Typical relaxation of perturbed quantum many-body systems

Relaxation of isolated quantum systems beyond chaos

In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is -- to say the least -- fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be establish…

开放量子系统中初始态典型性

Initial-State Typicality in Quantum Relaxation

研究揭示了开放量子系统中初始态对弛豫影响的典型性现象，提出新概念并提供实际应用意义。

Relaxation times of unstable states in systems with long range interactions

We consider several models with long-range interactions evolving via Hamiltonian dynamics. The microcanonical dynamics of the basic Hamiltonian Mean Field (HMF) model and perturbed HMF models with either global anisotropy or an on-site potential are studied both analytically and numerically. We find that in the magnetic phase, the initial zero magnetization state remains stable above a critical energy and is unstable below it. In the dynamically stable state, these models exhibit relaxation time scales that increase algebraically with the number $N$ of particles, indicating the robustness of t…

Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize

We consider isolated many-body quantum systems which do not thermalize, i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical theory is worked out for the typical temporal relaxation behavior in such cases. The main prerequisites are initial conditions which appreciably populate many energy levels and do not give rise to significant spatial inhomogeneities on macroscopic scales. The theory explains very well the experimental and numerical findings in a trapped-ion …

Typicality of Prethermalization

Prethermalization refers to the remarkable relaxation behavior which an integrable many-body system in the presence of a weak integrability-breaking perturbation may exhibit: After initial transients have died out, it stays for a long time close to some non-thermal steady state, but on even much larger time scales it ultimately switches over to the proper thermal equilibrium behavior. By extending Deutsch's conceptual framework from Phys. Rev. A 43, 2046 (1991), we analytically predict that prethermalization is a typical feature for a very general class of such weakly perturbed systems.

Stability of giant vortices in quantum liquids

We show how giant vortices can be stabilized in strong external potential Bose-Einstein condensates. We illustrate the formation of these vortices thanks to the relaxation Ginzburg-Landau dynamics for two typical potentials in two spatial dimensions. The giant vortex stability is studied for the particular case of the rotating cylindrical hard wall. The minimization of the perturbed energy is simplified into a one dimensional relaxation dynamics. The giant vortices can be stabilized only in a finite frequency range. Finally we obtain a curve for the minimum frequency needed to observe a giant …

Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time

We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation v…

弱扰动Ising模型中的完全宏观热化与薛定谔猫态的形成——Roos-Sugimoto-Teufel-Tumulka-Vogel理论的应用

Full macroscopic thermalization and the formation of Schrödinger's cats by unitary time evolution in the weakly perturbed Ising model - Applications of the Roos-Sugimoto-Teufel-Tumulka-Vogel theory

本研究证明弱随机扰动的铁磁Ising模型中，典型扰动使所有初始态在宏观可观测量上热化，并在有序相周期边界下形成宏观薛定谔猫态，结合RSTTV理论与Ising大偏差估计。

Critical dynamics at incommensurate phase transitions and NMR relaxation experiments

We study the critical dynamics of crystals which undergo a second-order phase transition from a high-temperature normal phase to a structurally incommensurate (IC) modulated phase. We give a comprehensive description of the critical dynamics of such systems, e.g. valid for crystals of the A_2BX_4 family. Using an extended renormalization scheme, we present a framework in which we analyze the phases above and below the critical temperature T_I. Above T_I, the crossover from the critical behavior to the mean-field regime is studied. Specifically, the resulting width of the critical region is inv…

受扰自旋链中磁化电流的非平凡阻尼

Nontrivial damping of magnetization currents in perturbed spin chains

本研究以自旋1/2 XXZ链为对象，通过动态量子典型性模拟和投影算符技术，揭示易轴区域磁化电流标准自相关函数的非平凡阻尼及修改版本的简单阻尼，其结果与Hubbard链粒子电流研究一致。

Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability den…