arXiv subjects

Mauro Schiulaz

Publications and source records attributed to Mauro Schiulaz.

9 recordsLinked to original sources

arXiv2020

Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase

The self-averaging behavior of interacting many-body quantum systems has been mostly studied at equilibrium. The present work addresses what happens out of equilibrium, as the increase of the strength of onsite disorder takes the system to the localized phase. We consider two local and two non-local quantities of great experimental and theoretical interest. In the delocalized phase, self-averaging depends on the observable and on the time scale, but the picture simplifies substantially when localization is reached. In the localized phase, the local observables become self-averaging at all times, while the non-local quantities are throughout non-self-averaging. These behaviors are explained and scaling analysis are provided using the $\ell$-bits model and a toy model.

cond-mat.stat-mech↗

arXiv2020

Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems

Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, Rényi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales.

cond-mat.stat-mech↗

arXiv2019

Thouless and relaxation time scales in many-body quantum systems

A major open question in studies of nonequilibrium quantum dynamics is the identification of the time scales involved in the relaxation process of isolated quantum systems that have many interacting particles. We demonstrate that long time scales can be analytically found by analyzing dynamical manifestations of spectral correlations. Using this approach, we show that the Thouless time, $t_{\text{Th}}$, and the relaxation time, $t_{\text{R}}$, increase exponentially with system size. We define $t_{\text{Th}}$ as the time at which the spread of the initial state in the many-body Hilbert space is complete and verify that it agrees with the inverse of the Thouless energy. $t_{\text{Th}}$ marks the point beyond which the dynamics acquire universal features, while relaxation happens later when the evolution reaches a stationary state. In chaotic systems, $t_{\text{Th}}\ll t_{\text{R}}$, while for systems approaching a many-body localized phase, $t_{\text{Th}}\rightarrow t_{\text{R}}$. Our analytical results for $t_{\text{Th}}$ and $t_{\text{R}}$ are obtained for the survival probability, which is a global quantity. We show numerically that the same time scales appear also in the evolution of the spin autocorrelation function, which is an experimental local observable. Our studies are carried out for realistic many-body quantum models. The results are compared with those for random matrices.

cond-mat.stat-mech↗

arXiv2018

Magnetoenhancement of superconductivity in composite D-wave superconductors

We study composite D-wave superconductors consisting of randomly oriented and randomly distributed superconducting droplets embedded into a matrix. In a certain range of parameters the application of a small magnetic field enhances the superconductivity in these materials while larger fields suppress superconductivity as usual in conventional superconductors. We investigate the magnetic field dependence of the superfluid density and the critical temperature of such superconductors.

cond-mat.supr-con↗

arXiv2018

From few- to many-body quantum systems

How many particles are necessary to make a quantum system many-body? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with $N$ particles, gradually increasing $N$ from 1. We show that convergence for the static properties of the system with few particles to the many-body limit is fast. For $N \gsim 4$, the density of states is already very close to Gaussian and signatures of many-body quantum chaos, such as level repulsion and fully extended eigenstates, become evident. The dynamics, on the other hand, depend on the initial state and time scale. In dilute systems, as the particles move away from each other, the entropy growth changes in time from linear, as typical for many-body systems, to logarithmic.

cond-mat.stat-mech↗

arXiv2018

Theory of combustion in disordered media

The conventional theory of combustion describes systems where all of the parameters are spatially homogeneous. On the other hand, combustion in disordered explosives has long been known to occur after local regions of the material, called "hot spots", are ignited. In this article we show that a system of randomly distributed hot spots exhibits a dynamic phase transition, which, depending on parameters of the system can be either first or second order. These two regimes are separated by a tri-critical point. We also show that on the qualitative level the phase diagram of the system is universal. It is valid in two and three dimensions, in the cases when the hot spots interact either by heat or sound waves and in a broad range of microscopic disorder models.

cond-mat.dis-nn↗

arXiv2017

Theory of deflagration in disordered media

The conventional theory of burning works well in the case of uniform media where all system parameters are spatially independent. We develop a theory of burning in disordered media. In this case, rare regions (hot spots) where the burning process is more effective than on average may control the heat propagation in an explosive sample. We show that most predictions of the theory of burning are quite different from the conventional case. In particular, we show that a system of randomly distributed hot spots exhibits a dynamic phase transition, which is similar to the percolation transition. Depending on parameters of the system the phase transition can be either first or second order. These two regimes are separated by a tricritical point. The above results may be applicable to dynamics of any over-heated disordered system with a first order phase transition.

cond-mat.stat-mech↗

arXiv2016

Absence of many-body mobility edges

Localization transitions as a function of temperature require a many-body mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because local fluctuations into the ergodic phase within the supposedly localized phase can serve as mobile bubbles that induce global delocalization. Such fluctuations inevitably appear with a low but finite density anywhere in any typical state. We conclude that the only possibility for many-body localization to occur are lattice models that are localized at all energies. Building on a close analogy with a model of assisted two-particle hopping, where interactions induce delocalization, we argue why hot bubbles are mobile and do not localize upon diluting their energy. Numerical tests of our scenario show that previously reported mobility edges cannot be distinguished from finite-size effects.

cond-mat.dis-nn↗

arXiv2015

Dynamics in many-body localized quantum systems without disorder

We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation-invariant Hamiltonian. We show that dynamics starting from a random initial configuration is nonperturbatively slow in the hopping strength, and potentially genuinely nonergodic in the thermodynamic limit. In finite systems with periodic boundary conditions, density relaxation takes place in two stages, which are separated by a long out-of-equilibrium plateau whose duration diverges exponentially with the system size. We estimate the phase boundary of this quantum glass phase, and discuss the role of local resonant configurations. We suggest experimental realizations and methods to observe the discussed nonergodic dynamics.

cond-mat.dis-nn↗