Han等人[Phys. Rev. Lett. 132, 137102 (2024)]最近引入了一个经典随机晶格气体模型，该模型除了粒子数守恒外，还守恒粒子的偶极矩。由于其固有的非线性，该模型表现出异常的宏观标度行为，不同于仅守恒粒子数的晶格气体。本文研究该模型在大尺度和长时间下的一些基本弛豫和涨落性质。这些性质关键取决于总粒子数是无限还是有限。我们找到了相似解，描述了偶极守恒气体（DCG）在若干标准设置下的弛豫。我们工作的主要部分是将宏观涨落理论（MFT）扩展到该模型，该理论此前是为仅守恒粒子数的晶格气体发展的。我们将MFT应用于计算当从t=0时的（确定性或随机）恒定密度出发时，正半轴上过剩粒子数的非平衡涨落方差。利用MFT，我们还确定了DCG的平衡Boltzmann-Gibbs分布。最后，基于这些结果，我们确定了在平衡态下初始均匀的DCG中，以给定尺寸的宏观空洞形式出现的大偏差的概率分布，以及导致该大偏差的最概然密度历史。
英文摘要：
Han et al. [Phys. Rev. Lett. \textbf{132}, 137102 (2024)] have recently introduced a classical stochastic lattice gas model which, in addition to particle conservation, also conserves the particles' dipole moment. Because of its intrinsic nonlinearity this model exhibits unusual macroscopic scaling behaviors, different from those of lattice gases that conserve only the number of particles. Here we investigate some basic relaxation and fluctuation properties of this model at large scales and at long times. These properties crucially depend on whether the total number of particles is infinite or finite. We find similarity solutions, describing relaxation of the dipole-conserving gas (DCG) in several standard settings. A major part of our effort is an extension to this model of the macroscopic fluctuation theory (MFT), previously developed for lattice gases where only the number of particles is conserved. We apply the MFT to the calculation of the variance of nonequilibrium fluctuations of the excess number of particles on the positive semi-axis when starting from an (either deterministic, or random) constant density at $t=0$. Using the MFT, we also identify the equilibrium Boltzmann-Gibbs distribution for the DCG. Finally, based on these results, we determine the probability distribution of, and the most probable density history leading to, a large deviation in the form of a macroscopic void of a given size in an initially uniform DCG at equilibrium.
We investigate the coupled dynamics of charge and energy in interacting lattice models with dipole conservation. We formulate a generic hydrodynamic theory for this combination of fractonic constraints and numerically verify its applicability to the late-time dynamics of a specific bosonic quantum system by developing a microscopic non-equilibrium quantum field theory. Employing a self-consistent $1/N$ approximation in the number of field components, we extract all entries of a generalized diffusion matrix and determine their dependence on microscopic model parameters. We discuss the relation …
We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the steady-state of the system can be expressed in terms of a linear superposition Bernoulli shock measures with random walk dynamics. The dynamics of a shock position is studied in detail. The spectrum of the transfer matrix and the relaxation times to the steady-state have also been studied in the large-system-size limit.
Kosterlitz--Thouless Criticality in a Dipole-Conserving XY Model
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, and School of Physics, Sun Yat-sen University（中山大学物理学院）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University（西湖大学理学院）；Institute of Natural Sciences, Westlake Institute for Advanced Study（西湖高等研究院自然科学研究中心）
We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase where locally …
We show that the combination of charge and dipole conservation---characteristic of fracton systems---leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total $S^z$) and its associated dipole moment. First, we consider a minimal model including only three-site terms and find that the infinite temperature auto-correlation saturates to a finite value---showcasing non-thermal behavior. The absence of thermalizat…
The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is that the local electron equilibrium distribution must have a space- and time-dependent chemical potential, drift velocity and temperature. Both quantum kinetic and semi-classical arguments are given, and we calculate and analyze the corresponding analytical d-dimensional dielectric function. Dynamical correlation, arising from relaxation effects, is shown to…
The effect of long range dipole-dipole interactions on the thermal fluctuations of the magnetization of an assembly of single-domain ferromagnetic particles is considered. If orientational correlations between the particles are neglected, the evolution of the magnetization orientations may be described by a nonlinear Fokker-Planck equation (FPE) reducing to the usual linear one in the limit of infinite dilution [W.F. Brown Jr, Phys. Rev. 130, 1677 (1963)]. The thermally activated relaxation time scale of the assembly is estimated, leading to a simple modification of the axially symmetric asymp…
For growing inhomogeneous thin films with an island nanostructure similar as observed in experiment, we determine the nonequilibrium and equilibrium remanent magnetization. The single-island magnetic anisotropy, the dipole coupling, and the exchange interaction between magnetic islands are taken into account within a micromagnetic model. A cluster Monte Carlo method is developed which includes coherent magnetization changes of connected islands. This causes a fast relaxation towards equilibrium for irregularly connected systems. We analyse the transition from dipole coupled islands at low cove…
Spin tunneling in molecular magnets controlled by dipole-dipole interactions (DDI) in the disordered state has been considered numerically on the basis of the microscopic model using the quantum mean-field approximation. In the actual case of a strong DDI spin coherence is completely lost and there is a slow relaxation of magnetization, described by t^{3/4} at short times. Fast precessing nuclear spins, included in the model microscopically, only moderately speed up the relaxation.
The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric dipoles and magnetic moments is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tensors leads to three types of dissipation terms: scalars, vectors and pseudo-vectors. The scalar terms account for chemical reactivities, the vectorial terms account for transport and the pseudo-vectorial terms account for relaxation. The linear phenomenological relations, derived from the irreversible evolution, describe notably the Leh…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which diverge algebraically with the system size. To test the robustness of this phenomenon to non-deterministic dynamical processes, we have generalized the paradigmatic model exhibiting such a behavior, the Hamiltonian Mean-Field model, to include energy-conserving stochastic processes. Analysis, based on the Boltzmann equation, a scaling approach and numerical studie…
We present the nonlinear fluctuating hydrodynamics which governs the late time dynamics of a chaotic many-body system with simultaneous charge/mass, dipole/center of mass, and momentum conservation. This hydrodynamic effective theory is unstable below four spatial dimensions: dipole-conserving fluids at rest become unstable to fluctuations, and are governed not by hydrodynamics, but by a fractonic generalization of the Kardar-Parisi-Zhang universality class. We numerically simulate many-body classical dynamics in one-dimensional models with dipole and momentum conservation, and find evidence f…
The interaction-site-density-fluctuation correlators, the dipole-relaxation functions, and the mean-squared displacements of a system of symmetric dumbbells of fused hard spheres are calculated for two representative elongations of the molecules within the mode-coupling theory for the evolution of glassy dynamics. For large elongations, universal relaxation laws for states near the glass transition are valid for parameters and time intervals similar to the ones found for the hard-sphere system. Rotation-translation coupling leads to an enlarged crossover interval for the mean-squared displacem…
When a strongly disordered system of interacting quantum dipoles is locally excited, the excitation relaxes on some (potentially very long) timescale. We analyze this relaxation process, both for electron glasses with strong Coulomb interactions - in which particle-hole dipoles are emergent excitations - and for systems (e.g., quantum magnets or ultracold dipolar molecules) made up of microscopic dipoles. We consider both energy relaxation rates ($T_1$ times) and dephasing rates ($T_2$ times), and their dependence on frequency, temperature, and polarization. Systems in both two and three dimen…
The spatial components of the autocorrelation function of noninteracting dipoles are analytically obtained in terms of rotational Brownian motion on the surface of a unit sphere using multi-level jumping formalism based on Debye's rotational relaxation model, and the rotational relaxation functions are evaluated.
We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. This model is based on a 16-discrete-velocity model. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compres…
