相关论文: Quantum stochastic convolution cocycles
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
The classical notion of L\'evy process is generalized to one that takes as its values probabilities on a first order model equipped with a commutative semigroup. This is achieved by applying a convolution product on definable probabilities…
In this paper for the first time, we construct quantum analogs starting from classical stochastic processes, by replacing random which path decisions with superpositions of all paths. This procedure typically leads to non-unitary quantum…
In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously…
A covariant generalization of a non-relativistic stochastic quantum mechanics introduced by de la Pe\~na and Cetto is formulated. The analysis is done in space-time and avoids the use of a non-covariant time evolution parameter in order to…
Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
Covariant stochastic partial (pseudo-)differential equations are studied in any dimension. In particular a large class of covariant interacting local quantum fields obeying the Morchio-Strocchi system of axioms for indefinite quantum field…
We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…
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…
Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic…
It is shown how nonlinear versions of quantum mechanics can be refolmulated in terms of a (linear) C*-algebraic theory. Then also their symmetries are described as automorphisms of the correspondong C*-algebra. The requirement of…
We continue the investigation of the Levy processes on a q-deformed full Fock space started in a previous paper. First, we show that the vacuum vector is cyclic and separating for the algebra generated by such a process. Next, we describe a…
To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…
$P$-divisibility is a central concept in both classical and quantum non-Markovian processes; in particular, it is strictly related to the notion of information backflow. When restricted to a fixed commutative algebra generated by a complete…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…