An analytic formula of one-dimensional Franck-Condon factors for linear harmonic oscillators

With the aid of an addition theorem for harmonic oscillator wave functions, the Franck-Condon factors between two displaced linear oscillators with unequal vibrational frequencies are transformed into an analytic form which is programmable for numerical evaluations. Franck-Condon factors for the A¹Σ_u⁺-X¹Σ_g⁺ system and the B¹Π_u-X¹Σ_g⁺ system of ⁷Li₂ are calculated via this analytic formula.     

关于线性阻尼振子第一积分的研究

通过引入一维线性阻尼振子基本积分来构造其他第一积分, 包括不含时的积分. 将这种方法推广到多维情形, 构造二维和n维线性阻尼振子不同形式的第一积分; 证明不同类型的二维线性阻尼振子都存在三个独立的不含时的第一积分, n维线性阻尼振子存在2n-1个独立的不含时的第一积分. 利用变量变换将线性阻尼振子的第一积分变换成简谐振子形式的第一积分. 关键词： 线性阻尼振子 第一积分 基本积分 简谐振子     

On the interaction between a charged drop and an external acoustic field

An interaction between capillary oscillations of a charged drop and an external acoustic field is investigated under conditions in which nonlinear components of the acoustic pressure on the drop surface may be neglected. It is shown that equations describing the temporal evolution of modes of the capillary waves in this case may be either the Mathieu-Hill equations or ordinary inhomogeneous equations of the second order describing forced oscillations. In both cases, the drop instability (of a parametric or resonance type) may result in its disintegration due to deformation caused by the acoustic field at its own drop charge, subcritical in the sense of the Rayleigh criterion.     

On nonlinear resonant four-mode interaction between capillary vibrations of a charged drop

Energy transfer from higher modes of capillary vibrations of an incompressible liquid charged drop to the lowest fundamental mode under four-mode resonance is studied. The resonance appears when the problem of nonlinear axisymmetric capillary vibration of a drop is solved in the third-order approximation in amplitude of the multimode initial deformation of the equilibrium shape of the drop. Although the resonant interaction mentioned above builds up the fundamental mode even in the first order of smallness, its amplitude turns out to be comparable to a quadratic (in small parameter) correction arising from nonresonant nonlinear interaction, since the associated numerical coefficients are small.     

电解液中带电平板与带电胶体球之间的有效相互作用

用Poisson-Boltzmann方程，计算了在具有单价离子的电解质溶液中均匀地带同号电荷的两无限大平行平板间的有效相互作用，以及用Derjaguin近似研究了边界对带电胶体球的影响.不考虑微离子相互作用时，两带电平板只有排斥作用，而且边界条件(面电荷密度)的改变对它们之间的有效相互作用影响不大.带电平板与带电胶体球之间的相互作用也有类似规律. 关键词： Poisson-Boltzmann方程 Derjaguin近似 双电层 渗透压     

两块带电导体的相互作用能

导出了两块导体在给定电量,给定电势时和一块给定电量,另一块给定电势时,3种情况下的相互作用能公式,并从电磁场能量和导体有量两个角度来表示互作用能公式,指出带电导体之间的互作用能一般由电势能,导体带电状态改变做功和外电源提供的能量这3部分构成。     

Quantum action-angle variables for harmonic oscillators

The well-known difficulties of defining a phase operator of an oscillator, caused by the lower bound on the number operator, is overcome by enlarging the physical Hilbert space by means of a spin-like, two-valued quantum number. On the enlarged space a phase representation exists on which trigonometric functions of the phase are numbers, and the “number of quanta” is a differential operator. Physical results are recovered by projection on the “upper components.” Coherent states, indeterminacy relations, as well as generalizations to other Hamiltonians, including the quantum analog of the quasi-periodic case, are discussed.     

Superbroadcasting of harmonic oscillators mixed states

We consider the problem of broadcasting quantum information encoded in the displacement parameter for an harmonic oscillator, from N to M > N copies of a thermal state. We show the Weyl-Heisenberg covariant broadcasting map that optimally reduces the thermal photon number, and we prove that it minimizes the noise in conjugate quadratures at the output for general input states. We find that from two input copies broadcasting is feasible, with the possibility of simultaneous purification (superbroadcasting). The text was submitted by the authors in English.     

Work fluctuation theorems for harmonic oscillators

The work fluctuations of an oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally and theoretically within the context of fluctuation theorems. The oscillator dynamics is modeled by a second order Langevin equation. Both the transient and stationary state fluctuation theorems hold and the finite time corrections are very different from those of a first order Langevin equation. The periodic forcing of the oscillator is also studied; it presents new and unexpected short time convergences. Analytical expressions are given in all cases.     

On the absence of charge symmetry in electrostatic interaction between charged drops and hard particles

It is shown that the analytical expressions for the energy and force of electrostatic interaction between charged conducting particles (drops), a point charge, and a finite-size particle, as well as between a particle (a drop or a point charge) and a conducting plane, are asymmetric with respect to the sign of one of the charges. This is because the polarization interaction is always attractive irrespective of the signs of interacting particles. The absence of this symmetry leads to the self-constriction of charged aerodispersed systems containing a condensed phase, for example, plasma or liquid-droplet systems.     

Optical RKKY interaction between charged semiconductor quantum dots

We show how a spin interaction between electrons localized in neighboring quantum dots can be induced and controlled optically. The coupling is generated via virtual excitation of delocalized excitons and provides an efficient coherent control of the spins. This quantum manipulation can be realized in the adiabatic limit and is robust against decoherence by spontaneous emission. Applications to the realization of quantum gates, scalable quantum computers, and to the control of magnetization in an array of charged dots are proposed.     

Inversion in harmonic noise driven bistable oscillators

We consider the dynamics in a asymmetrical bistable oscillator driven externally by a noisy harmonic oscillator. The basic for our approach is the energy dynamics in each well of the oscillator in the low friction limit. We discuss the possibility of energy inversion states generated by harmonic noise and show this effect by simulations.     

Properties of r-centroids for equal-frequency harmonic oscillators

Basic properties of r-centroids are discussed in the model of harmonic oscillators with equal frequencies and different oscillation centers (r_e values). In this approximation, r-centroids are found to be given by a very simple formula. They are characteristic of each Δυ=constant sequence and change regularly from one sequence to the next. The corresponding change in r-centroid is inversely proportional to the distance between the oscillation centers. The important special case of two abutting levels is studied and it is found that the r-centroid of the two levels is their common turning point. The conditions under which r-centroids can be considered as mean internuclear distances are specified. Applications of these simple results to molecular vibronic interactions are discussed. It is shown that the r-centroid of degenerate perturbing vibronic levels is located at the crossing of the corresponding electronic potential curves, so that, contrary to transition moments, the variation of electronic perturbation parameters with the internuclear separation R cannot be accurately deduced from only experimental data.     

Exact wave functions for generalized harmonic oscillators

We transform the time-dependent Schrödinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time evolution of exact wave functions of generalized harmonic oscillators is determined in terms of the solutions of certain Ermakov and Riccatitype systems. In addition, we show that the classical Arnold transform is naturally connected with Ehrenfest’s theorem for generalized harmonic oscillators.     

Stationary entanglement between two nanomechanical oscillators induced by Coulomb interaction

We propose a scheme for entangling two nanomechanical oscillators by Coulomb interaction in an optomechanical system. We find that the steady-state entanglement of two charged nanomechanical oscillators can be obtained when the coupling between them is stronger than a critical value which relies on the detuning. Remarkably, the degree of entanglement can be controlled by the Coulomb interaction and the frequencies of the two charged oscillators.     

Bound states of two-dimensional relativistic harmonic oscillators

We give the exact normalized bound state wavefunctions and energy expressions of the Klein－Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.     

关于谐振子第一积分的研究

提出一维谐振子基本积分的概念, 并利用它们构造其他积分. 将上述概念和方法推广到多维谐振子, 利用直接构造法证明不同类型的二维谐振子都存在三个与时间无关的独立的第一积分, n维谐振子系统存在2n-1个与时间无关的独立的第一积分. 讨论了分振动频率比为有理数和无理数的二维非对称谐振子的特征. 关键词： 谐振子 第一积分 基本积分 不含时积分     

Path integral for the relativistic particle and harmonic oscillators

The action for a massive particle in special relativity can be expressed as the invariant proper length between the end points. In principle, one should be able to construct the quantum theory for such a system by the path integral approach using this action. On the other hand, it is well known that the dynamics of a free, relativistic, spinless massive particle is best described by a scalar field which is equivalent to an infinite number of harmonic oscillators. We clarify the connection between these two—apparently dissimilar—approaches by obtaining the Green function for the system of oscillators from that of the relativistic particle. This is achieved through defining the path integral for a relativistic particle rigorously by two separate approaches. This analysis also shows a connection between square root Lagrangians and the system of harmonic oscillators which is likely to be of value in more general context.     

Effect of geometrical confinement on the interaction between charged colloidal suspensions

The effective interaction between charged colloidal particles confined between two planar like-charged walls is investigated using computer simulations of the primitive model describing asymmetric electrolytes. In detail, we calculate the effective force acting onto a single macroion and onto a macroion pair in the presence of slitlike confinement. For moderate Coulomb coupling, we find that this force is repulsive. Under strong-coupling conditions, however, the sign of the force depends on the distance to the plates and on the interparticle distance. In particular, the particle-plate interaction becomes strongly attractive for small distances which may explain the occurrence of colloidal crystalline layers near the plates observed in recent experiments.