Related papers: Thermalization of Strongly Disordered Nonlinear Ch…
The thermodynamics of the discrete nonlinear Schr\"odinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a…
We present a detailed account of a first-order localization transition in the Discrete Nonlinear Schr\"odinger Equation, where the localized phase is associated to the high energy region in parameter space. We show that, due to ensemble…
We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion for plane-wave solutions. We also find…
Suitable Langevin thermostats are introduced which are able to control both the temperature and the chemical potential of a one-dimensional lattice of nonlinear Schr\"odinger oscillators. The resulting non-equilibrium stationary states are…
The idea of a thermalized non-equilibrated state of matter offers a conceptually new understanding of the strong angular asymmetry. In this compact review we present some clarifications, corrections and further developments of the approach,…
We consider the problem of short-term prediction of rare, extreme water waves in unidirectional fields, a critical topic for ocean structures and naval operations. One possible mechanism for the occurrence of such rare, unusually-intense…
We describe a Peierls dimerization which occurs in ferromagnetic spin chains at finite temperature, within the modified spin-wave theory. Usual spin-wave theory is modified by introducing a Lagrange multiplier which enforces a nonmagnetic…
Treating the nonlinear term of the Gross-Pitaevskii nonlinear Schrodinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem one obtains a Rayleigh-Schrodinger power series. This power series is proved to be…
The dynamics in a nonlinear Schrodinger chain in an homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster…
Thermalization in isolated quantum systems is governed by the eigenstate thermalization hypothesis, while strong disorder can induce its breakdown via many-body localization. Here we show that disorder can also generate a narrow band of…
We study the effect of disorder in strongly interacting small atomic chains. Using the Kotliar- Ruckenstein slave-boson approach we diagonalize the Hamiltonian via scattering matrix theory. We numerically solve the Kondo transmission and…
A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we…
In this paper we obtain a stabilization result for the Schr\"odinger equation under generic assumptions on the potential. Then we consider the Schr\"odinger equation with a potential which has a random time-dependent amplitude. We show that…
Localization marks the breakdown of thermalization in subregions of quantum many-body systems in the presence of sufficiently large disorder. In this paper, we use numerical techniques to study thermalization and localization in a many-body…
We study the emergence over time of a universal, uniform distribution of quantum states supported on a finite subsystem, induced by projectively measuring the rest of the system. Dubbed deep thermalization, this phenomenon represents a form…
We consider a chain of one-dimensional dipole moments connected to two thermal baths with different temperatures. The system is in nonequilibrium steady state and heat flows through it. Assuming that fluctuation of the dipole moment is a…
We show that the one dimensional discrete nonlinear Schr\"odinger chain (DNLS) at finite temperature has three different dynamical regimes (ultra-low, low and high temperature regimes). This has been established via (i) one point…
The purpose of this work is to evidence a pathological set of initial data for which the regularized solutions by convolution experience a norm-inflation mechanism, in arbitrarily short time. The result is in the spirit of the construction…
In this paper we consider the nonlinear one-dimensional time-dependent Schroedinger equation with a periodic potential and a local perturbation. In the limit of large periodic potential the time behavior of the wavefunction can be…
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…