We previously showed that a quantum quench in a one-dimensional translation invariant system produces undamped oscillations of a local observable when the post-quench state includes a single-quasiparticle mode and the observable couples to that mode [J. Phys. A 47 (2014) 402001]. Here we consider quenches that break initial translation invariance. Focusing on quenches performed only on an interval of the whole system, we analytically determine the time evolution of local observables, which occurs inside a truncated light cone spreading away from the quenched interval as time increases. If the quench excites a single-quasiparticle mode, oscillations with the frequency of the quasiparticle mass stay undamped until a time increasing with the length of the quenched interval, before eventually decaying as $t^{-1/2}$. The translation invariant case with no damping is recovered as the length of the interval goes to infinity.
We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of…
We obtain analytical results for the time evolution of local observables in systems undergoing quantum quenches in $d$ spatial dimensions. For homogeneous systems we show that oscillations undamped in time occur when the state produced by the quench includes single-quasiparticle modes and the observable couples to those modes. In particular, a quench of the transverse field within the ferromagnetic phase of the Ising model produces undamped oscillations of the order parameter when $d>1$. For the more general case in which the quench is performed only in a subregion of the whole $d$-dimensional…
We study the problem of a quantum quench in which the initial state is the ground state of an inhomogeneous hamiltonian, in two different models, conformal field theory and ordinary free field theory, which are known to exhibit thermalisation of finite regions in the homogeneous case. We derive general expressions for the evolution of the energy flow and correlation functions, as well as the entanglement entropy in the conformal case. Comparison of the results of the two approaches in the regime of their common validity shows agreement up to a point further discussed. Unlike the thermal analog…
Entanglement dynamics after quenches with inhomogeneous Hamiltonians
Dipartimento di Fisica dell’Università di Pisa（比萨大学物理系）；Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova（帕多瓦大学伽利略·伽利莱物理与天文学系）；INFN Sezione di Pisa（意大利国家核物理研究所比萨分部）；Istituto di Informatica e Telematica, CNR（意大利国家研究委员会信息学与电信研究所）
We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan-Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we compute analytically the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles.…
Mott insulator - superfluid transition in a periodic lattice of Josephson junctions can be driven by tunneling rate increase. Resulting winding numbers $W$ of the condensate wavefunction decrease with increasing quench time in accord with the Kibble-Zurek mechanism (KZM). However, in very slow quenches Bose-Hubbard dynamics rearranges wavefunction phase so that its random walk cools, $\bar{W^2}$ decreases and eventually the wavefunction becomes too cold to overcome potential barriers separating different $W$. Thus, in contrast with KZM, in very slow quenches $\bar{W^2}$ is set by random walk w…
We consider the non-equilibrium physics induced by joining together two tight binding fermionic chains to form a single chain. Before being joined, each chain is in a many-fermion ground state. The fillings (densities) in the two chains might be the same or different. We present a number of exact results for the correlation functions in the non-interacting case. We present a short-time expansion, which can sometimes be fully resummed, and which reproduces the so-called `light cone' effect or wavefront behavior of the correlators. For large times, we show how all interesting physical regimes ma…
Universality and weak-ergodicity breaking in quantum quenches
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institut für Theoretische Physik, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；CNR-INO（意大利国家研究委员会光电研究所）
We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply th…
A dc voltage induced by an external ac current is observed in system of asymmetric mesoscopic superconducting loops. The value and sign of this dc voltage, like the one of the persistent current, depend in a periodical way on a magnetic field with period corresponded to the flux quantum within the loop. The amplitude of the oscillations does not depend on the frequency of the external ac current (in the investigated region 100 Hz - 1 MHz) and depends on its amplitude. The latter dependence is not monotonous. The observed phenomenon of rectification is interpreted as a consequence of a dynamic …
We extend the semiclassical picture for the spreading of entanglement and correlations to quantum quenches with several species of quasiparticles that have non-trivial pair correlations in momentum space. These pair correlations are, for example, relevant in inhomogeneous lattice models with a periodically-modulated Hamiltonian parameter. We provide explicit predictions for the spreading of the entanglement entropy in the space-time scaling limit. We also predict the time evolution of one- and two-point functions of the order parameter for quenches within the ordered phase. We test all our pre…
We provide a new hydrodynamic framework to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions. Our result builds up on the recently-introduced Generalized Hydrodynamics (GHD). The method allows to analytically describe the dynamics during generic space-time-dependent smooth modulations of the interactions. As a proof of concept, we study experimentally-motivated interaction quenches in the trapped interacting Bose gas, which cannot be treated with current analytical or numerical methods. We also benchmark our results in the XXZ spin chain and in the class…
Persistent homology (PH) was applied to probe the structural changes of glasses under shear. PH associates each local atomistic structure in an atomistic configuration to a geometric object, namely, a hole, and evaluates the robustness of these holes against noise. We found that the microscopic structures were qualitatively different before and after yielding. The structures before yielding contained robust holes, the number of which decreased after yielding. We also observed that the structures after yielding approached those of quickly quenched glass. This work demonstrates the crucial role …
We study the interplay between an inhomogeneous quantum quench of the external potential in a system of relativistic fermions in one dimension and the well-known Klein tunneling. We find that the large time evolution is characterized by particle production at a constant rate which we derive analytically. The produced particles can be physically interpreted according to a semiclassical picture and the state reached in the long time limit can be classified as a non-equilibrium-steady-state. Such a quantum quench can be used in order to observe macroscopic effects of Klein tunneling in transport,…
We study a loop of Josephson junctions that is quenched through its critical temperature. For three or more junctions, symmetry breaking states can be achieved without thermal activation, in spite of the fact that the relaxation time is practically constant when the critical temperature is approached from above. The probability for these states decreases with quenching time, but the dependence is not allometric. For large number of junctions, cooling does not have to be fast. For this case, we evaluate the standard deviation of the induced flux. Our results are consistent with the available ex…
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theo…
We investigate the dynamical effects of a magnetic flux quench in the Su-Schrieffer-Heeger model in a one-dimensional ring geometry. We show that, even when the system is initially in the half-filled insulating state, the flux quench induces a time-dependent current that eventually reaches a finite stationary value. Such persistent current, which exists also in the thermodynamic limit, cannot be captured by the linear response theory and is the hallmark of nonlinear dynamical effects occurring in the presence of dimerization. Moreover, we show that, for a range of values of dimerization streng…
The generalized hydrodynamics (GHD) formalism has become an invaluable tool for the study of spatially inhomogeneous quantum quenches in (1+1)-dimensional integrable models. The main paradigm of the GHD is that at late times local observables can be computed as generalized Gibbs ensemble averages with space-time dependent chemical potentials. It is, however, still unclear how this semiclassical GHD picture emerges out of the full quantum dynamics. We evaluate the quantum time evolution of local observables in spatially inhomogeneous quenches, based on the quench action method, where observable…
We construct exact steady states of unitary non-equilibrium time evolution in the gapless XXZ spin-1/2 chain where integrability preserves ballistic spin transport at long-times. We characterize the quasi-local conserved quantities responsible for this feature and introduce a computationally effective way to evaluate their expectation values on generic matrix product initial states. We employ this approach to reproduce the long-time limit of local observables in all quantum quenches which explicitly break particle-hole or time-reversal symmetry. We focus on a class of initial states supporting…
Entanglement has become central for the characterization of quantum matter both in and out of equilibrium. In a dynamical context entanglement exhibits universal linear temporal growth in generic systems, which stems from the underlying linear light cones as they occur in planar geometries. Inhomogeneous spacetimes can lead, however, to strongly bent trajectories. While such bent trajectories crucially impact correlation spreading and therefore the light-cone structure, it has remained elusive how this influences the entanglement dynamics. In this work we investigate the real-time evolution of…
We show that for particles performing Brownian motion in a frozen array of scatterers long-time correlations emerge in the mean-square displacement. Defining the velocity autocorrelation function (VACF) via the second time-derivative of the mean-square displacement, power-law tails govern the long-time dynamics similar to the case of ballistic motion. The physical origin of the persistent memory is due to repeated encounters with the same obstacle which occurs naturally in Brownian dynamics without involving other scattering centers. This observation suggests that in this case the VACF exhibit…
Ordering dynamics of self-propelled particles in an inhomogeneous medium in two-dimensions is studied. We write coarse-grained hydrodynamic equations of motion for coarse-grained density and velocity fields in the presence of an external random disorder field, which is quenched in time. The strength of inhomogeneity is tuned from zero disorder (clean system) to large disorder. In the clean system, the velocity field grows algebraically as $L_{\rm V} \sim t^{0.5}$. The density field does not show clean power-law growth; however, it follows $L_{\rm ρ} \sim t^{0.8}$ approximately. In the inhomoge…
The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require solution of the bi-Laplace rather than the Laplace equation. For all cases we can consider quenched randomness in the brittle material itself, as well as randomness in the succession of fracture events. While mode III calls for the advance (in time) of one analytic function, mode I and II call for the advance of two analytic functions. This fundamental difference …
We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule $54$. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all Rényi entropies in the thermodynamic limit and th…
We consider a persistent random walk on an inhomogeneous environment where the reflection probability depends only on the distance from the origin. Such an environment is the result of an average over all realizations of disorder of a Lévy-Lorentz (LL) gas. Here we show that this averaged Lévy-Lorentz gas yields nontrivial results even when the related LL gas is trivial. In particular, we investigate its long time transport properties such as the mean square displacement and the statistics of records, as well as the occurrence of ageing phenomena.
