Related papers: W*-Dynamics of Infinite Dissipative Quantum System…
We construct a family of semimartingales that describes the behavior of a particle system with sticky-reflecting interaction. The model is a physical improvement of the Howitt-Warren flow, an infinite system of diffusion particles on the…
The spin transport in isotropic Heisenberg model in the sector with zero magnetization is generically super-diffusive. Despite that, we here demonstrate that for a specific set of domain-wall-like initial product states it can instead be…
We consider separable $C^*$-dynamical systems $(A,G,\alpha)$ for which the induced action of the group $G$ on the spectrum $\hat A$ of the $C^*$-algebra $A$ is free. We study how the representation theory of the associated crossed-product…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane…
This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of…
We examine the fluctuation theorems which traditionally have been studied for classical systems and enquire if they can be extended to the quantum domain, especially at low temperatures. The example chosen is that of a problem which has…
We study the near-equilibrium critical dynamics of the $O(3)$ nonlinear sigma model describing isotropic antiferromagnets with non-conserved order parameter reversibly coupled to the conserved total magnetization. To calculate response and…
The macroscopic fluctuation theory provides a complete hydrodynamic description of non-equilibrium classical diffusive systems. As a first step towards a diffusive theory of open quantum systems, we show how to construct a microscopic open…
A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature $T>0$. We show that for fixed, small values of the coupling constant $\lambda$, the true reduced dynamics of the system is…
The dissipative models in string theory can have more broad range of application: 1) Noncritical strings are dissipative systems in the "coupling constant" phase space. 2) Bosonic string in the affine-metric curved space is dissipative…
On the basis of qualitative theory of differential equations it is shown that dynamic system based on the system of Einstein - Klein - Gordon equations with regard to Friedman Universe has a stable center corresponding to zero values of…
We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric…
We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions…
This paper surveys the recent advances in the interactions between symbolic dynamics and C*-algebras. We explain how conjugacies and orbit equivalences of both two-sided (invertible) and one-sided (noninvertible) symbolic systems may be…
We have introduced a notion of $C^*$-symbolic dynamical system in [K. Matsumoto: Actions of symbolic dynamical systems on $C^*$-algebras, to appear in J. Reine Angew. Math.], that is a finite family of endomorphisms of a $C^*$-algebra with…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
We presents a unified and concise exposition of key topics in the mathematical theory of open quantum systems, developed within the framework of operator algebras. The manuscript consolidates and extends a series of invited articles…