Related papers: Equilibration problem for the generalized Langevin…
We propose a generalized parity-time ($\mathcal{PT}$) -symmetric Li\'enard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of…
In this work, we analyze the relaxation of a classical spin interacting with a heat bath, starting from the fully dynamical Hamiltonian description. An analogous problem in the framework of generalized Langevin equation (GLE) with anomalous…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…
We initially prepare a quantum linear oscillator weakly coupled to a bath in equilibrium at an arbitrary temperature. We disturb this system by varying a Hamiltonian parameter of the coupled oscillator, namely, either its spring constant or…
We show that limit cycle systems in Langevin bath exhibit uncertainty in observables that define the limit-cycle plane, and maintain a positive lower bound. The uncertainty-bound depends on the parameters that determine the shape and…
System of the quantum Langevin equations for two quantum coupling oscillators within independent heat baths of quantum oscillators are obtained using a model Hamiltonian and corresponding Heisenberg equations of motion. Expressions for mean…
In statistical mechanics, any quantum system in equilibrium with its weakly coupled reservoir is described by a canonical state at the same temperature as the reservoir. Here, by studying the equilibration dynamics of a harmonic oscillator…
Systems governed by a multivariate Langevin equation featuring an exact potential exhibit straightforward dynamics but are often difficult to recognize because, after a general coordinate change, the gradient flow becomes obscured by the…
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a…
The application of quantum Langevin equations for the study of non-equilibrium relaxations is illustrated in the exactly solved quantum spherical model. Tutorial sections on the physical background of non-markovian quantum noise, the…
Baths produce friction and random forcing on particles suspended in them. The relation between noise and friction in (generalized) Langevin equations is usually referred to as the second fluctuation-dissipation theorem. We show what is the…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to a large number of environmental micro-oscillating particles. Then, the Langevin equation is obtained for the…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…
A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal…
We study a harmonic system coupled to chain of first neighbor interacting oscillators. After deriving the exact dynamics of the system, we prove that one can effectively describe the exact dynamics by considering a suitable shorter chain.…
The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the…
It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model…