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Journal articles on the topic 'Geometric Phase Transition'

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Author: Grafiati

Published: 7 September 2023

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1

ZHU, SHI-LIANG. "GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS." International Journal of Modern Physics B 22, no. 06 (March 10, 2008): 561–81. http://dx.doi.org/10.1142/s0217979208038855.

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Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

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2

Wei, Shao-Wen, Yu-Xiao Liu, Chun-E. Fu, and Hai-Tao Li. "Geometric Curvatures of Plane Symmetry Black Hole." Advances in High Energy Physics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/734138.

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We study the properties and thermodynamic stability of the plane symmetry black hole from the viewpoint of geometry. We find that the Weinhold curvature gives the first-order phase transition atN=1, whereNis a parameter of the plane symmetry black hole while the Ruppeiner one shows first-order phase transition points for arbitraryN≠1. Considering the Legendre invariant proposed by Quevedo et al., we obtain a unified geometry metric, which contains the information of the second-order phase transition. So, the first-order and second-order phase transitions can be both reproduced from the geometry curvatures. The geometry is also found to be curved, and the scalar curvature goes to negative infinity at the Davie phase transition points beyond semiclassical approximation.

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3

Gebhart, Valentin, Kyrylo Snizhko, Thomas Wellens, Andreas Buchleitner, Alessandro Romito, and Yuval Gefen. "Topological transition in measurement-induced geometric phases." Proceedings of the National Academy of Sciences 117, no. 11 (March 2, 2020): 5706–13. http://dx.doi.org/10.1073/pnas.1911620117.

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The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states—a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement.

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4

Liu, Kun, and Shujuan Yi. "Geometric Phase and Quantum Phase Transition in Charge-Qubit Array." International Journal of Theoretical Physics 57, no. 9 (June 16, 2018): 2828–30. http://dx.doi.org/10.1007/s10773-018-3802-7.

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5

DEMIRTÜRK, SEMRA, and YIĞIT GÜNDÜÇ. "A GEOMETRIC APPROACH TO THE PHASE TRANSITIONS." International Journal of Modern Physics C 12, no. 09 (November 2001): 1361–73. http://dx.doi.org/10.1142/s0129183101002632.

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In this work, we have proposed a new geometrical method for calculating the critical temperature and critical exponents by introducing a set of bond breaking probability values. The probability value Pc corresponding to the Coniglio–Klein probability for the transition temperature is obtained among this set of trial probabilities. Critical temperature, thermal and magnetic exponents are presented for d = 2 and d = 3, q = 2 Potts model and for the application of the method to the system with first order phase transition, q = 7 Potts model on different size lattices are employed. The advantage of this method can be that the bond breaking probability can be applied, where the clusters are defined on a set of dynamic variables, which are different from the dynamic quantities of the actual Hamiltonian or the action of the full system. An immediate application can be to use the method on finite temperature lattice gauge theories.

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Franzosi, Roberto, Domenico Felice, Stefano Mancini, and Marco Pettini. "A geometric entropy detecting the Erdös-Rényi phase transition." EPL (Europhysics Letters) 111, no. 2 (July 1, 2015): 20001. http://dx.doi.org/10.1209/0295-5075/111/20001.

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7

Bel-Hadj-Aissa, Ghofrane, Matteo Gori, Vittorio Penna, Giulio Pettini, and Roberto Franzosi. "Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions." Entropy 22, no. 4 (March 26, 2020): 380. http://dx.doi.org/10.3390/e22040380.

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In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of ϕ 4 models with either nearest-neighbours and mean-field interactions.

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8

Viotti, Ludmila, Ana Laura Gramajo, Paula I. Villar, Fernando C. Lombardo, and Rosario Fazio. "Geometric phases along quantum trajectories." Quantum 7 (June 2, 2023): 1029. http://dx.doi.org/10.22331/q-2023-06-02-1029.

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A monitored quantum system undergoing a cyclic evolution of the parameters governing its Hamiltonian accumulates a geometric phase that depends on the quantum trajectory followed by the system on its evolution. The phase value will be determined both by the unitary dynamics and by the interaction of the system with the environment. Consequently, the geometric phase will acquire a stochastic character due to the occurrence of random quantum jumps. Here we study the distribution function of geometric phases in monitored quantum systems and discuss when/if different quantities, proposed to measure geometric phases in open quantum systems, are representative of the distribution. We also consider a monitored echo protocol and discuss in which cases the distribution of the interference pattern extracted in the experiment is linked to the geometric phase. Furthermore, we unveil, for the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle and show how this critical behavior can be observed in an echo protocol. For the same parameters, the density matrix does not show any singularity. We illustrate all our main results by considering a paradigmatic case, a spin-1/2 immersed in time-varying a magnetic field in presence of an external environment. The major outcomes of our analysis are however quite general and do not depend, in their qualitative features, on the choice of the model studied.

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9

Zhang, Ruifeng, and Xiaojing Wang. "On generalized geometric domain-wall models." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 4 (July 15, 2011): 881–95. http://dx.doi.org/10.1017/s0308210510001198.

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We study domain walls that are topological solitons in one dimension. We present an existence theory for the solutions of the basic governing equations of some extended geometrically constrained domain-wall models. When the cross-section and potential density are both even, we establish the existence of an odd domain-wall solution realizing the phase-transition process between two adjacent domain phases. When the cross-section satisfies a certain integrability condition, we prove that a domain-wall solution always exists that links two arbitrarily designated domain phases.

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10

Cui, H. T., K. Li, and X. X. Yi. "Geometric phase and quantum phase transition in the Lipkin–Meshkov–Glick model." Physics Letters A 360, no. 2 (December 2006): 243–48. http://dx.doi.org/10.1016/j.physleta.2006.08.040.

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11

Wang, L. C., and X. X. Yi. "Geometric phase and quantum phase transition in the one-dimensional compass model." European Physical Journal D 57, no. 2 (March 2, 2010): 281–86. http://dx.doi.org/10.1140/epjd/e2010-00045-4.

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12

Pachos, Jiannis K., and Angelo C. M. Carollo. "Geometric phases and criticality in spin systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1849 (October 19, 2006): 3463–76. http://dx.doi.org/10.1098/rsta.2006.1894.

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A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behaviour is presented. This opens up the way for the use of geometric phases as a tool to probe regions of criticality without having to undergo a quantum phase transition. As a concrete example, a spin-1/2 chain with XY interactions is considered and the corresponding geometric phases are analysed. Finally, a generalization of these results to the case of an arbitrary spin system is presented.

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13

Lü, J. M., X. P. Li, and L. C. Wang. "Geometric phase and the influence of the Dzyaloshinski–Moriya interaction in the one-dimensional quantum compass model." Modern Physics Letters B 29, no. 25 (September 20, 2015): 1550146. http://dx.doi.org/10.1142/s0217984915501468.

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Geometric phase and quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model with the Dzyaloshinski–Moriya (DM) interaction are investigated, and the effect of the DM interaction to the properties of geometric phase and QPTs of the model are discussed in this paper. Our study is an extension of the relation between the geometric phase and QPTs in the 1D spin systems.

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14

Fan, Annan, and Shi‐Dong Liang. "Geometric Criterion of Topological Phase Transition for Non‐Hermitian Systems." Annalen der Physik 534, no. 4 (January 11, 2022): 2100520. http://dx.doi.org/10.1002/andp.202100520.

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15

Argollo de Menezes, M., C. F. Moukarzel, and T. J. P. Penna. "Geometric phase-transition on systems with sparse long-range connections." Physica A: Statistical Mechanics and its Applications 295, no. 1-2 (June 2001): 132–39. http://dx.doi.org/10.1016/s0378-4371(01)00065-6.

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16

Wu, Wei, and Jing-Bo Xu. "Geometric phase, quantum Fisher information, geometric quantum correlation and quantum phase transition in the cavity-Bose–Einstein-condensate system." Quantum Information Processing 15, no. 9 (June 14, 2016): 3695–709. http://dx.doi.org/10.1007/s11128-015-1186-7.

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17

Klatt, Michael A., and Steffen Winter. "Geometric functionals of fractal percolation." Advances in Applied Probability 52, no. 4 (December 2020): 1085–126. http://dx.doi.org/10.1017/apr.2020.33.

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AbstractFractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system-spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the percolation thresholds have been approximated well using additive geometric functionals, known as intrinsic volumes. Motivated by the question of whether a similar approach is possible for fractal models, we introduce corresponding geometric functionals for the fractal percolation process F. They arise as limits of expected functionals of finite approximations of F. We establish the existence of these limit functionals and obtain explicit formulas for them as well as for their finite approximations.

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18

Lin, Hai, Junling Han, and Xufeng Jing. "Electromagnetic radiation focusing lens based on phase transition all-dielectric microstructure." Journal of Laser Applications 35, no. 1 (February 2023): 012026. http://dx.doi.org/10.2351/7.0000956.

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Metasurface can adjust the polarization, amplitude, phase, polarization mode, and propagation mode of electromagnetic waves flexibly and efficiently. Based on Pancharatnam–Berry phase theory, an all-medium geometric phase element structure was proposed to construct a transmission-coded metasurface metalens. In the mid-infrared band, a phase change material (GST) is used to regulate the unit structure in order to achieve the tunability of lens focus. In order to prove that the designed hyperlens has a good focusing effect, we numerically simulate the focusing electromagnetic field distribution characteristics, and the results show that the designed geometric phase hyperlens has a good focusing effect. Using the crystal and amorphous states of phase change materials, we can dynamically control the focus of the superlens.

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19

Chepak, Alexander Konstantinovich, Leonid Lazarevich Afremov, and Alexander Yuryevich Mironenko. "Concentration Phase Transition in a Two-Dimensional Ferromagnet." Solid State Phenomena 312 (November 2020): 244–50. http://dx.doi.org/10.4028/www.scientific.net/ssp.312.244.

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The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values of the critical concentration and critical indices of the CPT are calculated.

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20

Cai, Xiaoya, Hui Pan, and Z. S. Wang. "Geometric phase of two-qubit system in dephasing environment." International Journal of Modern Physics B 29, no. 32 (December 17, 2015): 1550236. http://dx.doi.org/10.1142/s0217979215502367.

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We investigated the geometric phase for interaction between superconducting two-qubit system in dephased environment. The Pancharatnam phase and the Berry phase are studied. Numerical results are discussed. By considering the differently initial conditions, we find that the time-dependent Pancharatnam phase keeps the initial entangling message. On the other hand, the transition of Pancharatnam phase is dependent of the phase change in the superconducting two-qubit coupling system. Our results may be helpful to implement the time-dependent geometric quantum computation.

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21

Meng, Xiang Bao, Lei Wang, and Zi Jian Pan. "Parametric Modeling of Transition Tube with Constant Section Area along Straight, Circular and Oblique Central Route on CATIA." Advanced Materials Research 619 (December 2012): 18–21. http://dx.doi.org/10.4028/www.scientific.net/amr.619.18.

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Parametric modeling of transition tubes were implemented based on constant cross section area assumption along the main central routes on CATIA software. The key objective of modeling these similar structures is to provide more geometric configuration options and modifications of micro channels for multi phase flow systems. The modeling processes were parameterized and analyzed by CATIA “Generative Shape Design” module with the help of “Parameters” and “Relations” functions. The surface models are all designed in circular cross sections that are constrained in two ways: one is perpendicular to the main central routes of the tube for planar transitional junction, and another is, perpendicular to the sub-branch central routes for oblique transitional junction three dimensionally. Next work is emphasized on numerical simulation and experimental investigation with these geometric structures in a multi phase flow system.

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22

MIZUNO, Hiroki, and Hiroshi KOIBUCHI. "103 Phase transition of a surface model with internal geometric variable." Proceedings of Ibaraki District Conference 2010.18 (2010): 5–6. http://dx.doi.org/10.1299/jsmeibaraki.2010.18.5.

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23

Fuji, Hiroyuki, and Yutaka Ookouchi. "Confining phase superpotentials for SO/Sp gauge theories via geometric transition." Journal of High Energy Physics 2003, no. 02 (February 17, 2003): 028. http://dx.doi.org/10.1088/1126-6708/2003/02/028.

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24

Wang, Lei, Xiao Yu Wang, and Xiang Bao Meng. "Extended Parametric Modeling of Transition Tube with Constant Section Area along Arbitrary Central Routes on CATIA." Applied Mechanics and Materials 392 (September 2013): 197–200. http://dx.doi.org/10.4028/www.scientific.net/amm.392.197.

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Extended parametric models of transition tube structures were implemented based on authors previous work [11] on constant cross section area assumption along arbitrary central routes like straight, circular and oblique curves on CATIA platform. It is aimed at that these structures can provide more flexible geometric configuration options and modifications to tube channel transitions for multi phase flow systems and pipeline junctions. Details of parameterized modeling process were exhibited on CATIA Generative Shape Design module with the help of Parameters and Relations functions. The tube surface models are all in circular cross sections and constrained in many ways along arbitrary coplanar or cylindrical sub-central routes three dimensionally for various layouts. Future work is emphasized on numerical simulation and experimental investigation with these geometric structures in multi phase flow systems and pipeline application.

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25

Guan, Shian, Aline Rougier, Matthew R. Suchomel, Nicolas Penin, Kadiali Bodiang, and Manuel Gaudon. "Geometric considerations of the monoclinic–rutile structural transition in VO2." Dalton Transactions 48, no. 25 (2019): 9260–65. http://dx.doi.org/10.1039/c9dt01241a.

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Geometrical and experimental examinations of VO₂ show how hysteretic phase transition phenomena across the MIT can be driven by positive crystal energy effects of increasing unit cell volume.

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26

Seddon, John M., Adam M. Squires, Charlotte E. Conn, Oscar Ces, Andrew J. Heron, Xavier Mulet, Gemma C. Shearman, and Richard H. Templer. "Pressure-jump X-ray studies of liquid crystal transitions in lipids." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1847 (August 21, 2006): 2635–55. http://dx.doi.org/10.1098/rsta.2006.1844.

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In this paper, we give an overview of our studies by static and time-resolved X-ray diffraction of inverse cubic phases and phase transitions in lipids. In §1 , we briefly discuss the lyotropic phase behaviour of lipids, focusing attention on non-lamellar structures, and their geometric/topological relationship to fusion processes in lipid membranes. Possible pathways for transitions between different cubic phases are also outlined. In §2 , we discuss the effects of hydrostatic pressure on lipid membranes and lipid phase transitions, and describe how the parameters required to predict the pressure dependence of lipid phase transition temperatures can be conveniently measured. We review some earlier results of inverse bicontinuous cubic phases from our laboratory, showing effects such as pressure-induced formation and swelling. In §3 , we describe the technique of pressure-jump synchrotron X-ray diffraction. We present results that have been obtained from the lipid system 1 : 2 dilauroylphosphatidylcholine/lauric acid for cubic–inverse hexagonal, cubic–cubic and lamellar–cubic transitions. The rate of transition was found to increase with the amplitude of the pressure-jump and with increasing temperature. Evidence for intermediate structures occurring transiently during the transitions was also obtained. In §4 , we describe an IDL-based ‘ AXcess ’ software package being developed in our laboratory to permit batch processing and analysis of the large X-ray datasets produced by pressure-jump synchrotron experiments. In §5 , we present some recent results on the fluid lamellar– Pn 3 m cubic phase transition of the single-chain lipid 1-monoelaidin, which we have studied both by pressure-jump and temperature-jump X-ray diffraction. Finally, in §6 , we give a few indicators of future directions of this research. We anticipate that the most useful technical advance will be the development of pressure-jump apparatus on the microsecond time-scale, which will involve the use of a stack of piezoelectric pressure actuators. The pressure-jump technique is not restricted to lipid phase transitions, but can be used to study a wide range of soft matter transitions, ranging from protein unfolding and DNA unwinding and transitions, to phase transitions in thermotropic liquid crystals, surfactants and block copolymers.

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27

FORTUNATO, L., C. E. ALONSO, J. M. ARIAS, M. BÖYÜKATA, and A. VITTURI. "ODD NUCLEI AND SHAPE PHASE TRANSITIONS: THE ROLE OF THE UNPAIRED FERMION." International Journal of Modern Physics E 20, no. 02 (February 2011): 207–12. http://dx.doi.org/10.1142/s0218301311017533.

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Shape phase transitions in even and odd systems are reviewed within the frameworks of the Interacting Boson Model(IBM) and the Interacting Boson Fermion Model(IBFM), respectively and compared with geometric models when available. We discuss, in particular, the case of an odd j = 3/2 particle coupled to an even-even boson core that undergoes a transition from the spherical limit U(5) to the γ-unstable limit O(6). Energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviors qualitatively similar to those of the even core and they agree qualitatively with the model based on the E (5/4) boson-fermion symmetry. We describe then the UBF(5) to SUBF(3) transition when a fermion is allowed to occupy the orbits j = 1/2, 3/2, 5/2. The additional particle characterizes the properties at the critical points in finite quantum systems.

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28

TONG, YU. "NON-ADIABATIC ARBITRARY GEOMETRIC PHASE GATE IN 2-QUBIT SPIN MODEL." Modern Physics Letters B 21, no. 15 (June 20, 2007): 909–21. http://dx.doi.org/10.1142/s0217984907013353.

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We study a 2-qubit spin model for the possibility of realizing an arbitrary geometric quantum phase gate in terms of a single coherent magnetic pulse with multi-harmonic frequency. Using resonant transition approximation, the time-dependent Hamiltonian of two coupled spins can be solved analytically. The time evolution of the wave function is obtained without adiabatic approximation. The parameters of magnetic pulse, such as the frequency, amplitude, phase of each harmonic part as well as the time duration of the pulse are determined for achieving an arbitrary non-adiabatic geometric phase gate. The requirement of materials for realizing such a gate is analyzed. As a result, the non-adiabatic geometric controlled phase gates and A–A phase are also addressed.

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29

Basu, B., and P. Bandyopadhyay. "The geometric phase and the dynamics of quantum phase transition induced by a linear quench." Journal of Physics A: Mathematical and Theoretical 43, no. 35 (August 12, 2010): 354023. http://dx.doi.org/10.1088/1751-8113/43/35/354023.

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30

MAHDIFAR, A., R. ROKNIZADEH, and M. H. NADERI. "DETECTION OF THE SPATIAL CURVATURE EFFECTS THROUGH PHYSICAL PHENOMENA: THE NONLINEAR COHERENT STATES APPROACH." International Journal of Geometric Methods in Modern Physics 09, no. 01 (February 2012): 1250009. http://dx.doi.org/10.1142/s0219887812500090.

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In this paper, by using the nonlinear coherent states approach, we find a relation between the geometric structure of the physical space and the geometry of the corresponding projective Hilbert space. To illustrate the approach, we explore the quantum transition probability and the geometric phase in the curved space.

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31

Nagahata, Yutaka, Rigoberto Hernandez, and Tamiki Komatsuzaki. "Phase space geometry of isolated to condensed chemical reactions." Journal of Chemical Physics 155, no. 21 (December 7, 2021): 210901. http://dx.doi.org/10.1063/5.0059618.

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The complexity of gas and condensed phase chemical reactions has generally been uncovered either approximately through transition state theories or exactly through (analytic or computational) integration of trajectories. These approaches can be improved by recognizing that the dynamics and associated geometric structures exist in phase space, ensuring that the propagator is symplectic as in velocity-Verlet integrators and by extending the space of dividing surfaces to optimize the rate variationally, respectively. The dividing surface can be analytically or variationally optimized in phase space, not just over configuration space, to obtain more accurate rates. Thus, a phase space perspective is of primary importance in creating a deeper understanding of the geometric structure of chemical reactions. A key contribution from dynamical systems theory is the generalization of the transition state (TS) in terms of the normally hyperbolic invariant manifold (NHIM) whose geometric phase-space structure persists under perturbation. The NHIM can be regarded as an anchor of a dividing surface in phase space and it gives rise to an exact non-recrossing TS theory rate in reactions that are dominated by a single bottleneck. Here, we review recent advances of phase space geometrical structures of particular relevance to chemical reactions in the condensed phase. We also provide conjectures on the promise of these techniques toward the design and control of chemical reactions.

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32

Maguid, Elhanan, Michael Yannai, Arkady Faerman, Igor Yulevich, Vladimir Kleiner, and Erez Hasman. "Disorder-induced optical transition from spin Hall to random Rashba effect." Science 358, no. 6369 (December 14, 2017): 1411–15. http://dx.doi.org/10.1126/science.aap8640.

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Disordered structures give rise to intriguing phenomena owing to the complex nature of their interaction with light. We report on photonic spin-symmetry breaking and unexpected spin-optical transport phenomena arising from subwavelength-scale disordered geometric phase structure. Weak disorder induces a photonic spin Hall effect, observed via quantum weak measurements, whereas strong disorder leads to spin-split modes in momentum space, a random optical Rashba effect. Study of the momentum space entropy reveals an optical transition upon reaching a critical point where the structure’s anisotropy axis vanishes. Incorporation of singular topology into the disordered structure demonstrates repulsive vortex interaction depending on the disorder strength. The photonic disordered geometric phase can serve as a platform for the study of different phenomena emerging from complex media involving spin-orbit coupling.

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33

Basu, B. "Dynamics of the geometric phase in the adiabatic limit of a quench induced quantum phase transition." Physics Letters A 374, no. 10 (February 2010): 1205–8. http://dx.doi.org/10.1016/j.physleta.2009.12.072.

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34

MICHEL, E. G. "INTERPLAY OF ELECTRONIC AND GEOMETRIC STRUCTURE IN A MODEL SYSTEM: EPITAXIAL IRON SILICIDES." Surface Review and Letters 04, no. 02 (April 1997): 319–26. http://dx.doi.org/10.1142/s0218625x97000316.

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In this article, the interplay between electronic and geometric properties in transition metal silicide systems is presented using as a model system Fe–Si binary compounds. When iron silicides are epitaxially grown on Si(111), several different phases can be obtained, depending on the preparation conditions. In particular, for a 1:1 Fe:Si stoichiometry, there are two different phases possible: FeSi(CsCl) and ∊-FeSi. The former is a metastable phase, stabilized through epitaxy, while the latter is the bulk-stable phase for a 1:1 composition. Although the two have nominally the same composition, their different structures give rise to distinct electronic properties in each material. Their electronic structures have been probed by angle-resolved photoemission. In this article the results of this analysis will be presented along with the main properties of both compounds.

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35

Laux, Tim, and Yuning Liu. "Nematic–Isotropic Phase Transition in Liquid Crystals: A Variational Derivation of Effective Geometric Motions." Archive for Rational Mechanics and Analysis 241, no. 3 (June 28, 2021): 1785–814. http://dx.doi.org/10.1007/s00205-021-01681-0.

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AbstractIn this work, we study the nematic–isotropic phase transition based on the dynamics of the Landau–De Gennes theory of liquid crystals. At the critical temperature, the Landau–De Gennes bulk potential favors the isotropic phase and nematic phase equally. When the elastic coefficient is much smaller than that of the bulk potential, a scaling limit can be derived by formal asymptotic expansions: the solution gradient concentrates on a closed surface evolving by mean curvature flow. Moreover, on one side of the surface the solution tends to the nematic phase which is governed by the harmonic map heat flow into the sphere while on the other side, it tends to the isotropic phase. To rigorously justify such a scaling limit, we prove a convergence result by combining weak convergence methods and the modulated energy method. Our proof applies as long as the limiting mean curvature flow remains smooth.

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36

Shan, Chuan-Jia, Jin-Xin Li, Wei-Wen Cheng, Ji-Bing Liu, and Tang-Kun Liu. "Scaling of geometric phases close to the topological quantum phase transition in Kitaev's quantum wire model." Laser Physics Letters 11, no. 3 (January 29, 2014): 035202. http://dx.doi.org/10.1088/1612-2011/11/3/035202.

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37

Gracar, Peter, Lukas Lüchtrath, and Peter Mörters. "Percolation phase transition in weight-dependent random connection models." Advances in Applied Probability 53, no. 4 (November 22, 2021): 1090–114. http://dx.doi.org/10.1017/apr.2021.13.

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AbstractWe investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a non-trivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.

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38

Byczuk, Krzysztof, Walter Hofstetter, and Dieter Vollhardt. "ANDERSON LOCALIZATION VS. MOTT–HUBBARD METAL–INSULATOR TRANSITION IN DISORDERED, INTERACTING LATTICE FERMION SYSTEMS." International Journal of Modern Physics B 24, no. 12n13 (May 20, 2010): 1727–55. http://dx.doi.org/10.1142/s0217979210064575.

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We review recent progress in our theoretical understanding of strongly correlated fermion systems in the presence of disorder. Results were obtained by the application of a powerful nonperturbative approach, the dynamical mean-field theory (DMFT), to interacting disordered lattice fermions. In particular, we demonstrate that DMFT combined with geometric averaging over disorder can capture Anderson localization and Mott insulating phases on the level of one-particle correlation functions. Results are presented for the ground state phase diagram of the Anderson–Hubbard model at half-filling, both in the paramagnetic phase and in the presence of antiferromagnetic order. We find a new antiferromagnetic metal which is stabilized by disorder. Possible realizations of these quantum phases with ultracold fermions in optical lattices are discussed.

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39

Hansen, Ulrik Thinggaard, and Frederik Ravn Klausen. "Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd." Journal of Mathematical Physics 64, no. 1 (January 1, 2023): 013302. http://dx.doi.org/10.1063/5.0105283.

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Ising and Potts models can be studied using the Fortuin–Kasteleyn representation through the Edwards–Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength h > 0. In this representation, which is also known as the random-cluster model, the Kertész line is the curve that separates two regions of the parameter space defined according to the existence of an infinite cluster in [Formula: see text]. This signifies a geometric phase transition between the ordered and disordered phases even in cases where a thermodynamic phase transition does not occur. In this article, we prove strict monotonicity and continuity of the Kertész line. Furthermore, we give new rigorous bounds that are asymptotically correct in the limit h → 0 complementing the bounds from the work of Ruiz and Wouts [J. Math. Phys. 49, 053303 (2008)], which were asymptotically correct for h → ∞. Finally, using a cluster expansion, we investigate the continuity of the Kertész line phase transition.

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Koibuchi, Hiroshi, and Andrey Shobukhov. "Internal phase transition induced by external forces in Finsler geometric model for membranes." International Journal of Modern Physics C 27, no. 04 (February 23, 2016): 1650042. http://dx.doi.org/10.1142/s012918311650042x.

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In this paper, we numerically study an anisotropic shape transformation of membranes under external forces for two-dimensional triangulated surfaces on the basis of Finsler geometry. The Finsler metric is defined by using a vector field, which is the tangential component of a three-dimensional unit vector [Formula: see text] corresponding to the tilt or some external macromolecules on the surface of disk topology. The sigma model Hamiltonian is assumed for the tangential component of [Formula: see text] with the interaction coefficient [Formula: see text]. For large (small) [Formula: see text], the surface becomes oblong (collapsed) at relatively small bending rigidity. For the intermediate [Formula: see text], the surface becomes planar. Conversely, fixing the surface with the boundary of area A or with the two-point boundaries of distance L, we find that the variable [Formula: see text] changes from random to aligned state with increasing of A or L for the intermediate region of [Formula: see text]. This implies that an internal phase transition for [Formula: see text] is triggered not only by the thermal fluctuations, but also by external mechanical forces. We also find that the frame (string) tension shows the expected scaling behavior with respect to [Formula: see text] ([Formula: see text]) at the intermediate region of A (L) where the [Formula: see text] configuration changes between the disordered and ordered phases. Moreover, we find that the string tension [Formula: see text] at sufficiently large [Formula: see text] is considerably smaller than that at small [Formula: see text]. This phenomenon resembles the so-called soft-elasticity in the liquid crystal elastomer, which is deformed by small external tensile forces.

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41

Nakano, Akitoshi, Kento Sugawara, Shinya Tamura, Naoyuki Katayama, Kazuyuki Matsubayashi, Taku Okada, Yoshiya Uwatoko, et al. "Pressure-induced coherent sliding-layer transition in the excitonic insulator Ta2NiSe5." IUCrJ 5, no. 2 (January 26, 2018): 158–65. http://dx.doi.org/10.1107/s2052252517018334.

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The crystal structure of the excitonic insulator Ta2NiSe5has been investigated under a range of pressures, as determined by the complementary analysis of both single-crystal and powder synchrotron X-ray diffraction measurements. The monoclinic ambient-pressure excitonic insulator phase II transforms upon warming or under a modest pressure to give the semiconductingC-centred orthorhombic phase I. At higher pressures (i.e.>3 GPa), transformation to the primitive orthorhombic semimetal phase III occurs. This transformation from phase I to phase III is a pressure-induced first-order phase transition, which takes place through coherent sliding between weakly coupled layers. This structural phase transition is significantly influenced by Coulombic interactions in the geometric arrangement between interlayer Se ions. Furthermore, upon cooling, phase III transforms into the monoclinic phase IV, which is analogous to the excitonic insulator phase II. Finally, the excitonic interactions appear to be retained despite the observed layer sliding transition.

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42

Cheng, W. W., C. J. Shan, Y. B. Sheng, L. Y. Gong, S. M. Zhao, and B. Y. Zheng. "Geometric discord approach to quantum phase transition in the anisotropy XY spin model." Physica E: Low-dimensional Systems and Nanostructures 44, no. 7-8 (April 2012): 1320–23. http://dx.doi.org/10.1016/j.physe.2012.02.011.

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De Biasio, Davide, and Dieter Lüst. "Geometric Flow Equations for Schwarzschild‐AdS Space‐Time and Hawking‐Page Phase Transition." Fortschritte der Physik 68, no. 8 (July 17, 2020): 2000053. http://dx.doi.org/10.1002/prop.202000053.

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Moses, Amos. "Frustrated Magnetism: A Case Study of Geometric Frustration." Advanced Journal of Science, Technology and Engineering 3, no. 1 (February 22, 2023): 17–33. http://dx.doi.org/10.52589/ajste-gwzic1wk.

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In this research work, frustrations arising from the geometries of triangular lattices have been studied with the aid of Ising and Heisenberg models. The study reveals that geometrical frustrations can generate multiple degeneracies in the ground state. The quantum spin flip terms in the Heisenberg model are observed to play a vital role in the partial lifting up of these degeneracies. Hence, multiple degeneracies as consequence of frustrations are more pronounced for the Ising systems, which are devoid of quantum fluctuations. The observed six- and four-fold ground state degeneracies at zero field for three spins Ising and Heisenberg systems respectively are broken down to half at finite longitudinal fields. For this three-spin system, quantum phase transitions (QPT) are observed at critical longitudinal fields of J and 1.5J respectively for the Ising and Heisenberg models. At these critical fields, the ground states are observed to shift from quasi-antiferromagnet to ferromagnet. However, for the Heisenberg three-spin system in the presence of a transverse field, no transition is observed.

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45

Prüser, Axel, Imre Kondor, and Andreas Engel. "Aspects of a Phase Transition in High-Dimensional Random Geometry." Entropy 23, no. 7 (June 24, 2021): 805. http://dx.doi.org/10.3390/e23070805.

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A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current regulatory market risk measure Expected Shortfall. Others include portfolio optimization with a ban on short-selling, the storage capacity of the perceptron, the solvability of a set of linear equations with random coefficients, and competition for resources in an ecological system. These examples shed light on various aspects of the underlying geometric phase transition, create links between problems belonging to seemingly distant fields, and offer the possibility for further ramifications.

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Du, Yun-Zhi, Huai-Fan Li, Yang Zhang, Xiang-Nan Zhou, and Jun-Xin Zhao. "Restricted Phase Space Thermodynamics of Einstein-Power-Yang–Mills AdS Black Hole." Entropy 25, no. 4 (April 19, 2023): 687. http://dx.doi.org/10.3390/e25040687.

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We consider the thermodynamics of the Einstein-power-Yang–Mills AdS black holes in the context of the gauge-gravity duality. Under this framework, Newton’s gravitational constant and the cosmological constant are varied in the system. We rewrite the thermodynamic first law in a more extended form containing both the pressure and the central charge of the dual conformal field theory, i.e., the restricted phase transition formula. A novel phenomena arises: the dual quantity of pressure is the effective volume, not the geometric one. That leads to a new behavior of the Van de Waals-like phase transition for this system with the fixed central charge: the supercritical phase transition. From the Ehrenfest’s scheme perspective, we check out the second-order phase transition of the EPYM AdS black hole. Furthermore the effect of the non-linear Yang–Mills parameter on these thermodynamic properties is also investigated.

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Anyanwu, Victor O., Holger B. Friedrich, Abdul S. Mahomed, Sooboo Singh, and Thomas Moyo. "Phase Transition of High-Surface-Area Glycol–Thermal Synthesized Lanthanum Manganite." Materials 16, no. 3 (February 2, 2023): 1274. http://dx.doi.org/10.3390/ma16031274.

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Cubic and rhombohedral phases of lanthanum manganite were synthesized in a high-pressure reactor. A mixture of La and Mn nitrates with ethylene glycol at a synthesis temperature of 200 °C and a calcination temperature of up to 1000 °C, resulted in a single-phase perovskite, LaMnO3 validated using X-ray diffraction. Significant changes in unit cell volumes from 58 to 353 Å3 were observed associated with structural transformation from the cubic to the rhombohedral phase. This was confirmed using structure calculations and resistivity measurements. Transmission electron microscopy analyses showed small particle sizes of approximately 19, 39, 45, and 90 nm (depending on calcination temperature), no agglomeration, and good crystallinity. The particle characteristics, high purity, and high surface area (up to 33.1 m2/g) of the material owed to the inherent PAAR reactor pressure, are suitable for important technological applications, that include the synthesis of perovskite oxides. Characteristics of the synthesized LaMnO3 at different calcination temperatures are compared, and first-principles calculations suggest a geometric optimization of the cubic and rhombohedral perovskite structures.

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Hong, Xuanmiao, Guangwei Hu, Wenchao Zhao, Kai Wang, Shang Sun, Rui Zhu, Jing Wu, et al. "Structuring Nonlinear Wavefront Emitted from Monolayer Transition-Metal Dichalcogenides." Research 2020 (April 5, 2020): 1–10. http://dx.doi.org/10.34133/2020/9085782.

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The growing demand for tailored nonlinearity calls for a structure with unusual phase discontinuity that allows the realization of nonlinear optical chirality, holographic imaging, and nonlinear wavefront control. Transition-metal dichalcogenide (TMDC) monolayers offer giant optical nonlinearity within a few-angstrom thickness, but limitations in optical absorption and domain size impose restriction on wavefront control of nonlinear emissions using classical light sources. In contrast, noble metal-based plasmonic nanosieves support giant field enhancements and precise nonlinear phase control, with hundred-nanometer pixel-level resolution; however, they suffer from intrinsically weak nonlinear susceptibility. Here, we report a multifunctional nonlinear interface by integrating TMDC monolayers with plasmonic nanosieves, yielding drastically different nonlinear functionalities that cannot be accessed by either constituent. Such a hybrid nonlinear interface allows second-harmonic (SH) orbital angular momentum (OAM) generation, beam steering, versatile polarization control, and holograms, with an effective SH nonlinearity χ2 of ~25 nm/V. This designer platform synergizes the TMDC monolayer and plasmonic nanosieves to empower tunable geometric phases and large field enhancement, paving the way toward multifunctional and ultracompact nonlinear optical devices.

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Domichev, K. "MODELING THE BEHAVIOR OF THE PHYSICAL AND GEOMETRIC NON-LINEAR FUNCTIONAL HETEROGENEOUS MATERIALS." Innovative Solution in Modern Science 1, no. 45 (February 17, 2021): 82. http://dx.doi.org/10.26886/2414-634x.1(45)2021.5.

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The work is devoted to the problem of modeling the behavior of functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity under complex loads, in particular at large strains (up to 20%), when geometric nonlinearity in Cauchy relations must be taken into account. In previous works of the authors, functionally heterogeneous materials were studied in a geometrically linear formulation, which is true for small deformations (up to 7%). When predicting work with material at large deformations, it is necessary to take into account geometric nonlinearity in Cauchy relations.Studying the behavior of bodies made of functionally heterogeneous materials under unsteady load requires the development of special approaches, methods and algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at the point is represented as the sum of the elastic component, the jump in deformation during the phase transition, plastic deformation and deformation caused by temperature changes.A physical relationship in a nonlinear setting is proposed for modeling the behavior of bodies made of functionally heterogeneous materials. Formulas are obtained that nonlinearly relate strain rates and Formulas are obtained that nonlinearly relate strain rates and displacement rates.Keywords: mathematical modeling, functional heterogeneous materials, geometric nonlinearity, spline functions, pseudo-elastic plasticity, phase transitions

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50

Bianchi, Silvia De, and Luciano Gabbanelli. "Re-thinking geometrogenesis: Instantaneity in quantum gravity scenarios." Journal of Physics: Conference Series 2533, no. 1 (June 1, 2023): 012001. http://dx.doi.org/10.1088/1742-6596/2533/1/012001.

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Abstract Recent Quantum Gravity approaches revealed that spacetime emergence opens conceptual difficulties when the theory allows for cosmological scenarios compatible with geometrogenesis. In particular, it appears extremely difficult to think of an a-temporal transition from a non-geometric to a geometric phase and vice versa. In this paper we advance the proposal of a concept of atemporality, i.e., instantaneity that is suitable for the description of the transition occurring among fundamental phases from which spacetime emerges in some Quantum Gravity approaches, including Group Field Theory and its cosmological implications. After discussing the ontology at different levels of spacetime emergence in a theory of Quantum Gravity in Section 2, we shall focus on the definition of the notion of instantaneity to interpret the atemporal transition of geometrogenesis (Section 3.1), thereby arguing that atemporality dominates at Renormalization Group flow fixed points (Section 3.2). In Section 4, we apply for the first time our notion of instantaneity to the study of geometrogenesis in the context of tensorial Group Field Theory and we conclude by suggesting that atemporality plays a significant role for the understanding of our world at different scales.

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