Related papers: On Stochastic Generators of Positive Definite Expo…
In the paper, the transition probability density of isotropic $\alpha$-stable stochastic process in a finite dimensional Euclidean space is considered. The results of applying pseudo differential operators with respect spatial variables to…
The purpose of this note is to propose a new approach for the probabilistic interpretation of Hamilton-Jacobi-Bellman equations associated with stochastic recursive optimal control problems, utilizing the representation theorem for…
Construct a random set by independently selecting each finite subset of the integers with some probability depending on the set up to translations and taking the union of the selected sets. We show that when the only sets selected with…
The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of…
We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard GKLS generator. These…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
We consider a self-decimated generator of pseudorandom numbers and examine the preperiod $\lambda$ and the period $\mu$ of its state sequence. We obtain the expectations and variances of $\lambda$ and $\mu$ for the case when decimation…
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…
In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, $2$- and $3$-isometries…
We use the It\^o stochastic calculus to give a simple derivation of the Lindblad form for the generator of a completely positive density matrix evolution, by specialization from the corresponding global form for a completely positive map.…
We propose a hybrid quantum-classical approach to model continuous classical probability distributions using a variational quantum circuit. The architecture of the variational circuit consists of two parts: a quantum circuit employed to…
We develop a fundamental framework for the quantum mechanics of stochastic systems (QMSS), showing that classical discrete stochastic processes emerge naturally as perturbations of the quantum harmonic oscillator (QHO). By constructing…
In the present work the electroproduction for diffractive $\rho$ and $\phi$ mesons by considering AdS/QCD correspondence and Color Glass Condensate (CGC) approximation are studied with respect to the associated dipole cross section, whose…
The pseudo scalar form factor, which represents the pseudo scalar quark density distribution due to finite quark masses on the nucleon, is shown to manifest itself with the induced pseudo scalar form factor in the $L_0^+$ amplitude for the…
The supergenerator of superparamagnetic system quantum evolution is investigated in discrete orientation model (DOM). It is shown that the generator is J-self-adjoint one at the case of potential drift field agreed upon magnetic anisotropy…
A completely positive master equation describing quantum dissipation for a Brownian particle is derived starting from microphysical collisions, exploiting a recently introduced approach to subdynamics of a macrosystem. The obtained equation…
In this paper, a stochastic Hamiltonian formulation (SHF) is proposed and applied to dissipative particle dynamics (DPD) simulations. As an extension of Hamiltonian dynamics to stochastic dissipative systems, the SHF provides necessary…
Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose…
The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description…
Although diffusion models have successfully extended to function-valued data, stochastic interpolants -- which offer a flexible way to bridge arbitrary distributions -- remain limited to finite-dimensional settings. This work bridges this…