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Passive states are special configurations of a quantum system which exhibit no energy decrement at the end of an arbitrary cyclic driving of the model Hamiltonian. When applied to an increasing number of copies of the initial density…
Here we show that noisy coupling can lead to diffusive lossless energy transfer between individual quantum systems retaining a quantum character leading to entangled stationary states. Coherence might flow diffusively while being summarily…
We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether…
As the fundamental quantum mechanical theory predicts, it is believed that electronic states can be bound only to potential wells and not to potential barriers in any dimension and their energies should be below the background potential.…
We study the Sinai model for the diffusion of a particle in a one dimensional quenched random energy landscape. We consider the particular case of discrete energy landscapes made of random +/- 1 jumps on the semi infinite line Z+ with a…
The minimum energy path (MEP) is the most probable transition path that connects two equilibrium states of a potential energy landscape. It has been widely used to study transition mechanisms as well as transition rates in the fields of…
We investigate the ground-state energy and spin of disordered quantum dots using spin-density-functional theory. Fluctuations of addition energies (Coulomb-blockade peak spacings) do not scale with average addition energy but remain…
We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that…
We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries, in order to investigate the so-called dynamical transition. The latter phenomenon appears as a singularity in the relaxation…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…
How much free energy is irreversibly lost during a thermodynamic process? For deterministic protocols, lower bounds on energy dissipation arise from the thermodynamic friction associated with pushing a system out of equilibrium in finite…
We address how the interplay between the finite availability and carrying capacity of particles at different parts of a spatially extended system can control the steady state currents and density profiles in the one-dimensional…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
We discuss the interplay between a slow continuous drift of temperature, which induces continuous phase separation, and the non-linear diffusion term in the $\phi^4$-model for phase separation of a binary mixture. This leads to a bound for…
We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an…
It was shown that an infinite sequence of improving non-increasing upper bounds to the ground state energy (GSE) of a slow-moving piezoeletric polaron can be devised.
We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an interface orthogonal to the cylinder axis. Let $L$ be…
Mobility edge (ME), representing the critical energy that distinguishes between extended and localized states, is a key concept in understanding the transition between extended (metallic) and localized (insulating) states in disordered and…