On the quantum motion of a generalized time-dependent forced harmonic oscillator

In this work, we use linear invariants and the dynamical invariant method to obtain exact solutions of the Schrödinger equation for the generalized time-dependent forced harmonic oscillator in terms of solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations between coordinate and momentum. It is shown that the width of the Gaussian packet, fluctuations and correlations do not depend on the external force. As a particular case, we consider the forced Caldirola-Kanai oscillator.     

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.     

1-D harmonic oscillator in MONDified inertia

In this paper we study the dynamics of a harmonic oscillator with laws of motion prescribed by MOND (Modified Newtonian Dynamics) in its modified inertia formulation. A differential equation for a 1D harmonic oscillator is obtained and several features of its solution are analyzed. Particular attention is given to the deep MOND limit regime, where the equations of motion are significantly different from the Newtonian one.     

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.     

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...     

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.     

Hausdorff dimension for the quantum harmonic oscillator

We show that the measured path of a nonrelativistic quantum particle in a harmonic oscillator potential is a fractal curve with Hausdorff dimension equal to two.     

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.     

Phase-space treatment of the driven quantum harmonic oscillator

A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.     

On the moment of inertia of a proto neutron star

The influences of σ* and Φ mesons,temperature and coupling constants of nucleons on the moment of inertia of the proto neutron star(PNS) are examined in the framework of relativistic mean field theory for the baryon octet {n,p,Λ,Σ+,Σ0,Σ+,Ξ-,Ξ0} system.It is found that,compared with that without considering σ* and Φ mesons,the moment of inertia decreases.It is also found that the higher the temperature,the larger the incompressibility and symmetry energy coeficient,and the larger the moment of inertia of a PNS.The influence of temperature and coupling constants of the nucleons on the moment of inertia of a PNS is larger than that of the σ* and Φ mesons.     

前身中子星转动惯量的研究

The influences of σ^＊ and Ф mesons, temperature and coupling constants of nucleons on the moment of inertia of the proto neutron star （PNS） are examined in the framework of relativistic mean field theory for the baryon octet {n, p, A, ∑^-, ∑^,∑^＋,^-, ^0} system. It is found that, compared with that without considering σ^＊ and Ф mesons, the moment of inertia decreases. It is also found that the higher the temperature, the larger the incompressibility and symmetry energy coefficient, and the larger the moment of inertia of a PNS. The influence of temperature and coupling constants of the nucleons on the moment of inertia of a PNS is larger than that of the σ^＊ and Ф mesons.     

Truncated harmonic oscillator and parasupersymmetric quantum mechanics

We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary orderp can also be rewritten in terms ofp supercharges (i.e. all of which obeyQ _i ² =0). However, the Hamiltonian cannot be expressed in a simple form in terms of thep supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, thep supercharges, thep conformal supercharges along with HamiltonianH, conformal generatorK and dilatation generatorD form a closed algebra.     

Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas

The superfluid fraction of an atomic cloud is defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. A fully quantum mechanical calculation of this moment is based on the dispersion of L_z instead of quasi-classical averages. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples. Received 30 June 2000     

量子阻尼振子的两种解析解法

应用u变换与不变量理论，求解一维量子阻尼振子，两种解法的不同仅在于交换了u变换与相因子的顺序。     

Measuring nonlinear functionals of quantum harmonic oscillator states

Using only linear interactions and a local parity measurement we show how entanglement can be detected between two harmonic oscillators. The scheme generalizes to measure both linear and nonlinear functionals of an arbitrary oscillator state. This leads to many applications including purity tests, eigenvalue estimation, entropy, and distance measures--all without the need for nonlinear interactions or complete state reconstruction. Remarkably, experimental realization of the proposed scheme is already within the reach of current technology with linear optics.     

A no-go result for the quantum damped harmonic oscillator

In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.     

Limiting distribution of periodic position measurements of a quantum harmonic oscillator

We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the number of measurements tends to infinity. We derive the expression for the limiting position distribution and validate it with numerical simulation.     

Deformed quantum harmonic oscillator with diffusion and dissipation

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 equation and of equations of motion for observables depend on the deformation function. The steady-state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.