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When driven by a potential bias between two finite reservoirs, the particle current across a quantum system evolves from an initial loading through a coherent, followed by a metastable phase, and ultimately fades away upon equilibration. We…
A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state $|\Psi_0>$ and the particle-bath interaction operator,…
The purpose of this paper is to present a quantum statistical theory of 2-dimensional vortex gas based on the generalized Hamiltonian dynamics recently developed. The quantized spectrum is evaluated for a pair of vortex on the basis of the…
Stochastic quantisation is applied to the problem of calculating real-time evolution on a Minkowskian space-time lattice. We employ optimized updating using reweighting, or gauge fixing, respectively. These procedures do not affect the…
We study the dynamics of condensation for a stochastic continuous mass transport process defined on a one-dimensional lattice. Specifically we introduce three different variations of the truncated random average process. We generalize…
We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent's dynamics can spend finite time both in the interior of the edges and at the vertices. The…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
We investigate bias-driven non-equilibrium quantum phase transitions in a paradigmatic quantum-transport setup: an interacting quantum dot coupled to non-interacting metallic leads. Using the Random Phase Approximation, which is exact in…
We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition…
We investigate theoretically the dynamics of squeezed state generation in nonlinear systems possessing a transition from regular to chaotic dynamics in the limit of a large number of photons. As an example, the model of a kicked Kerr…
In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
By studying a modified (unbiased) quantum multibaker map, we were able to obtain a {\em finite} asymptotic quantum current without a classical analogue. This result suggests a general method for the design of {\em purely} quantum ratchets,…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how…
We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady-state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about…
We consider particle transport under the influence of time-varying driving forces, where fluctuation relations connect the statistics of pairs of time reversed evolutions of physical observables. In many "mesoscopic" transport processes,…
The quantum adiabatic theorem ensures that a slowly changing system, initially prepared in its ground state, will evolve to its final ground state with arbitrary precision. As a first result this thesis extends the original theorem to…
Stochastic mechanics (SM), as proposed by Edward Nelson and others in the 20th century, aims to reconstruct quantum mechanics (QM) from a more fundamental theory of classical point particles interacting with a classical-like ether, where…
We present generalized adiabatic theorems for closed and open quantum systems that can be applied to slow modulations of rapidly varying fields, such as oscillatory fields that occur in optical experiments and light induced processes. The…