相关论文: Theory of the strongly-damped quantum harmonic osc…

The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and…

In this paper, we study high-dimensional nonlinear quantum harmonic oscillator equation. We show the equation admits many time quasi-periodic solutions by establishing an abstract infinite dimensional KAM theorem with multiple normal…

The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or…

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…

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature…

In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…

We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…

We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…

We consider a quantum linear oscillator coupled to a bath in equilibrium at an arbitrary temperature and then exposed to an external field arbitrary in form and strength. We then derive the reduced density operator in closed form of the…

The Morse potential is relatively closed to the harmonic oscillator quantum system. Thus, following the idea used for the latter, we study the possibility of creating entanglement using squeezed coherent states of the Morse potential as an…

In this study, we introduce a two dimensional complex harmonic oscillator potential with space and time reflection symmetries. The corresponding time independent Schr\"odinger equation yields real eigenvalues with complex eigenfunctions. We…

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.

We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…

Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive…

There are discussed the exact solution of the time--dependent Schr\"{o}dinger equation for a damped quantum oscillator subject to a periodical frequency delta--kicks describing squeezed states which are expressed in terms of Chebyshev…

The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field…

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…

A recent paper [J. Math. Phys. {\bf 59}, 082105 (2018)] constructs a Hamiltonian for the (dissipative) damped harmonic oscillator. We point out that non-Hermiticity of this Hamiltonian has been ignored to find real discrete eigenvalues…

We investigate two prototypical dissipative bosonic systems under slow driving and arbitrary system-bath coupling strength, recovering their dynamic evolution as well as the heat and work rates, and we verify that thermodynamic laws are…

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…