相关论文: New classical brackets for dissipative systems
A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…
The problem of the initial conditions for the oscillator model of quantum dissipative systems is studied. It is argued that, even in the classical case, the hypothesis that the environment is in thermal equilibrium implies a statistical…
We discuss the well known Einstein and the Kubo Fluctuation Dissipation Relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multi-variate linear Langevin model, which…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
The classical binomial process has been studied by \citet{jakeman} (and the references therein) and has been used to characterize a series of radiation states in quantum optics. In particular, he studied a classical birth-death process…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter extensive efforts have been made but…
Self-oscillatory and self-rotatory process driven by non-conservative forces have usually been treated as applications of the concepts of Hopf bifurcation and limit cycle in the theory of differential equations, or as instability problems…
The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the…
The Riccati equation method is used to establish a new stability criteria for linear systems of ordinary differential equations. Two examples are presented in which the obtained result is compared with the results obtained by the Lyapunov…
In general relativity, it is difficult to localise observables such as energy, angular momentum, or centre of mass in a bounded region. The difficulty is that there is dissipation. A self-gravitating system, confined by its own gravity to a…
The Generalized Langevin Equation (GLE) can be derived from a particle-bath Hamiltonian, in both classical and quantum dynamics, and provides a route to the (both Markovian and non-Markovian) fluctuation-dissipation theorem (FDT). All…
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A non-covariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically,…
A conservative Newton system (d/dt)^2 q = -grad V(q) in R^n is called separable when the Hamilton--Jacobi equation for the natural Hamiltonian H = (1/2) p^2 + V(q) can be solved through separation of variables in some curvilinear…
A large class of classical dynamical systems with an external rapidly oscillating driving action is considered and the effective Hamiltonian-like equations for the mean motion are obtained. The respective Liouville equation for the…
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…
The dynamics of some non-conservative and dissipative systems can be derived by calculating the first variation of an action-dependent action, according to the variational principle of Herglotz. This is directly analogous to the variational…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…
Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure…