Related papers: Stationary quantum stochastic processes from the c…
We study several problems related to properties of non-negative matrices that arise at the boundary between quantum and classical probabilistic computation. Our results are twofold. First, we identify a large class of quantum Hamiltonians…
$M_n(\mathbb{C})$ denotes the set of $n$ by $n$ complex matrices. Consider continuous time quantum semigroups $\mathcal{P}_t= e^{t\, \mathcal{L}}$, $t \geq 0$, where $\mathcal{L}:M_n(\mathbb{C}) \to M_n(\mathbb{C})$ is the infinitesimal…
In this lecture we present a brief outline of boson Fock space stochastic calculus based on the creation, conservation and annihilation operators of free field theory, as given in the 1984 paper of Hudson and Parthasarathy. We show how a…
Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular…
We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme…
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…
In this paper, Stieltjes electrostatic model and quantum Hamilton Jacobi formalism is analogous to each other is shown. This analogy allows, the bound state problem to mimics as $n$ unit moving imaginary charges $i\hbar$, which are placed…
A noncommutative *-algebra that generalizes the canonical commutation relations and that is covariant under the quantum groups SOq(3) or SOq(1,3) is introduced. The generating elements of this algebra are hermitean and can be identified…
In this paper we provide a systematic way of producing representations of cohomological, K-theoretical and categorified Hall algebras, and study the output of our construction in several cases. We thus recover and categorify in a unified…
We derive a model of quantum-classical hybrids for a simplified model of quantum electrodynamics in the framework of the stochastic variational method. In this model, charged particle trajectories are affected by the interaction with…
We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…
In this paper, we investigate decoherence of Knill, Laflamme, and Milburn's nonlinear sign-shift gate that is implemented with the Jaynes-Cummings model. Introducing a stochastic variable as an external electric field, we let it couple with…
We present a new perturbation theory for quantum mechanical energy eigenstates when the potential equals the sum of two localized, but not necessarily weak potentials $V_{1}(\vec{r})$ and $V_{2}(\vec{r})$, with the distance $L$ between the…
We consider a Volterra convolution equation in $\mathbb{R}^d$ perturbed with an additive fractional Brownian motion of Riemann-Liouville type with Hurst parameter $H\in (0,1)$. We show that its solution solves a stochastic partial…
We provide a new perturbation theorem for substochastic semigroups on abstract AL spaces extending Kato's perturbation theorem to non-densely defined operators. We show how it can be applied to piecewise deterministic Markov processes and…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary non-exponential distribution of the residence times, is developed. The formally exact expression…
We discuss Hilbert space-valued stochastic differential equations associated with the heat semi-groups of the standard model of non-relativistic quantum electrodynamics and of corresponding fiber Hamiltonians for translation invariant…