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Liu, Jianxing, and Yihui Zhang. "A Mechanics Model of Soft Network Materials With Periodic Lattices of Arbitrarily Shaped Filamentary Microstructures for Tunable Poisson's Ratios." Journal of Applied Mechanics 85, no. 5 (March 2, 2018). http://dx.doi.org/10.1115/1.4039374.

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Soft network materials that incorporate wavy filamentary microstructures have appealing applications in bio-integrated devices and tissue engineering, in part due to their bio-mimetic mechanical properties, such as “J-shaped” stress–strain curves and negative Poisson's ratios. The diversity of the microstructure geometry as well as the network topology provides access to a broad range of tunable mechanical properties, suggesting a high degree of design flexibility. The understanding of the underlying microstructure-property relationship requires the development of a general mechanics theory. Here, we introduce a theoretical model of infinitesimal deformations for the soft network materials constructed with periodic lattices of arbitrarily shaped microstructures. Taking three representative lattice topologies (triangular, honeycomb, and square) as examples, we obtain analytic solutions of Poisson's ratio and elastic modulus based on the mechanics model. These analytic solutions, as validated by systematic finite element analyses (FEA), elucidated different roles of lattice topology and microstructure geometry on Poisson's ratio of network materials with engineered zigzag microstructures. With the aid of the theoretical model, a crescent-shaped microstructure was devised to expand the accessible strain range of network materials with relative constant Poisson's ratio under large levels of stretching. This study provides theoretical guidelines for the soft network material designs to achieve desired Poisson's ratio and elastic modulus.

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Durand, Marc, Andrew M. Kraynik, Frank van Swol, Jos Käfer, Catherine Quilliet, Simon Cox, Shirin Ataei Talebi, and François Graner. "Statistical mechanics of two-dimensional shuffled foams: Geometry-topology correlation in small or large disorder limits." Physical Review E 89, no. 6 (June 19, 2014). http://dx.doi.org/10.1103/physreve.89.062309.

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Buldum, Alper, and Jian Ping Lu. "Quantum Transport Through Intermolecular Nanotube Junctions." MRS Proceedings 633 (2000). http://dx.doi.org/10.1557/proc-633-a3.3.

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AbstractQuantum transport properties of intermolecular nanotube contacts are investigated. We find that atomic structure in the contact region plays important roles and resistance of contacts varies strongly with geometry and nanotube chirality. Nanotube end-end contacts have low resistance and show negative differential resistance (NDR) behavior. Exerting small pressure/force between the tubes can dramatically decrease contact resistance, if the contact is commensurate. Significant variation and nonlinearity of contact resistance may lead to new device applications.

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Tokura, Yoshinori. "Quantum materials at the crossroads of strong correlation and topology." Nature Materials, August 24, 2022. http://dx.doi.org/10.1038/s41563-022-01339-6.

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Grinev, Dmitri V., and Sam F. Edwards. "Statistical Mechanics of Stress Transmission in Static Arrays of Rigid Grains." MRS Proceedings 627 (2000). http://dx.doi.org/10.1557/proc-627-bb6.1.

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ABSTRACTWe develop the statistical-mechanical theory that delivers the fundamental equations of stress equilibrium for static arrays of rigid grains. The random geometry of static granular packing composed of rigid cohesionless particles can be visualised as a network of intergranular contacts. The contact network and external loading determine the network of intergranular forces. In general, the contact network can have an arbitrary coordination number varying within the system. It follows then that the network of intergranular forces is indeterminate i.e. the number of unknown forces is larger than the number of Newton's equations of mechanical equilibrium. Thus, in order for the network of intergranular forces to be determined, the number of equations must equal the number of unknowns. We argue that this determines the contact network with a certain fixed coordination number. The complete system of equations for the stress tensor is derived from the equations of intergranular force and torque balance, given the geometric specification of the packing. The granular material fabric gives rise to corrections to the Euler-Cauchy equation that become significant at mesoscopic lengthscales. The stress-geometry equation establishes the relation between various components of the stress tensor, and depends on the topology of the granular array.

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Chen, Xianyang, Jiacai Lu, Stéphane Zaleski, and Gretar Tryggvason. "Characterizing Interface Topology in Multiphase Flows using Skeletons." Physics of Fluids, August 17, 2022. http://dx.doi.org/10.1063/5.0109333.

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The unsteady motion of a gas-liquid interface, such as during splashing or atomization, often results in complex liquid structures embedded in the ambient fluid. Here we explore the use of skeletonization to identify the minimum amount of information needed to describe their geometry. We skeletonize a periodic liquid jet by a modification of a recently introduced approach to coarsen multiphase flows while retaining a sharp interface. The process consists of diffusing an index function and at the same time moving the interfaces with it, until they "collapse" into each other and form skeletons. The skeleton represents the basic topology of the jet and we also keep track of how much the interface is moved (or how much volume is "accumulated") during the process, which can be used to approximately reconstruct the jet. We explore various quantitative measures to characterize and distinguish the skeletons. Those include standard morphometrics such as branch length distribution, after segmenting the skeletons into branches, and a more sophisticated representation of the skeleton structures called Topology Morphology Descriptor (TMD), to obtain an "equivalent" description of the skeletons by retaining information about the topology in a compact way.

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Rodríguez, Arezky H., C. Trallero-Giner, J. Marín-Antuña, and S. E. Ulloa. "Electronic States of Self-Assembled Quantum Dots: Symmetries in a Quantum Lens." MRS Proceedings 579 (1999). http://dx.doi.org/10.1557/proc-579-129.

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ABSTRACTElectronic states in self-assembled quantum dots with a lens geometry are studied. A conformal analytical map is used to transform the quantum dot boundary into a dot with semi-spherical shape. The Hamiltonian for a carrier confined in the quantum lens is also mapped into an equivalent operator and its eigenvalues and eigenfunctions for the corresponding Dirichlet problem, of confinement by infinite walls, are analyzed. A modified Rayleigh-Schrddinger perturbation theory is developed to obtain analytical expressions for the energy levels and wavefunctions depending on the height b and radius a of the circular cross section of the spherical cap lens. Numerical calculations are shown for typical cases. The effects of decreasing rotational symmetry on the energy states and eigenfunctions of the quantum dot with lens-shape are presented: The degeneracy due to the z-component of the angular momentum m is broken for b ∦ a. Energy states and wavefunctions with m = 0 present the most pronounced influence on the b ∦ a case. Analytical expressions presented here can be used to estimate the sizes of actual self-assembled quantum dots.

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Hertle, H., G. Schuberth, E. Gornik, G. Abscreiter, and F. Schäffler. "Intersubband Absorption in the Conduction Band of Si/Si1−xGex Multiple Quantum Wells." MRS Proceedings 220 (1991). http://dx.doi.org/10.1557/proc-220-379.

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ABSTRACTThe intersubband absorption of electrons in modulation doped Si/Si1−xGex multiple quantum wells has been observed [1]. Various samples with different well widths and carrier densities have been studied. Narrow absorption lines are observed in waveguide geometry. Self consistent subband calculations are in good agreement with the experimental values.

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Bazilevs, Yuri, Kenji Takizawa, Tayfun E. Tezduyar, Artem Korobenko, Takashi Kuraishi, and Yuto Otoguro. "Computational Aerodynamics With Isogeometric Analysis." Journal of Mechanics, February 17, 2023. http://dx.doi.org/10.1093/jom/ufad002.

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Abstract The superior accuracy isogeometric analysis (IGA) brought to computations in fluid and solid mechanics has been yielding higher fidelity in computational aerodynamics. The increased accuracy we achieve with the IGA is in the flow solution, in representing the problem geometry, and, when we use the IGA basis functions also in time in a space–time (ST) framework, in representing the motion of solid surfaces. It is of course as part of a set of methods that the IGA has been very effective in computational aerodynamics, including complex-geometry aerodynamics. The set of methods we have been using can be categorized into those that serve as a core method, those that increase the accuracy, and those that widen the application range. The core methods are the residual-based variational multiscale (VMS), ST-VMS, and arbitrary Lagrangian–Eulerian VMS methods. The IGA and ST-IGA are examples of the methods that increase the accuracy. The complex-geometry IGA mesh generation method is an example of the methods that widen the application range. The ST Topology Change method is another example of that. We provide an overview of these methods for IGA-based computational aerodynamics and present examples of the computations performed. In computational flow analysis with moving solid surfaces and contact between the solid surfaces, it is a challenge to represent the boundary layers with an accuracy attributed to moving-mesh methods and represent the contact without leaving a mesh protection gap.

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Journal articles on the topic 'Geometry and topology in quantum mechanics and condensed matter'

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