Related papers: Nonlinear perturbation of Random Matrix Theory
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and…
Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed…
We investigate the non-linear evolution of the matter power spectrum by using a large set of high-resolution N-body/hydrodynamic simulations. The linear matter power in the initial conditions is consistently modified to accommodate warm…
We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…
We investigate the energy relaxation process produced by thermal baths at zero temperature acting on the boundary atoms of chains of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit…
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of…
We analyze the behavior of a network of quantum oscillators coupled with a number of external environments. We show that the dynamics is such that the quantum state of the network always obeys a local master equation with a simple…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
The formalism of linear response theory can be extended to encompass physical situations where an open quantum system evolves towards a non-equilibrium steady-state. Here, we use the framework put forward by Konopik and Lutz [Phys. Rev.…
We show that the rate of switching between the vibrational states of a modulated nonlinear oscillator is characterized by a quantum critical temperature $T_c\propto\hbar^2$. The rate is independent of $T$ for $T<T_c$. Above $T_c$ there…
Time-translation symmetry breaking is a mechanism for the emergence of non-stationary many-body phases, so-called time-crystals, in Markovian open quantum systems. Dynamical aspects of time-crystals have been extensively explored over the…
Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS)…
Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical…
We study the energy flow between a one dimensional oscillator and a chaotic system with two degrees of freedom in the weak coupling limit. The oscillator's observables are averaged over an initially microcanonical ensemble of trajectories…
Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet conceptually simpler, setup for this phenomenon. We consider a---possibly nonintegrable---reference dynamics, weakly perturbed…
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We contrast this motion with the motion of a quantum particle in a potential which varies randomly in space and in time,…
We perform a numerical analysis of the effects of a nonlinear perturbation on the quantum dynamics of two models describing non-interacting cold atoms in a standing wave of light with a periodical modulated amplitude $A(t)$. One model is…