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Thermodynamics of the Quantum Mpemba Effect

Physical Review Letters 2024年第14期133卷 140404页

作者： Mattia Moroder Oisín Culhane Krissia Zawadzki John Goold Department of Physics Arnold Sommerfeld Center for Theoretical Physics (ASC) Munich Center for Quantum Science and Technology (MCQST) School of Physics Instituto de Física de São Carlos Universidade de São Paulo CP 369 13560-970 São Carlos São Paulo Brazil Trinity Quantum Alliance Unit 16 Trinity Technology and Enterprise Centre Pearse Street Dublin 2 D02YN67

We investigate the quantum Mpemba effect from the perspective of nonequilibrium quantum thermodynamics by studying relaxation dynamics of quantum systems coupled to a Markovian heat bath, which are described by Davies maps. Starting from a state with coherences in the energy eigenbasis, we demonstrate that an exponential speedup to equilibrium will always occur if the state is transformed to a diagonal state in the energy eigenbasis, provided that the spectral gap of the generator is defined by a complex eigenvalue. When the transformed state has a higher nonequilibrium free energy, we argue using thermodynamic reasoning that this is a genuine quantum Mpemba effect. Furthermore, we show how a unitary transformation on an initial state can always be constructed to yield the effect and demonstrate our findings by studying the dynamics of both the nonequilibrium free energy and the irreversible entropy production in single and multiqubit examples.

关键词： Entropy production Nonequilibrium & irreversible thermodynamics Open quantum systems Quantum thermodynamics Nonequilibrium systems Quantum spin models Exact diagonalization Lindblad equation Master equation metropolis algorithm Numerical approximation & analysis

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Spontaneous symmetry lowering of Si (001) towards two-dimensional ferro/antiferroelectric behavior

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Physical Review Materials 2019年第4期3卷 044410-044410页

作者： Chengcheng Xiao Xinwei Wang Xiaodong Pi Shengyuan A. Yang Yuanping Feng Yunhao Lu Shengbai Zhang State Key Laboratory of Silicon Materials School of Materials Science and Engineering Zhejiang University Hangzhou 310027 China Research Laboratory for Quantum Materials Singapore University of Technology and Design Singapore 487372 Singapore Department of Physics National University of Singapore Singapore 117542 Singapore Department of Physics Zhejiang University Hangzhou 310027 China Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy New York 12180 USA

Electronic polarization, manifested in numerous physical phenomena such as ferroelectricity, piezoelectricity, and pyroelectricity, is of great importance to many technological applications. The presence of ferroelectricity in bulk elemental materials is extremely rare due to the high symmetry of the underlying lattices. However, the presence of a surface lowers the symmetry, which may provide a future avenue for achieving robust ferroelectric polarization. Using first-principles calculations, we show that a spontaneous electrical polarization can be realized on the silicon reconstructed (001) surface. The magnitude of this polarization is 0.45×10−10C/m, comparable to those in benchmarking two-dimensional ferroelectric compounds such as SnTe and SnSe. The symmetry lowering is originated from a Peierls instability that removes the degeneracy of surface dangling bonds, whereby opening a band gap. Although flip-flop of the surface dimers may destroy the ordered phase at elevated temperatures, we find that a modest compressive strain, which increases the local stress and interdimer coupling, can drastically increase the robustness of the ferroelectric state towards room-temperature operations. The technology for processing Si has been well developed and the Si (001) surface has also been widely used in various electronic devices. Our discovery here thus holds high promise in a multitude of fields, ranging from nanoscale random access memory to low power consumption energy storage devices.

关键词： Antiferroelectrics Structural phase transition Elemental semiconductors Surfaces Density functional theory metropolis algorithm Nonequilibrium Green's function Wannier function methods

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Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature

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Physical Review E 2018年第1期98卷 012124-012124页

作者： Wei Zhong Debabrata Panja Gerard T. Barkema Robin C. Ball Department of Information and Computing Sciences Utrecht University Princetonplein 5 3584 CC Utrecht The Netherlands Department of Physics University of Warwick Coventry CV4 7AL United Kingdom

We consider the two- (2D) and three-dimensional (3D) Ising models on a square lattice at the critical temperature Tc, under Monte Carlo spin flip dynamics. The bulk magnetization and the magnetization of a tagged line in the 2D Ising model, and the bulk magnetization and the magnetization of a tagged plane in the 3D Ising model, exhibit anomalous diffusion. Specifically, their mean-square displacements increase as power laws in time, collectively denoted as ∼tc, where c is the anomalous exponent. We argue that the anomalous diffusion in all these quantities for the Ising model stems from time-dependent restoring forces, decaying as power laws in time—also with exponent c —in striking similarity to anomalous diffusion in polymeric systems. Prompted by our previous work that has established a memory-kernel based generalized Langevin equation (GLE) formulation for polymeric systems, we show that a closely analogous GLE formulation holds for the Ising model as well. We obtain the memory kernels from spin-spin correlation functions, and the formulation allows us to consistently explain anomalous diffusion as well as anomalous response of the Ising model to an externally applied magnetic field in a consistent manner.

关键词： Anomalous diffusion Critical phenomena Equilibrium lattice models Ising model Langevin equation metropolis algorithm

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Self-assembly of a dimer system

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Physical Review E 2019年第4期99卷 042133-042133页

作者： Mobolaji Williams Department of Physics Harvard University Cambridge Massachusetts 02138 USA

In the self-assembly process which drives the formation of cellular membranes, micelles, and capsids, a collection of separated subunits spontaneously binds together to form functional and more ordered structures. In this work, we study the statistical physics of self-assembly in a simpler scenario: the formation of dimers from a system of monomers. The properties of the model allow us to frame the microstate counting as a combinatorial problem whose solution leads to an exact partition function. From the associated equilibrium conditions, we find that such dimer systems come in two types: ”search-limited” and ”combinatorics-limited,” only the former of which has states where partial assembly can be dominated by correct contacts. Using estimates of biophysical quantities in systems of single-stranded DNA dimerization, transcription factor and DNA interactions, and protein-protein interactions, we find that all of these systems appear to be of the search-limited type, i.e., their fully correct dimerization regimes are more limited by the ability of monomers to find one another in the constituent volume than by the combinatorial disadvantage of correct dimers. We derive the parameter requirements for fully correct dimerization and find that rather than the ratio of particle number and volume (i.e., number density) being the relevant quantity, it is the product of particle diversity and volume that is constrained. Ultimately, this work contributes to an understanding of self-assembly by using the simple case of a system of dimers to analytically study the combinatorics of assembly.

关键词： Biomolecular self-assembly Classical statistical mechanics DNA-protein interactions Phase diagrams Protein-protein interactions Self-organized systems Biomolecules Combinatorics Exact solutions for many-body systems metropolis algorithm Monte Carlo methods

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Frustrated ground states of a generalized XY model and their mapping to nonmagnetic structural analogs

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Physical Review B 2016年第1期94卷 014438-014438页

作者： Milan Žukovič Institute of Physics Faculty of Science P. J. Šafárik University Park Angelinum 9 041 54 Košice Slovakia

Ground-state phases of a generalized XY model with magnetic and generalized nematic couplings on a nonbipartite triangular lattice are investigated in the exchange interactions parameter space. We demonstrate that the model displays a number of ordered and quasiordered phases as a result of geometrical frustration and/or competition between the magnetic and the generalized nematic interactions. The nature and the extent of the respective phases depend on the parameter q that characterizes the higher-order harmonics term in the Hamiltonian. Motivated by a recent discovery of the experimental realization of the model with q=2 in a seemingly unrelated field of the system chemistry [A. B. Cairns, M. J. Cliffe, J. A. M. Paddison, D. Daisenberger, M. G. Tucker, F.-X. Coudert, and A. L. Goodwin, Nature Chemistry 8, 442 (2016)], the model with q≥2 is discussed in the context of the prediction of structural phases of a class of bimetallic cyanides based on a mapping between the two systems.

关键词： Antiferromagnetism Classical statistical mechanics Critical phenomena Ferromagnetism Frustrated magnetism Magnetic phase transitions Order parameters Phase diagrams Phase separation Phase transitions Lattice models in condensed matter metropolis algorithm Monte Carlo methods Spin lattice models

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Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas

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Physical Review Letters 2022年第7期129卷 076403-076403页

作者： Yuan-Yao He Hao Shi Shiwei Zhang Institute of Modern Physics Northwest University Xi’an 710127 China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi’an 710127 China Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Physics and Astronomy University of Delaware Newark Delaware 19716 USA

We perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wave functions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact has a nonmonotonic temperature dependence, first increasing as temperature is lowered, and then showing a slight decline below the BKT transition temperature to approach the ground-state value from above.

关键词： Fermi gases Superfluidity Ultracold gases Finite-size scaling metropolis algorithm Monte Carlo methods Quantum Monte Carlo

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Alternative algorithms for simultaneous modeling of ordering and intermediate compound growth during reactive diffusion

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COMPUTATIONAL MATERIALS SCIENCE 2021年 187卷 110114-110114页

作者： Pasichna, Viktoriia Gusak, Andriy Bohdan Khmelnytsky Natl Univ Cherkasy Cherkassy Ukraine

Standard Monte Carlo algorithms with constant pair interactions within the first coordination shell are usually quite effective for the description of ordering, tracer diffusion, chemical diffusion (but without Kirkendall shift effect) within any already existing ordered intermediate phase. Yet, one encounters big problems if one tries to simulate the formation and growth of ordered intermediate phase or, especially, simultaneous formation and growth of several intermediate phases during interdiffusion. Two algorithms providing solution of this problem, are discussed. The first algorithm is known (but not widely used for reactive growth) - account of interactions in the two coordination shells with negative mixing energy in the first coordination shell and positive mixing energy in the second one. The second algorithm is new: interactions only within the first coordination shell of each atom but depending on the local composition within the cluster around interacting atoms. Both algorithms are shown to provide formation and growth of the ordered intermediate phases with rather narrow concentration ranges, growing with time (after some initial period) according to parabolic law.

关键词： Diffusion Ordering Intermediate phase Phase growth Monte Carlo simulation metropolis algorithm Residence Time algorithm BCC-lattice FCC-lattice Kinetics

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Discontinuous evolution of the structure of stretching polycrystalline graphene

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Physical Review B 2019年第16期100卷 161402(R)-161402(R)页

作者： Federico D'Ambrosio Vladimir Juričić Gerard T. Barkema Department of Information and Computing Sciences Utrecht University Princetonplein 5 3584 CC Utrecht The Netherlands Nordita KTH Royal Institute of Technology and Stockholm University Roslagstullsbacken 23 10691 Stockholm Sweden

Polycrystalline graphene has an inherent tendency to buckle, i.e., develop out-of-plane, three-dimensional structure. A force applied to stretch a piece of polycrystalline graphene influences the out-of-plane structure. Even if the graphene is well relaxed, this happens in nonlinear fashion: Occasionally, a tiny increase in stretching force induces a significant displacement, in close analogy to avalanches, which in turn can create vibrations in the surrounding medium. We establish this effect in computer simulations: By continuously changing the strain, we follow the displacements of the carbon atoms that turn out to exhibit a discontinuous evolution. Furthermore, the displacements exhibit a hysteretic behavior upon the change from low to high stress and back. These behaviors open up another direction in studying dynamical elasticity of polycrystalline quasi-two-dimensional systems, and in particular the implications on their mechanical and thermal properties.

关键词： Mechanical deformation Mechanical properties of membranes 2-dimensional systems Graphene metropolis algorithm Molecular dynamics

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Diffusion dynamics and steady states of systems of hard rods on a square lattice

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Physical Review E 2018年第2期97卷 022108-022108页

作者： Saugata Patra Dibyendu Das R. Rajesh Mithun K. Mitra Department of Physics Indian Institute of Technology Bombay Powai Mumbai-400076 India The Institute of Mathematical Sciences CIT Campus Taramani Chennai-600113 India Homi Bhabha National Institute Training School Complex Anushakti Nagar Mumbai 400094 India

It is known from grand canonical simulations of a system of hard rods on two-dimensional lattices that an orientationally ordered nematic phase exists only when the length of the rods is at least seven. However, a recent microcanonical simulation with diffusion kinetics, conserving both total density and zero nematic order, reported the existence of a nematically phase-segregated steady state with interfaces in the diagonal direction for rods of length six [Phys. Rev. E 95, 052130 (2017)], violating the equivalence of different ensembles for systems in equilibrium. We resolve this inconsistency by demonstrating that the kinetics violate detailed balance condition and drives the system to a nonequilibrium steady state. By implementing diffusion kinetics that drive the system to equilibrium, even within this constrained ensemble, we recover earlier results showing phase segregation only for rods of length greater than or equal to seven. Furthermore, in contrast to the nonequilibrium steady state, the interface has no preferred orientational direction. In addition, by implementing different nonequilibrium kinetics, we show that the interface between the phase segregated states can lie in different directions depending on the choice of kinetics.

关键词： Nonequilibrium statistical mechanics Phase separation Phase transitions Equilibrium lattice models Lattice models in statistical physics Nonequilibrium lattice models metropolis algorithm

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Sampling vacancy configurations with large relaxations using Smart Darting

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Physical Review Materials 2024年第3期8卷 033604-033604页

作者： D. Tanguy Université Lyon Université Claude Bernard Lyon 1 CNRS Institut Lumière Matière Villeurbanne F-69622 France

Markov chain Monte Carlo simulations, combining the sampling of the position of the particles and their chemical nature, are very useful when calculating, for example, average site occupancies at crystalline defects in alloys. Unfortunately, when the relaxations around the solutes are large, the exchange moves can be systematically rejected because of atoms overlapping. As a consequence, the simulations are often trapped in nonphysical configurations. In this paper, the “Smart Darting” method from Andricioaei et al. is adapted and extended to propose a solution to this limitation. The method is tested in a particularly demanding case: the sampling of the arrangements of delocalized vacancies and divacancies in grain boundaries, both in the fcc and the bcc structure. Beyond the methodological aspects, intergranular vacancy clusters are interesting in several contexts, such as ductile fracture, irradiation, or thin-film dewetting, and therefore several properties have been measured that can be useful for mesoscale modeling: segregation energies, effective diffusion barriers in and out of the grain boundaries, vacancy-vacancy binding energies, and elastic dipole tensors.

关键词： Fracture Grain boundaries Point defects Self-diffusion metropolis algorithm

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