Study of Certain Aspects of Anharmonic,Time-Dependent and Damped Harmonic Oscillator Systems

The present review is devoted to the study of certain aspects of anharmonic, time-dependent and damped oscillator(s) system using different theoretical techniques. A theoretical understanding of these systems is important for application in many problems in physics, mechanics and other fields. We discuss in detail the difficulties in the theoretical analysis of the problem. In particular we discuss here the regular, well-behaved perturbative solution, the large quantum number behaviour of anharmonic oscillator(s) using the technique of coherent states, exact solution of quantum anharmonic oscillators, the electromagnetic radiation emitted by a charged particle executing damped anharmonic oscillator motion using Krylov-Bogoliubov approximation method, use of invariants to obtain solution and coherent states of time-dependent oscillator(s), the derivation of perturbative frequencies of a damped coupled anharmonic oscillators system using suitable canonical transformation in the framework of Hamilton-Jacobi formalism and the quantisation and construction of coherent states of a damped oscillator using time-dependent operators.     

Quark pair creation in color electric fields and effects of magnetic fields

The time evolution of a system where a uniform and classical SU(3) color electric field and quantum fields of quarks interact with each other is studied focusing on non-perturbative pair creation and its back reaction. We characterize a color direction of an electric field in a gauge invariant way, and investigate its dependence. Momentum distributions of created quarks show plasma oscillation as well as quantum effects such as the Pauli blocking and interference. Pressure of the system is also calculated, and we show that pair creation moderates degree of anisotropy of pressure. Furthermore, enhancement of pair creation and induction of chiral charge under a color magnetic field which is parallel to an electric field are discussed.     

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.     

Two interacting spins in external fields and application to quantum computation

We study the four-level-system given by two quantum dots immersed in a time-dependent magnetic field, which are coupled to each other by an effective Heisenberg-type interaction. We describe the construction of the corresponding evolution operator in a special case of different time-dependent parallel external magnetic fields. We find a relation between the external field and the effective interaction function. The obtained results are used to analyze the theoretical implementation of a universal quantum gate.     

失谐量子频率转换系统薛定谔方程的显式解析解

根据光和频产生过程的动力学演化总是保持闲置光和信号光的光子数之和守恒这一性质,构建出了光学谐振腔中频率转换系统的含时不变量.并运用此不变量及Lewis-Riesenfeld量子不变量方法,在失谐情形下,对这一双模量子化电磁场耦合系统相应的薛定谔方程进行了求解.得到了系统随时间演化的量子态和演化算符的显示解析表达式.此解对于进一步研究系统各种量子性质是有用的.     

Cumulative quantum work-deficit versus entanglement in the dynamics of an infinite spin chain

We find that the dynamical phase transition (DPT) in nearest-neighbor bipartite entanglement of time-evolved states of the anisotropic infinite quantum XY spin chain, in a transverse time-dependent magnetic field, can be quantitatively characterized by the dynamics of an information-theoretic quantum correlation measure, namely, quantum work-deficit (QWD). We show that only those nonequilibrium states exhibit entanglement resurrection after death, on changing the field parameter during the DPT, for which the cumulative bipartite QWD is above a threshold. The results point to an interesting inter-relation between two quantum correlation measures that are conceptualized from different perspectives.     

含时耦合谐振子系统的时间演化与双模压缩态

运用Lewis Riesenfeld不变量理论,通过适当地选取厄米不变量,得到了含驱动项和双模耦合项的含时耦合谐振子系统薛定谔方程的封闭解,给出了系统的演化算符及其产生双模光场的压缩态的条件,并得出系统压缩态的量子涨落与驱动项无关但与系统所处的初态有关的结论. 关键词： 含时耦合谐振子系统 Lewis Riesenfeld不变量理论 双模压缩态     

Quantum ring states in magnetic field and delayed half-cycle pulses

The present work is dedicated to the time evolution of excitation of a quantum ring in external electric and magnetic fields. Such a ring of mesoscopic dimensions in an external magnetic field is known to exhibit a wide variety of interesting physical phenomena. We have studied the dynamics of the single electron quantum ring in the presence of a static magnetic field and a combination of delayed half-cycle pulse pair. Detailed calculations have been worked out and the impact on dynamics by variation in the ring radius, intensity of external electric field, delay between the two pulses, and variation in magnetic field have been reported. A total of 19 states have been taken and the population transfer in the single electron quantum ring is studied by solving the time-dependent Schrödinger equation (TDSE), using the efficient fourth-order Runge–Kutta method. Many interesting features have been observed in the transition probabilities with the variation of magnetic field, delay between pulses and ring dimensions. A very important aspect of the present work is the persistent current generation in a quantum ring in the presence of external magnetic flux and its periodic variation with the magnetic flux, ring dimensions and pulse delay.     

Concerning Measurement of Gravitomagnetism in Electromagnetic Systems

Measurement of gravitomagnetic field is of fundamental importance as a test of general relativity. Here we present a new theoretical project for performing such a measurement based on detection of the electric field arising from the interplay between the gravitomagnetic and magnetic fields in the stationary axial-symmetric gravitational field of a slowly rotating massive body. Finally it is shown that precise magnetometers based on superconducting quantum interferometers could not be designed for measurement of the gravitomagnetically induced magnetic field in the cavity of a charged capacitor since they measure the circulation of a vector potential of electromagnetic field, i.e., an invariant quantity including the sum of electric and magnetic fields, and the general-relativistic magnetic part will be totally cancelled by the electric one which is in good agreement with the experimental results.     

Time Evolution and Squeezing of Degenerate and Non-degenerate Coupled Parametric Down-Conversion with Driving Term

By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the degenerate and non-degenerate coupled parametric down-conversion system with driving term. By means of this invariant and the Lewis-Riesenfeld quantum invariant theory, we obtain closed formulae of the quantum state and the evolution operator of the system. We show that the time evolution of the quantum system directly leads to production of various generalized one- and two-mode combination squeezed states, and the squeezed effect is independent of the driving term of the Hamiltonian. In somespecial cases, the current solution can reduce to the results of the previous works.     

Emission from neutral and charged excitons in a single quantum dot in a magnetic field

We report on optical spectroscopy of self-assembled InAs quantum dots in a magnetic field. We describe how we measure the emission characteristics of a single quantum dot (QD) in high magnetic fields at low temperature using a miniature, fiber-based confocal microscope. Example results are presented on a QD whose charge can be controlled using a field-effect device. For the uncharged, singly and doubly charged excitons we find a diamagnetism and the spin Zeeman effect. In contrast, for the triply-charged exciton we find a fundamentally different behavior. Anti-crossings in magnetic field imply that confined states of the QD are hybridized with Landau-like levels associated with the two-dimensional continuum.     

电场调控下不对称耦合量子点中激子的发光特性

使用有效质量模型,从理论上对GaAs/A10.35Ga0.65As不对称耦合量子点在不同耦合强度下束缚态和反束缚态的能级分裂情况进行了详细分析,重点探讨了电子和空穴的耦合隧穿对量子点体系能级特征及激子发光强度的影响.研究发现:不对称耦合量子点在外电场作用下价带束缚态和反束缚态能级出现反交现象,反交处的能级分裂值和临界电...     

Landau levels of scalar QED in time-dependent magnetic fields

The Landau levels of scalar QED undergo continuous transitions under a homogeneous, time-dependent magnetic field. We analytically formulate the Klein–Gordon equation for a charged spinless scalar as a Cauchy initial value problem in the two-component first order formalism and then put forth a measure that classifies the quantum motions into the adiabatic change, the nonadiabatic change, and the sudden change. We find the exact quantum motion and calculate the pair-production rate when the magnetic field suddenly changes as a step function.     

Direct calculation of time varying Aharonov-Bohm effect

The Aharonov-Bohm effect (ABE) for steady magnetic fields is a well known phenomenon. However, if the current in the infinite solenoid that creates the magnetic field is time-dependent, that is in the presence of both magnetic and electric fields, there is no agreement whether the effect would be present. In this note, we try to investigate time varying ABE by a direct calculation in a set-up with a weak time dependent magnetic field. We find that the electric field arising out of the time-varying magnetic field in the path of the electrons does not enter the action integral but only changes the path of the electron from the source to the slits and then on to the detector. We find a frequency dependent AB phase shift. At low frequencies the result smoothly approaches the one for a constant field as the frequency tends towards zero. On the other hand, for high frequencies such that the AB-phase induced in the path of the wave packet oscillates rapidly, the net effect will be very small which is borne out by our results.     

Factorizing coupled quantum systems and damped nonlinear Schrödinger equations

We show that the wave function of a coupled quantum system may factorize for certain coupling operators, resulting in wave functions and effective nonlinear Hamiltonians for the subsystems. Systems of coupled harmonic oscillators with discrete or continuous spectra are considered, where all degrees of freedom move in time-dependent coherent Glauber states.We present the general formalism and study two examples in detail. The problem of radiation damping results under drastic assumptions in exponentially damped harmonic motion, obeying a nonlinear Schrödinger equation. In the second example, a different type of coupling is studied which yields inverse power law damping.     

Scattering mechanism of integer quantum Hall conductance in a model system

We consider a large class of two-dimensional systems of charged particles in crossed electric and strong magnetic fields in the presence of a static substrate potentialV(x,y), which contains disorder. The time dependence of the single-particle Schroedinger functions are investigated. It is found on general grounds, that adiabatic states are dc-insulating and, that the macroscopic Hall current is carried by the non-adiabatic states. Hall conductance plateaus correspond to spectral domains, which contain only adiabatic states. The plateaus disappear, when these states become non-adiabatic at sufficiently high electric fields, i.e., at sufficiently large Hall currents. An explicit model system is investigated with a substrate potential composed of disorder and of a sequence of smooth barriers and wells. Here the non-adiabatic states can be calculated in a weak-disorder approximation, whenever the electric field (and hence the Hall current) is sufficiently low. In this case the quantum mechanical scattering process leading, to the quantisation of the Hall conductance can be understood in detail. Non-classical particle propagation plays a crucial role in this process. Our analysis opens new perspectives for the theory of the integer quantum Hall effect.     

Ground State Transitions in Vertically Coupled Four-Layer Single Electron Quantum Dots

We study a four-electron system in a vertically coupled four-layer quantum dot under a magnetic field by the exact diagonalization of the Hamiltonian matrix. We find that discontinuous ground-state energy transitions are induced by an external magnetic field. We find that dot-dot distance and electron-electron interaction strongly affect the low-lying states of the coupled quantum dots. The inter-dot correlation leads to some sequences of possible disappearances of ground state transitions, which are present for uncoupled dots.     

Quantum integrals of motion for variable quadratic Hamiltonians

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.