Related papers: Ermakov equations in quantum mechanics
The features for the unsteady process of thermal equilibration ("the fast motions") in a one-dimensional harmonic crystal lying in a viscous environment (e.g., a gas) are under investigation. It is assumed that initially the displacements…
We discuss Einstein-Klein-Gordon system in an environment of an infinite number of scalar fields leading to an external thermal noise. In the lowest order of metric and field perturbations the quadratic fluctuations consist of a sum of…
For the electromagnetic interaction of two particles the relativistic quantum mechanics equations are proposed. These equations are solved for the case when one particle has a small mass and moves freely. The initial wave functions are…
The theory of cosmological perturbations is extended to spacetimes displaying isotropic expansion but anisotropic curvature. The perturbed Einstein equation and Boltzmann equations for massless and massive particles are derived in a general…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
Different quantum Langevin equations obtained by coupling a particle to a field are examined. Instabilities or violations of causality affect the motion of a point charge linearly coupled to the electromagnetic field. In contrast, coupling…
An atom, coupled linearly to an environment, is considered in a harmonic approximation in thermal equilibrium inside a cavity. The environment is modeled by an infinite set of harmonic oscillators. We employ the notion of dressed states to…
In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles.…
In the present paper we study the entanglement properties of thermal (a.k.a. Gibbs) states of quantum harmonic oscillator systems as functions of the Hamiltonian and the temperature. We prove the physical intuition that at sufficiently high…
We quantify the total, quantum, and classical correlations with entropic measures, and quantitatively compare these correlations in a quantum system, as exemplified by a Heisenberg dimer which is subjected to the change of environmental…
The function exp(iwt) describes an oscillating motion. Energy of the oscillator is proportional to the square of w. exp(iwt) is the solution of a differential equation. We have replaced this differential equation by the corresponding…
Many physical, chemical and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally…
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
The dynamics of a pair of coupled harmonic oscillators in separate or common thermal environments is studied, focusing on different indicators of quantumness, such as entanglement, twin oscillators correlations and quantum discord. We…
We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising…
Asymptotical formulas for the photon distribution function of a quantum oscillator with time-dependent frequency and damping coefficients, interacting with a thermal reservoir, are derived in the case of a large mean number of quanta.…
The model quantum system of fermions in a one dimensional harmonic oscillator potential is investigated by a molecular dynamics method at constant temperature. Although in quantum mechanics the equipartition theorem cannot be used like in…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium…
Heat fluctuations of a harmonic oscillator in contact with a thermostat and driven out of equilibrium by an external deterministic force are studied experimentally and theoretically within the context of Fluctuation Theorems. We consider…