Related papers: Damped harmonic oscillator: pure states of the bat…
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the…
We study properties of steady states (states with time-independent density operators) of systems of coupled harmonic oscillators. Formulas are derived showing how adiabatic change of the Hamiltonian transforms one steady state into another.…
The exact master equation for a harmonic oscillator coupled to a heat bath, derived recently by Hu, Paz and Zhang, is simplified by taking the weak-coupling, late-time limit. The unique time-independent solution to this simplified master…
An explicit demonstration is given of a harmonic oscillator in equilibrium approaching the equilibrium of a corresponding interacting system by coupling it to a thermal bath consisting of a continuum of harmonic oscillators.
Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath…
We present an exact analytical solution of the Hu-Paz-Zhang master equation in a precise Markovian limit for a system of two harmonically coupled harmonic oscillators interacting with a common thermal bath of harmonic oscillators. The…
We investigate the exact dynamics of the damped quantum harmonic oscillator under the (un)correlated initial conditions. The master equation is generalized to the cases of the arbitrary factorized state and/or Gaussian state. We show that…
We consider a harmonic oscillator under periodic driving and coupled to two harmonic-oscillator heat baths at different temperatures. We use the thermofield transformation with chain mapping for this setup, which allows us to study the…
We study the dissipative dynamics of a harmonic oscillator which couples linearly through its position and its momentum to two independent heat baths at the same temperature. We argue that this model describes a large spin in a ferromagnet.…
Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of non-interacting oscillators. We follow a non-perturbative approach, proposed earlier by us for the free Brownian particle. The…
Quantum dynamics of a damped harmonic oscillator has been extensively studied since the sixties of the last century. Here, with a distinct tool termed the ``group-theoretical characteristic function" (GCF), we investigate analytically how a…
We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four…
In the following, we study the dissipative time-evolution of a quantum chain consisting of three coupled harmonic oscillators, the first and third of which weakly interact quadratically with two independent thermal baths in equilibrium at…
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of…
The dissipative harmonic oscillator has two representations. In the first representation the central oscillator couples with its position to an oscillator bath. In the second one it couples with its momentum to the bath. Both…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master…
We study the dissipative properties of a harmonic oscillator subject to two independent heat baths, one of which couples to its position and the other one to its momentum. This model describes a large spin impurity in a ferromagnet. We find…
The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory, for the case when the…
In this work, we calculate the exact asymptotic quantum correlations between two interacting non-resonant harmonic oscillators in a common Ohmic bath. We derive \emph{analytical formulas} for the covariances, fully describing any Gaussian…