Related papers: Reaction-Diffusion Processes, Critical Dynamics an…
We show that the master equation governing the dynamics of simple diffusion and certain chemical reaction processes in one dimension give time evolution operators (Hamiltonians) which are realizations of Hecke algebras. In the case of…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between the…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
One-dimensional reaction-diffusion systems are mapped through a similarity transformation onto integrable (and a priori non-stochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
We present a nonlinear stochastic Schroedinger equation for pure states describing non-Markovian diffusion of quantum trajectories. It provides an unravelling of the evolution of a quantum system coupled to a finite or infinite number of…
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient…
We consider the quantum and classical Liouville dynamics of a non-integrable model of two coupled spins. Initially localised quantum states spread exponentially to the system dimension when the classical dynamics are chaotic. The long-time…
In this paper we introduce a new approach to the diffusive limit of the weakly random Schrodinger equation, first studied by L. Erdos, M. Salmhofer, and H.T. Yau. Our approach is based on a wavepacket decomposition of the evolution…
The essentials of quantum theory, the Schr\"odinger equation and the Planck constant, are derived using classical statistical mechanics within the non-local Machan model. The appearance of complex wave function is connected with the…
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and…
Since the advent of quantum mechanics, classical probability interpretations have faced significant challenges. A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of…
The emergence of diffusion is one of the deepest physical phenomena observed in many-body interacting, chaotic systems. But establishing rigorously that correlation functions, say of the spin, expand diffusively, remains one of the most…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour…
We use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system exhibiting chaotic behavior in the classical limit. The spin coherent states are employed to define a…