Relevant bibliographies by topics / Geometry and topology in quantum mechanics and condensed matter

Academic literature on the topic 'Geometry and topology in quantum mechanics and condensed matter'

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Published: 11 March 2023

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Journal articles on the topic "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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Dissertations / Theses on the topic "Geometry and topology in quantum mechanics and condensed matter"

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Bianco, Raffaello. "Chern invariant and orbital magnetization as local quantities." Doctoral thesis, Università degli studi di Trieste, 2014. http://hdl.handle.net/10077/9959.

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2012/2013
La geometria, e la topologia in particolare, rivestono un profondo ruolo in molti campi della fisica ed in particolare in materia condensata ove è possibile identificare diversi stati quantistici della materia attraverso proprietà topologiche. L'invariante di Chern è un invariante topologico che caratterizza lo stato isolante dei cristalli. Esso è definito attraverso la descrizione in spazio reciproco di un cristallo perfetto, per cui è necessario considerare un sistema infinito oppure finito ma con condizioni periodiche al bordo. In questa tesi il concetto di invariante di Chern viene generalizzato definendo un opportuno marcatore locale di Chern in spazio reale. Infatti se si considera un cristallo perfetto infinito oppure finito e con condizioni periodiche al bordo, la media sulla cella elementare di questo marcatore restituisce il consueto invariante di Chern. Tuttavia, grazie al suo carattere locale, il marcatore di Chern è ben definito e può essere utilizzato per identificare il carattere locale di Chern anche di un sistema microscopicamente disordinato o macroscopicamente disomogeneo (ad esempio etorogiunzioni di diversi cristalli) e con qualsiasi tipo di condizioni al bordo (periodiche o aperte). Nella seconda parte della tesi l'invariante locale di Chern viene utilizzato per fornire una descrizione locale in spazio reale della magentizzazione orbitale. Questa descrizione è utilizzabile sia con condizioni al bordo aperte che periodiche e quindi unifica i due separati approcci utilizzati in questi due casi. La nuova formula permette, inoltre, di ottenere anche una migliore comprensione del ruolo che gli stati di bordo rivestono nella magnetizzazione di un sistema. In entrambi i casi vengono presentati i risultati di simulazioni numeriche che confermano i risultati teorici derivati.
The geometry and the topology play a profound role in many fields of physics and in particular in condensed matter where it is possible to identify different quantum states of matter through their topological properties. The Chern invariant is a topological invariant which characterizes the insulating state of crystals. It is defined through the description in the reciprocal space of a perfect crystal, which then has to be considered as an infinite system or a finite size system with periodic boundary conditions. In this thesis the concept of Chern invariant is generalized by defining a local Chern marker in the real space. For an infinite crystal or a finite crystal with periodic boundary conditions, the average of this marker over an elementary unit cell returns the usual invariant Chern. However, thanks to its local character, the Chern marker is well defined and can be used to identify the local Chern character also of microscopically disordered systems or macroscopically inhomogeneous systems (e.g. heterojunctions of different crystals) and with any kind of boundary conditions adopted (periodic boundary conditions or open bounday conditions as well). In the second part of the thesis the local Chern invariant is used to provide a local description in the real space of the orbital magnetization. This description can be used both with open and periodic boundary conditions, so it unifies the two separate approaches used in these different cases. Moreover, the new formula makes it possible to get a better understanding of the role that the edge states play in the magnetization of a system. In both cases we present the results of numerical simulations that confirm the theoretical results.
XXVI Ciclo
1979
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Bernard, Benjamin. "On the Quantization Problem in Curved Space." Wright State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=wright1344829165.

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"Symplectic Topology and Geometric Quantum Mechanics." Doctoral diss., 2011. http://hdl.handle.net/2286/R.I.9478.

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abstract: The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
Dissertation/Thesis
Ph.D. Mathematics 2011
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(10703055), Guodong Jiang. "INTERPLAY OF GEOMETRY WITH IMPURITIES AND DEFECTS IN TOPOLOGICAL STATES OF MATTER." Thesis, 2021.

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The discovery of topological quantum states of matter has required physicists to look beyond Landau’s theory of symmetry-breaking, previously the main paradigm for
studying states of matter. This has led also to the development of new topological theories for describing the novel properties. In this dissertation an investigation in this
frontier research area is presented, which looks at the interplay between the quantum geometry of these states, defects and disorder. After a brief introduction to the topological quantum states of matter considered herein, some aspects of my work in this area are described. First, the disorder-induced band structure engineering of topological insulator surface states is considered, which is possible due to their resilience from Anderson localization, and believed to be a consequence of their topological origin.
Next, the idiosyncratic behavior of these same surface states is considered, as observed in experiments on thin film topological insulators, in response to competition between
hybridization effects and an in-plane magnetic field. Then moving in a very different direction, the uncovering of topological ‘gravitational’ response is explained: the
topologically-protected charge response of two dimensional gapped electronic topological states to a special kind of 0-dimensional boundary – a disclination – that encodes spatial curvature. Finally, an intriguing relation between the gravitational response of quantum Hall states, and their response to an apparently unrelated perturbation – nonuniform electric fields is reported.
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Books on the topic "Geometry and topology in quantum mechanics and condensed matter"

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1925-, Lundqvist Stig, Morandi Giuseppe, Yü Lu 1937-, and International Centre for Theoretical Physics., eds. Low-dimensional quantum field theories for condensed matter physicists: Lecture notes of ICTP Summer Course, Trieste, Italy, September 1992. Singapore: World Scientific, 1995.

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Yu, Lu, and Italy) Ictp Summer Course (1992 Trieste. Low-Dimensional Quantum Field Theories for Condensed Matter Physicists: Lecture Notes of Ictp Summer Course Trieste, Italy September 1992 (Series on Modern Condensed Matter Physics, Vol 6). World Scientific Pub Co Inc, 1996.

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Book chapters on the topic "Geometry and topology in quantum mechanics and condensed matter"

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Shankar, R. "Quantum Geometry and Topology." In Topology and Condensed Matter Physics, 253–79. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6841-6_11.

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Abanov, Alexander. "Topology, geometry and quantum interference in condensed matter physics." In Topology and Condensed Matter Physics, 281–331. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6841-6_12.

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"Quantum Hall effect." In A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics, edited by Antonio Sergio Teixeira Pires. IOP Publishing, 2019. http://dx.doi.org/10.1088/2053-2571/aaec8fch7.

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Pires, Antonio Sergio Teixeira. "Quantum Hall effect." In A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics (Second Edition). IOP Publishing, 2021. http://dx.doi.org/10.1088/978-0-7503-3955-1ch7.

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Nitzan, Abraham. "Spectroscopy." In Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.003.0025.

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The interaction of light with matter provides some of the most important tools for studying structure and dynamics on the microscopic scale. Atomic and molecular spectroscopy in the low pressure gas phase probes this interaction essentially on the single particle level and yields information about energy levels, state symmetries, and intramolecular potential surfaces. Understanding environmental effects in spectroscopy is important both as a fundamental problem in quantum statistical mechanics and as a prerequisite to the intelligent use of spectroscopic tools to probe and analyze molecular interactions and processes in condensed phases. Spectroscopic observables can be categorized in several ways. We can follow a temporal profile or a frequency resolved spectrum; we may distinguish between observables that reflect linear or nonlinear response to the probe beam; we can study different energy domains and different timescales and we can look at resonant and nonresonant response. This chapter discusses some concepts, issues, and methodologies that pertain to the effect of a condensed phase environment on these observables. For an in-depth look at these issues the reader may consult many texts that focus on particular spectroscopies. With focus on the optical response of molecular systems, effects of condensed phase environments can be broadly discussed within four categories: 1. Several important effects are equilibrium in nature, for example spectral shifts associated with solvent induced changes in solute energy levels are equilibrium properties of the solvent–solute system. Obviously, such observables may themselves be associated with dynamical phenomena, in the example of solvent shifts it is the dynamics of solvation that affects their dynamical evolution. Another class of equilibrium effects on radiation– matter interaction includes properties derived from symmetry rules. A solvent can affect a change in the equilibrium configuration of a chromophore solute and consequently the associated selection rules for a given optical transition. Some optical phenomena are sensitive to the symmetry of the environment, for example, surface versus bulk geometry. 2. The environment affects the properties of the radiation field; the simplest example is the appearance of the dielectric coefficient ε in the theory of radiation–matter interaction.
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