量子谐振子与经典谐振子的比较

运用广义线性量子变换的普遍理论求解了量子谐振子,同经典谐振子比较给出了量子谐振子趋近于经典极限的条件,并得出相干态是最理想的经典极限态．     

Nonlinear modes of a macroscopic quantum oscillator

We consider the Bose–Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes — a nonlinear generalisation of the (symmetric and antisymmetric) Hermite–Gauss eigenmodes of a harmonic quantum oscillator.     

Two-photon cooling of a nonlinear quantum oscillator

The cooling effects of a nonlinear quantum oscillator via its interaction with an artificial atom (qubit) are investigated. The quantum dissipations through the environmental reservoir of the nonlinear oscillator are included, taking into account the nonlinearity of the qubit–oscillator interaction. For appropriate bath temperatures and the resonator’s quality factors, we demonstrate effective cooling below the thermal background. As the photon coherence functions behave differently for even and odd photon number states, we describe a mechanism distinguishing those states. The analytical formalism developed is general and can be applied to a wide range of systems.     

Brownian motion of a quantum harmonic oscillator

The problem of describing the Brownian motion of a quantum harmonic oscillator or free particle is treated in the formalism of quantum dynamical semigroups. Certain inequalities involving the friction and diffusion coefficients and Planck's constant are derived. The nature of the quantum Langevin equation is discussed.     

Evolution of a velocity-dependent quantum forced anharmonic oscillator

The exact solution to a velocity-dependent quantum forced anharmonic oscillator is derived by using integral operators and an iteration method. The study is carried out in operational form by use of the creation and annihilation operators of the oscillator. The time development of the displacement and momentum operators of the anharmonic oscillator is given. These operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals.     

One-dimensional model of a quantum nonlinear harmonic oscillator

In this paper we study the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan. This system with position-dependent mass allows a natural quantization procedure and is shown to display shape invariance. Its energy spectrum is found by factorization. The linear harmonic oscillator appears as the λ → 0 limit of this nonlinear oscillator, whose energy spectrum and eigenfunctions are compared to the linear ones.     

Energy features of a loaded quantum anharmonic oscillator

A quantum anharmonic oscillator in the ground state has been considered under the conditions of loading with an external force. The wave functions have been calculated for different forces, and the eigenvalues of the energy of the system have been determined as a function of the load. It has been established that the zero-point energy of the oscillator varies linearly with a variation in the force (decreases under tension and increases under compression) and that the average kinetic and potential components of the energy are also characterized by linear variations.     

Hemispheroidal quantum harmonic oscillator

A deformed single-particle shell model is derived for a hemispheroidal potential well. Only the negative parity states of the Z(z) component of the wave function are allowed, so new magic numbers are obtained. The influence of a term proportional to l² in the Hamiltonian is investigated. The maximum degeneracy is reached at a superdeformed hemispheroidal prolate shape whose magic numbers are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator. This remarkable property suggests an increased stability of such a distorted shape of deposited clusters when the planar surface remains opaque.     

Al-Salam-Chihara models of quantum oscillator

Models of the quantum oscillator, based on Al-Salam-Chihara orthogonal q-polynomials, are constructed. The position and momentum operators have the continuous simple spectra, covering a finite interval. Eigenfunctions of these operators are explicitly defined. The evolution operator is an integral operator with a kernel, whose explicit form is also derived.     

Parametric instability of quantum oscillator

It is shown that the dynamic symmetry group of an oscillator with variable frequency is the line or group SL(2, R). Classical and quantum oscillators are described respectively by two-dimensional representations of this group. The conditions for the appearance of parametric resonance are investigated. For the case of periodic frequency modulation, nonspreading coherent states are constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–12, May, 1979.     

二维耦合量子谐振子的本征值和本征函数

运用广义线性量子变换理论,给出一类二维耦合量子谐振子的能量本征值、本征函数、坐标和动量算符在能量表象中的矩阵元及演化算符.     

Integrals of the motion for a nonlinear quantum oscillator

We construct and discusss explicitly time dependent integrals of the motion of non-autonomous quantum systems. Such integrals may exist even when the classical limit of the dynamics is non-integrable.     

Non-equilibrium quantum statistical mechanics of a damped harmonic oscillator

we give some general remarks on the quantization of systems where the energy operator is not conserved in time. Explicitly, we consider a damped harmonic oscillator and transform the corresponding Schrödinger-Langevin equation to the dual picture where the observables are time dependent but not the states. In this picture the time evolution will be described by a completely positive dynamical semigroup. At finite temperatures the situation is more complicated.     

Quadratic open quantum harmonic oscillator

Letters in Mathematical Physics - We study the quantum open system evolution described by a Gorini–Kossakowski–Sudarshan–Lindblad generator with creation and annihilation...     

Theory of the singular quantum oscillator

We propose a number of arguments in favor of reevaluating the theory of a quantum oscillator described by the Hamiltonian H=–d²/dx² + 2²x² + x^–2(=2m=1). We propose that functions ₊(x) which continuously reduce to even harmonic oscillator solutions in the 0 limit be taken as the even solutions of the Hamiltonian in the –1/4 < < 3/4 range. In this scheme the problem becomes truly one-dimensional such that even and odd parity energy levels alternate, whereas the usual approach leads to parity degeneracy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 85–89, October, 1989.     

Wigner dynamics of quantum semi-relativistic oscillator

The integral Wigner–Liouville equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte Carlo procedure and molecular dynamics methods. The strong influence of the relativistic effects on the time evolution of the momentum, velocity and coordinate Wigner distribution functions and the average values of quantum operators have been studied. Unexpected ‘protuberances’ in time evolution of the distribution functions were observed. Relativistic proper time dilation for oscillator have been calculated.     

On the moment of inertia of a quantum harmonic oscillator

An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.