Related papers: Classical dilations \`a la Quantum Probability of …
Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…
A quantum Markov semigroup can be represented via classical diffusion processes solving a stochastic Schr\"odinger equation. In this paper we first prove that a quantum Markov semigroup is irreducible if and only if classical diffusion…
In the study of open quantum systems, one commonly describes the evolution of a system of interest through reduced dynamics, obtained by treating the environment indirectly rather than as a part of the full model. This thesis presents an…
The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…
The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such…
We study the behaviour of time evolved quantum mechanical expectation values in Lagrangian states in the limit $\hbar\to 0$ and $t\to\infty$. We show that it depends strongly on the dynamical properties of the corresponding classical…
We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…
Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…
We show that probability is locally conserved in discrete time quantum walks, corresponding to a particle evolving in discrete space and time. In particular, for a spatial structure represented by an arbitrary directed graph, and any…
A precise physical description and understanding of the classical dual content of quantum theory is necessary in many disciplines today: from concepts and interpretation to quantum technologies and computation. In this paper we investigate…
Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to…
The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…
This paper is an investigation of the class of real classical Markov processes without a birth process that will generate the Dirac equation in 1+1 dimensions. The Markov process is assumed to evolve in an extra (ordinal) time dimension.…
We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a…