Related papers: Classical dilations \`a la Hudson-Parthasarathy of…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
Given a finite state space E, we build a universal dilation for all possible discrete time Markov chains on E, homogeneous or not: we introduce a second system (an ``environment'') and a deterministic invertible time-homogeneous global…
We present, for the first time, the result (from 2008) that (normal, strongly continuous) Markov semigroups on $\mathscr{B}(G)$ ($G$ a separable Hilbert space) admit a Hudson-Parthasarathy dilation (that is, a dilation to a cocycle…
We consider the GNS Hilbert space $\mathcal{H}$ of a uniformly hyper-finite $C^*$- algebra and study a class of unbounded Lindbladian arises from commutators. Exploring the local structure of UHF algebra, we have shown that the associated…
We prove the existence of Hudson Parthasarathy dilation of a quantum dynamical semigroup on $B(\clh),$ which is symmetric with respect to the canonical normal trace on it.
This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
We describe an iterative approach to computing long-time semiclassical dynamics in the presence of chaos, which eliminates the need for summing over an exponentially large number of classical paths, and has good convergence properties even…
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…
This is a continuation of the study of the theory of quantum stochastic dilation of completely positive semigroups on a von Neumann or $C^*$ algebra, here with unbounded generators. The additional assumption of symmetry with respect to a…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
In this work we investigate Stinespring dilations of quantum-dynamical semigroups, which are known to exist by means of a constructive proof given by Davies in the early 70s. We show that if the semigroup describes an open system, that is,…
Hybrid classical-quantum systems are of interest in numerous fields, from quantum chemistry to quantum information science. A fully quantum effective description of them is straightforward to formulate when the classical subsystem is…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
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…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…