Related papers: Quantum Kinetic Equations and Evolution of Many-Pa…
We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the…
We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the…
In this paper, we would like to consider the Cauchy problem for a weakly coupled system of semi linear $sigma$ evolution equations with different damping mechanisms for any $\sigma>1$, parabolic like damping and $\sigma$ evolution like…
We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…
The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…
To describe stochastic quantum processes I propose an integral equation of Volterra type which is not generally transformable to any differential one. The process is a composition of ordinary quantum evolution which admits presence of a…
A quantum-kinetic formulation of the dynamical evolution of a high-energy non-equilibrium gluon system at finite density is developed, to study the interplay between quantum fluctuations of high-momentum (hard) gluons and the low-momentum…
The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global…
In this paper, we consider the linear evolution equation $dy(t)=Ay(t)dt+Gy(t)dx(t)$, where $A$ is a closed operator, associated to a semigroup, with good smoothing effects in a Banach space $E$, $x$ is a nonsmooth path, which is…
In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local…
In this paper, we develop a quantum hydrodynamics (QHD) method for the research of the quantum evolution of a system of spinning particles. We derived the fundamental equation for charged and neutral spinning particles - the energy…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…
We review and complete the kinetic theory of spatially inhomogeneous stellar systems when collective effects (dressing of the stars by their polarization cloud) are neglected. We start from the BBGKY hierarchy issued from the Liouville…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that…
We discuss relaxation in bosonic and fermionic many-particle systems. For integrable systems, the time evolution can cause a dephasing effect, leading for finite subsystems to certain steady states. We give an explicit derivation of those…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
The quantum dynamical evolution of atomic and molecular aggregates, from their compact to their fragmented states, is parametrized by a single collective radial parameter. Treating all the remaining particle coordinates in d dimensions…
The Cauchy problem for a quasi-linear parabolic equation with a small parameter at a higher derivative is considered. The initial step-like function contains another small parameter. Formal asymptotic solutions of the problem in small…