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Outline

Title
Cases Eluding the KZM or Apt
Eigenstate Thermalization Hypothesis
Results
Level Statistics Indicator
Introduction
Preliminary Results About the Disordered Case
Conclusions
References
All Topics
Art
Music

Quench dynamics of many-body systems

Profile image of Giuseppe SantoroGiuseppe Santoro

2010

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Dynamical crossover behaviour in the relaxation of quenched quantum many-body systems
Aamir Makki

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A crossover between different power-law relaxation behaviors of many-body periodically driven integrable systems has come to light in recent years. We demonstrate using integrable quantum systems, that similar kinds of dynamical transitions may also occur in the relaxation of such systems following a sudden quench. Particularly, we observe two distinct power-law relaxation behaviors following a sudden quench in the integrable XY model, depending upon whether the quenched Hamiltonian lies in the commensurate or the incommensurate phase. The relaxation behavior for quenches at and near the boundary line, called the disorder line (DL), separating these phases is also characterized. The relaxation at the DL shows a new scaling exponent previously unexplored. The transitions occur through a crossover from the commensurate/incommensurate scaling behavior to the DL scaling behavior. The crossover time diverges like a power law as the parameters of the final quenched Hamiltonian approach th...

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Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
Aamir Makki

Physical Review B

A crossover between different power-law relaxation behaviors of many-body periodically driven integrable systems has come to light in recent years. We demonstrate, using integrable quantum systems, that similar kinds of dynamical transitions may also occur in the relaxation of such systems following a sudden quench. Particularly, we observe two distinct power-law relaxation behaviors following a sudden quench in the integrable XY model, depending upon whether the quenched Hamiltonian lies in the commensurate or the incommensurate phase. The relaxation behavior for quenches at and near the boundary line, called the disorder line (DL), separating these phases is also characterized. The relaxation at the DL shows a scaling exponent different from that for quenches to either of the commensurate or incommensurate phases. The transitions occur through a crossover from the commensurate or incommensurate scaling behavior to the DL scaling behavior. The crossover time diverges as a power law as the parameters of the final quenched Hamiltonian approach the DL. The transitions are also observed to be robust under weak integrability-breaking perturbations but disappear following strongly chaotic quenches.

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Universal Energy Distribution of Quasiparticles Emitted in a Local Time-Dependent Quench
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Physical Review Letters, 2012

We study the emission of quasi-particles in the scaling limit of the 1D Quantum Ising chain at the critical point perturbed by a time dependent local transverse field. We compute exactly and for a generic time dependence the average value of the transverse magnetization, its correlation functions, as well as the statistic of both the inclusive and exclusive work. We show that, except for a cyclic perturbation, the probability distribution of the work at low energies is a power law whose exponent is universal, i.e. does not depend on the specific time dependent protocol, but only on the final value attained by the perturbation.

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The role of dimensionality and geometry in quench-induced nonequilibrium forces
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We present an analytical formalism, supported by numerical simulations, for studying forces that act on curved walls following temperature quenches of the surrounding ideal Brownian fluid. We show that, for curved surfaces, the post-quench forces initially evolve rapidly to an extremal value, whereafter they approach their steady state value algebraically in time. In contrast to the previously-studied case of flat boundaries (lines or planes), the algebraic decay for curved geometries depends on the dimension of the system. Specifically, steady-state values of the force are approached in time as t −d/2 in d-dimensional spherical (curved) geometries. For systems consisting of concentric circles or spheres, the exponent does not change for the force on the outer circle or sphere. However, the force exerted on the inner circles or sphere experiences an overshoot and, as a result, does not evolve to the steady state in a simple algebraic manner. The extremal value of the force also depe...

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Quench dynamics of isolated many-body quantum systems
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Physical Review A, 2014

We study isolated quantum systems with two-body interactions after a quench. In these systems, the energy shell is a Gaussian of width σ, and it gives the maximum possible spreading of the energy distribution of the initial states. When the distribution achieves this shape, the fidelity decay can be Gaussian until saturation. This establishes a lower bound for the fidelity decay in realistic systems. An ultimate bound for systems with many-body interactions is also derived based on the analysis of full random matrices. We find excellent agreement between numerical and analytical results. We also provide the conditions under which the short-time dynamics of few-body observables is controlled by σ. The analyses are developed for systems, initial states, and observables accessible to experiments.

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Quantifying nonequilibrium behavior with varying quenching rates
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We investigate nonequilibrium behavior in (1+1)-dimensional stochastic field theories in the context of Ginzburg-Landau models at varying cooling rates. We argue that a reliable measure of the departure from thermal equilibrium can be obtained from the absolute value of the rate of change of the momentum-integrated structure function, ∆Stot. We show that the peak of ∆Stot scales with the cooling, or quench, time-scale, τq, in agreement with the prediction by Laguna and Zurek for the scaling of freeze-out time in both over and under-damped regimes. Furthermore, we show that the amplitude of the peak scales as τ −6/5 q independent of the viscosity.

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Quench dynamics near a quantum critical point
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Physical Review B, 2010

We study the dynamical response of a system to a sudden small change of the tuning parameter starting at the quantum critical point. In particular we find the scaling laws of different physical quantities (the excitation probability, number of excited quasiparticles, heat and entropy) with the quench amplitude and the system size. We extend the analysis to quenches with arbitrary

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Progressive quenching: Globally coupled model
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We study the processes in which fluctuating elements of a system are progressively fixed (quenched) while keeping the interaction with the remaining unfixed elements. If the interaction is global among Ising spin elements and if the unfixed part is re-equilibrated each time after fixing an element, the evolution of a large system is martingale about the equilibrium spin value of the unfixed spins. Due to this property the system starting from the critical point yields the final magnetization whose distribution shows non-Gaussian and slow transient behavior with the system size.

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When the Well Runs Dry: Modeling Environmental Quenching in Massive Clusters at $\boldsymbol z \gtrsim 1$
Devontae C Baxter

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We explore models of massive (> 10 10 M ⊙ ) satellite quenching in massive clusters at z ≳ 1 using an MCMC framework, focusing on two primary parameters: R quench (the host-centric radius at which quenching begins) and τ quench (the timescale upon which a satellite quenches after crossing R quench ). Our MCMC analysis shows two local maxima in the 1D posterior probability distribution of R quench at approximately 0.25 and 1.0 R 200 . Analyzing four distinct solutions in the τ quench -R quench parameter space, nearly all of which yield quiescent fractions consistent with observational data from the GOGREEN survey, we investigate whether these solutions represent distinct quenching pathways and find that they can be separated between "starvation" and "core quenching" scenarios. The starvation pathway is characterized by quenching timescales that are roughly consistent with the total cold gas (H 2 +HI) depletion timescale at intermediate z, while core quenching is characterized by satellites with relatively high line-of-sight velocities that quench on short timescales (∼ 0.25 Gyr) after reaching the inner region of the cluster (< 0.30 R 200 ). Lastly, we break the degeneracy between these solutions by comparing the observed properties of transition galaxies from the GOGREEN survey. We conclude that only the "starvation" pathway is consistent with the projected phase-space distribution and relative abundance of transition galaxies at z ∼ 1. However, we acknowledge that ram pressure might contribute as a secondary quenching mechanism.

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Nonperturbative approach to quench dynamics. I. Exact time evolution and steady state of the nonequilibrium Kondo model
Natan Andrei

arXiv: Strongly Correlated Electrons, 2019

We present a nonperturbative method for calculating the time-dependent many body wavefunction that follows a local quench, and we use it to find the exact time evolution of the nonequilibrium Kondo model driven by a bias voltage. The method also works in other quantum impurity models and may be of even wider applicability; integrability does not appear to play any role. In the case of the Kondo model, we show that the long time limit (with the system size taken to infinity first) of the time-evolving wavefunction is a current-carrying nonequilibrium steady state. We find a series expression for the average electric current, which we use in the next paper to identify a new universal regime of strong ferromagnetic coupling with Kondo temperature $T_K = D e^{\frac{3\pi^2}{8} \rho J}$.

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