Related papers: Onset of Random Matrix Behavior in Scrambling Syst…
In this work, we develop a quantum metrological framework for quantum chaos by showing that local subsystems of information scrambling systems naturally function as quantum stopwatches. The reduced quantum state of a subsystem encodes the…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…
Our current understanding of quantum chaos in many-body quantum systems hinges on the random matrix theory(RMT) behavior of eigenstates and their energy level statistics. Although RMT has been remarkably successful in describing `coarse'…
Quantum small-worlds are quantum many-body systems that interpolate between completely ordered (nearest-neighbour, next-to-nearest-neighbour etc.) and completely random interactions. As such, they furnish a novel new laboratory to study…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding…
Understanding the timescales associated with relaxation to equilibrium in closed quantum many-body systems is one of the central focuses in the study of their non-equilibrium dynamics. At late times, these relaxation processes exhibit…
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
Random transformations are typically good at "scrambling" information. Specifically, in the quantum setting, scrambling usually refers to the process of mapping most initial pure product states under a unitary transformation to states which…
Quantum scrambling describes the spreading of local information into many degrees of freedom in quantum systems. This provides the conceptual connection among diverse phenomena ranging from thermalizing quantum dynamics to models of black…
We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor $K(t)$ analytically and numerically, we show that…
Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has…
Information scrambling refers to the unitary dynamics that quickly spreads and encodes localized quantum information over an entire many-body system and makes the information accessible from any small subsystem. While information scrambling…
Quantum speed limits such as the Mandelstam-Tamm or Margolus-Levitin bounds offer a quantitative formulation of the energy-time uncertainty principle that constrains dynamics over short times. We show that the spectral form factor, a…
We study the time evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes effectively a…
How quantum information is scrambled in the global degrees of freedom of non-equilibrium many-body systems is a key question to understand local thermalization. Here we propose that the scaling of the mutual information between two…
Is there a quantum many-body system that scrambles information as fast as a black hole? The Sachev-Ye-Kitaev model can saturate the conjectured bound for chaos, but it requires random all-to-all couplings of Majorana fermions that are hard…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
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,…