Related papers: Discrete time q-TASEPs
We consider Shannon entropy, Fisher information, R\'enyi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang…
We derive quantum evolution equations for the dynamics of dilute condensed Bose gases. The approach contains, at different orders of approximation, for cases close to equilibrium, the Gross Pitaevskii equation and the first order Hartree…
First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analyzed. In a companion paper, we showed how the positive P representation can be applied to these problems using…
In this paper, inspired by Tsallis' probability distribution based on a $q$-deformed Boltzmann factor, we stipulate a new $q$-deformed quantum dynamics by applying the inverse Wick rotation $ \beta \rightarrow i t$ to the Tsallis-deformed…
We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with a general initial condition and a deterministically moving wall in front of the particles. Using colour-position symmetry, we express the one-point…
We consider the generalized time-dependent Schr\"odinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a…
A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long range…
We analyze the stochastic thermodynamics of systems with continuous space of states. The evolution equation, the rate of entropy production, and other results are obtained by a continuous time limit of a discrete time formulation. We point…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
The engineering of new states of matter through Floquet driving has revolutionized the field of condensed matter physics. This technique enables the creation of hybrid topological states and ordered phases that are absent in normal systems.…
This paper is concerned with the decoupling of delayed linear forward-backward stochastic differential equations (D-FBSDEs), which is much more involved than the delay-free case due to the infinite dimension caused by the delay. A new…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
Driven diffusive systems have provided simple models for non-equilibrium systems with non-trivial structures. Steady state behaviour of these systems with constant boundary conditions have been studied extensively. Comparatively less work…
A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…
We consider the totally asymmetric exclusion process on a ring in discrete time with the backward-ordered sequential update and particle-dependent hopping probabilities. Using a combinatorial treatment of the Bethe ansatz, we derive the…
Designing distributed systems to have predictable performance under high load is difficult because of resource exhaustion, non-linearity, and stochastic behaviour. Timeliness, i.e., delivering results within defined time bounds, is a…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…