Related papers: Positive Definite Germs of Quantum Stochastic Proc…
A characterisation of quantum stochastic positive definite (PD) exponent is given in terms of the conditional positive definiteness (CPD) of their form-generator. The pseudo-Hilbert dilation of the stochastic form-generator and the…
A characterization of the unbounded stochastic generators of quantum completely positive flows is given. This suggests the general form of quantum stochastic adapted evolutions with respect to the Wiener (diffusion), Poisson (jumps), or…
A characterisation of the quantum stochastic bounded generators of irreversible quantum state evolutions is given. This suggests the general form of quantum stochastic evolution equation with respect to the Poisson (jumps), Wiener…
A characterisation of the stochastic bounded generators of quantum irreversible Master equations is given. This suggests the general form of quantum stochastic evolution with respect to the Poisson (jumps), Wiener (diffusion) or general…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…
With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of…
A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…
We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are…
We study representations of positive definite kernels $K$ in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes. Our initial results are stated for…
We establish a duality for two factorization questions, one for general positive definite (p.d) kernels $K$, and the other for Gaussian processes, say $V$. The latter notion, for Gaussian processes is stated via Ito-integration. Our…
Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a…
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…
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
A characterisation of the generators of quantum stochastic cocycles of completely positive (CP) maps is given in terms of the complete dissipativity (CD) of its form-generator. The pseudo-Hilbert dilation of the stochastic form-generator…
We discuss stochastic derivations, stochastic Hamiltonians and the flows that they generate, algebraic fluctuaion-dissipation theorems, etc., in a language common to both classical and quantum algebras. It is convenient to define distinct…
The paper shortly presents the role of Stochastic Processes Theory in the present day Quantum Theory, and the relation to Operational Quantum Physics. The dynamics of an open quantum system is studied on a usual example from Quantum Optics,…
In this work we introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective light-matter interactions and open…
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit…