相关论文: An extended liouville equation for variable partic…

An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need…

Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…

We consider the quantum and classical Liouville dynamics of a non-integrable model of two coupled spins. Initially localised quantum states spread exponentially to the system dimension when the classical dynamics are chaotic. The long-time…

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for…

Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…

We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…

We use the system-plus-reservoir approach to study the quantum dynamics of a bipartite continuous variable system (two generic particles). We present an extension of the traditional model of a bath of oscillators which is capable of…

Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…

By generalizing Bogolyubov's reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained…

Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…

Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that…

The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…

We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently…

The aim of this paper is to derive macroscopic equations for processes on large co-evolving networks, examples being opinion polarization with the emergence of filter bubbles or other social processes such as norm development. This leads to…

This work is an extension of the study into statistical mechanics of the early Universe that has been the subject in prior works of the author, the principal approach being the density matrix deformation. In the work it is demonstrated that…

In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.

Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…

We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…

Small perturbation of the Liouville equation under smooth initial data is considered. Asymptotic solution which is available for a long time interval is constructed by the two scale method.

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…