Completely inhomogeneous density-matrix theory for quantum-dots

The nonlinear (third-order) optical gain for quantum-dot structures is derived where the density matrix theory is defined by the inhomogeneous density matrix elements. Thus, the nonlinear gain becomes completely inhomogeneous. The total gain obtained under complete inhomogeneous density matrix is shown to be asymmetric. This is not included earlier.     

Eigenstates of the time-dependent density-matrix theory

An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying 2 ⁺ states in ²⁴O to understand the foundation of the rather successful time-dependent approach. It is found that the calculated strength distribution of the 2 ⁺ states has physically reasonable behavior and that the strength function is practically positive definite though the non-Hermitian Hamiltonian matrix obtained from TDDM does not guarantee it. A relation to an Extended RPA theory with hermiticity is also investigated. It is found that the density-matrix formalism is a good approximation to the Hermitian Extended RPA theory.Received: 26 May 2003, Revised: 30 October 2003, Published online: 26 January 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 21.10.Re Collective levels     

Giant quadrupole resonances in time-dependent density-matrix theory

Damping of an isoscalar giant quadrupole resonance (GQR) in ⁴⁰Ca is studied using an extended version of the time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). The Skyrme III force is used as an effective interaction for the calculation of both a mean-field potential and a two-body correlation function, and a correlated state is used as the ground state on which GQR is built. It is found that the calculated strength of GQR is split into a major component and a minor component. The spreading width of the major component is found small as compared with experimental data. A double giant quadrupole resonance (DGQR) is also studied in TDDM, and it is found that DGQR given in TDDM has properties of the double phonon state of GQR calculated in the random phase approximation.     

Time-dependent Hartree-Fock theory

The lowest singlet and triplet excited states of the two paired electrons in a chemical bond are treated by the time-dependent Hartree-Fock (H.F.) method, with the π electrons of the double bond in ethylene as an example. The results depend on a dimensionless parameter g which describes the strength of the electron correlation effects, and they are compared with a simple configuration interaction calculation. When g is small the frequencies and amplitudes of the Hartree-Fock oscillations give an accurate estimate of the energies and intensities of the two lowest transitions, the correlation energy and the pair distribution function of the gound state. The correlation energy is related to the zero-point energy of the oscillations. As g increases the H.F. method overestimates the correlation corrections and breaks down completely if g = 1. At this point the triplet oscillation becomes unstable, because the molecular orbital wave-function with two paired electrons ceases to be the state of lowest energy. When g is large the H.F. results violate spin conservation and the exclusion principle.     

Time-dependent Kohn-Sham theory with memory

In time-dependent density-functional theory, exchange and correlation (xc) beyond the adiabatic approximation can be described by viscoelastic stresses in the electron liquid. In the time domain, the resulting velocity-dependent xc vector potential has a memory containing short- and long-range components, leading to decoherence and energy relaxation. We solve the associated time-dependent Kohn-Sham equations, including the dependence on densities and currents at previous times, for the case of charge-density oscillations in a quantum well. We illustrate xc memory effects, clarify the dissipation mechanism, and extract intersubband relaxation rates for weak and strong excitations.     

KdV孤子的含时微扰理论

研究了周期性含时微扰对KdV(Korteweg de Vries)孤子的影响. 将微扰项展为时间变量的傅里叶级数,发现其常数项是导致长期项的根源. 在一阶近似下,消除长期项,求出了孤子参数(高度、宽度和速度)随时间的缓慢变化. 傅氏级数中的其他项决定了微扰对孤子波形的一阶修正. 关键词： KdV孤子 孤子微扰论     

Time-dependent perturbation theory with permanent effects

The presence of time-varying external fields invalidates usual perturbation theories as expressed by Feynman diagrams. We derive the correct Feynman graphs, which automatically ensure unitary and causality. The relevance of these considerations for cosmological problems is pointed out.     

Time-dependent density-functional theory with a self-interaction correction

We discuss an implementation of the self-interaction correction for the local-density approximation to time-dependent density-functional theory. A variational formulation is given, taking care of the necessary constraints. A manageable and transparent propagation scheme using two sets of wave functions is proposed and applied to laser excitation with subsequent ionization of a dimer molecule.     

Time-dependent mean field S-matrix theory

By using the path integral approach to many-body systems, we formulate a time-dependent mean field S-matrix theory of nuclear reactions. Many-body channel eigenstates are constructed by using projection techniques. In this way the S-matrix between the channel eigenstates is expressed as a superposition of S-matrix elements between wave-packet-like states localized in space and time. A field operator representation of the interaction picture S-matrix is derived which enables one to apply the path integral approach. Applying the stationary phase approximation to the path integral representation of the interaction picture S-matrix between the localized states an asymptotically constant time-dependent mean field approximation to this S-matrix is obtained. Finally, the S-matrix between the projected channel eigenstates is obtained by evaluating the integral, arising from the projections, over the space-time positions of the localized states in the stationary phase approximation. The stationary phase conditions select those localized states from the projected channel states for which the mean field values of energy and momentum coincide with their corresponding channel eigenvalues.     

Time-dependent perturbation theory with a classical limit

We construct a quantum mechanical perturbation theory which uses the multiple time scale technique. Working with the time translation operator, we use a variant on the method of Bender and Bettencourt. Our perturbation theory smoothly crosses over to the classical result as Planck's -->0. It is seen that this technique has a nonperturbative element built into it.     

Time-dependent density functional theory of classical fluids

We establish a rigorous time-dependent density functional theory of classical fluids for a wide class of microscopic dynamics. We obtain a stationary action principle for the density. We further introduce an exact practical scheme, to obtain hydrodynamical effects in density evolution, that is analogous to the Kohn-Sham theory of quantum systems. Finally, we show how the current theory recovers existing phenomenological theories in an adiabatic limit.     

Time-dependent perturbation theory for nonequilibrium lattice models

We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles. At a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state, which is absorbing. We present several methods for deriving series for the evolution starting from a single seed particle, including expansions for the ultimate survival probability in the super- and subcritical regions, expansions for the average number of particles in the subcritical region, and short-time expansions. Algorithms for computer generation of the various expansions are presented. Rather long series (24 terms or more) and precise estimates of critical parameters are presented.     

Time-dependent density functional theory for quantum transport

The rapid miniaturization of electronic devices motivates research interests in quantum transport. Recently time-dependent quantum transport has become an important research topic. Here we review recent progresses in the development of time-dependent density-functional theory for quantum transport including the theoretical foundation and numerical algorithms. In particular, the reducedsingle electron density matrix based hierarchical equation of motion, which can be derived from Liouville–von Neumann equation, is reviewed in details. The numerical implementation is discussed and simulation results of realistic devices will be given.     

Time-dependent shell-model theory of dissipative heavy-ion collisions

A transport theory is formulated within a time-dependent shell-model approach. Time averaging of the equations for macroscopic quantities lead to irreversibility and justifies weak-coupling limit and Markov approximation for the (energy-conserving) one- and two-body collision terms. Two coupled equations for the occupation probabilities of dynamical single-particle states and for the collective variable are derived and explicit formulas for transition rates, dynamical forces, mass parameters and friction coefficients are given. The applicability of the formulation in terms of characteristic quantities of nuclear systems is considered in detail and some peculiarities due to memory effects in the initial equilibration process of heavy-ion collisions are discussed.     

Time-dependent density-functional theory beyond the local-density approximation

Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.