Related papers: Quantum stochastic cocycles and completely bounded…
We compute the spectrum for a class of quantum Markov semigroups describing systems of $N$ particle interacting through a binary collision mechanism. These quantum Markov semgroups are associated to a novel kind of quantum random walk on…
A structure of generator of a quantum dynamical semigroup for the dynamics of a test particle interacting through collisions with the environment is considered, which has been obtained from a microphysical model. The related master-equation…
We find the structure of generators of norm continuous quantum Markov semigroups on B(h) that are symmetric with respect to the scalar product tr(\rho^{1/2}x\rho^{1/2}y) induced by a faithful normal invariant state invariant state \rho and…
The aim of this paper is twofold. On one hand, generalizing some recent results obtained in the quaternionic setting, but using simpler techniques, we prove the generation theorems for semigroups in Banach spaces whose set of scalars…
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…
In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. In this article we define the class of pair block diagonal…
The problem of constructing a consistent quantum-classical hybrid dynamics is afforded in the case of a quantum component in a separable Hilbert space and a continuous, finite-dimensional classical component. In the Markovian case, the…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
Two new approaches to the infinitesimal characterisation of quantum stochastic cocycles are reviewed. The first concerns mapping cocycles on an operator space and demonstrates the role of H\"older continuity; the second concerns contraction…
Non-Markovian quantum state diffusion provides a wavefunction-based framework for modeling open quantum systems. In this work, we introduce a novel machine learning approach based on an operator construction algorithm. This algorithm…
In this article we reconsider a version of quantum trajectory theory based on the stochastic Schr\"odinger equation with stochastic coefficients, which was mathematically introduced in the '90s, and we develop it in order to describe the…
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…
With the increasing crossover between quantum information and machine learning, quantum simulation of neural networks has drawn unprecedentedly strong attention, especially for the simulation of associative memory in Hopfield neural…
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators in the space of functions on a Hilbert space which are square integrable with respect to…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal…
A simple connection between the universal $R$ matrix of $U_q(sl(2))$ (for spins $\demi$ and $J$) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an…
The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent…
Quantum dynamical time-evolution of bosonic fields is shown to be equivalent to a stochastic trajectory in space-time, corresponding to samples of a statistical mechanical steady-state in a higher dimensional quasi-time. This is proved…
We construct a class of quantum stochastic models of reservoir driven many-particle systems that are the natural counterparts of certain extensively studied classical ones, which have been shown to exhibit good hydrodynamical behaviour. Our…