Kohn-Sham theory for ground-state ensembles

An electron density distribution n(r) which can be represented by that of a single-determinant ground state of noninteracting electrons in an external potential v(r) is called pure-state v-representable (P-VR). Most physical electronic systems are P-VR. Systems which require a weighted sum of several such determinants to represent their density are called ensemble v-representable (E-VR). This paper develops formal Kohn-Sham equations for E-VR physical systems, using the appropriate coupling constant integration. It also derives local density- and generalized gradient approximations, and conditions and corrections specific to ensembles.     

Non-universal critical behaviour in mean-field theory of inhomogeneous systems

We consider the layered magnetic systems with inhomogeneous inter-layer couplings and study their critical properties within the framework of mean-field theory. We consider two kinds of distribution of the couplings: (i) quasi-periodic, according to the Fibonacci sequence and (ii) smoothly inhomogeneous, in which the couplings deviate from the bulk couplings by an amount of Al⁻², where l measures the distance from a free surface. According to analytical and accurate numerical results the critical behaviour of both the problems is non-universal and the corresponding critical exponents are coupling dependent.     

Quantum theory of conductivity of spatially inhomogeneous systems

A quantum theory of conductivity is constructed for semiconductor objects such as quantum wells, wires, and dots. The mean values of current and charge densities induced by a weak electromagnetic field are calculated. It is shown that the mean values of current and charge densities consist of two parts, the first of which is expressed in terms of the electric field and the second is expressed in terms of derivatives of the electric field with respect to spatial coordinates. Appropriate expressions are derived for the conductivity tensor that depends on coordinates; these expressions can be applied to any spatially inhomogeneous systems. The results obtained can be used in the theory of secondary radiation from objects of reduced dimension in the cases of monochromatic or pulsed irradiation.     

Nonlinear response theory—I

A general nonlinear response theory for the case of linear coupling of physical systems to arbitrary external fields is formulated for applications in different branches of physics. This is done within the framework of non-relativistic density matrix approach of quantum mechanics. Some simple properties of response functions and other related functions, which are introduced here for convenience, are studied to obtain suitable representations of the nonlinear response functions, including important sum-rules. As an example, the sum rule for the second-order response function is applied to electronic dipole nonlinearity at optical frequencies which includes both the Raman nonlinearity arising from perturbation to the electronic motion from external ionic displacement field and the usual optical sum, difference and harmonic generations. This immediately allows us to visualize a rigorous connection between these two types of non-linearities.     

Density-functional theory of inhomogeneous electron systems in thin quantum wires

Motivated by current interest in strongly correlated quasi-one-dimensional (1D) Luttinger liquids subject to axial confinement, we present a novel density-functional study of few-electron systems confined by power-low external potentials inside a short portion of a thin quantum wire. The theory employs the 1D homogeneous Coulomb liquid as the reference system for a Kohn-Sham treatment and transfers the Luttinger ground-state correlations to the inhomogeneous electron system by means of a suitable local-density approximation (LDA) to the exchange-correlation energy functional. We show that such 1D-adapted LDA is appropriate for fluid-like states at weak coupling, but fails to account for the transition to a “Wigner molecules” regime of electron localization as observed in thin quantum wires at very strong coupling. A detailed analyzes is given for the two-electron problem under axial harmonic confinement.     

Conservative ensembles for nonequilibrium lattice-gas systems

We show how to set up a constant particle ensemble for the steady state of nonequilibrium lattice-gas systems which originally are defined on a constant rate ensemble. We focus on nonequilibrium systems in which particles are created and annihilated on the sites of a lattice and described by a master equation. We consider also the case in which a quantity other than the number of particle is conserved. The conservative ensembles can be useful in the study of phase transitions and critical phenomena particularly discontinuous phase transitions.     

Equilibrium ensembles of quantum dots in atomically inhomogeneous pentagonal nanowires

A theoretical model has been proposed for describing the relaxation of elastic stresses in an atomically inhomogeneous pentagonal nanowire due to the formation of quantum dots in the form of precipitates of the second phase. Quantum dots have been considered as finite-height coaxial cylindrical inclusions subjected to intrinsic axial dilatation and located along the axis of the nanowire. The optimum shape and sizes of the quantum dots have been calculated for specified nanowire parameters. It has been shown that such quantum dots can form different equilibrium periodic structures in the pentagonal nanowires.     

Nonlinear diffraction in inhomogeneous superlattice

We considered the propagation of laser monochromatic radiation in a superlattice that contains regions with an elevated concentration of carriers. The model of the energy spectrum of electrons is chosen in the strong coupling approximation. The electromagnetic field is described quasiclassically with Maxwell equations, which, as applied to the problem under study, are reduced to a non-one-dimensional sine-Gordon wave equation for the vector-potential. We analyzed the wave equation in the approximation of slowly varying amplitudes and phases and obtained and numerically solved an effective equation that describes the electromagnetic field in the superlattice. We studied different regimes of propagation of laser radiation, analyzed diffraction by regions with an elevated electron concentration.     

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.     

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

Current-conserving nonlinear response theory in driven systems

Employing the closed-time path 2PI effective action (CTP 2PI EA) approach, we study the response of an open interacting electronic system to time-dependent external electromagnetic fields. We show that the 2PI EA provides a systematic way of calculating the propagator and response functions of the system. Due to the invariance of the 2PI EA under external gauge transformations, the response functions calculated from it are such that the Ward–Takahashi hierarchy, which ensures current conservation beyond the expectation value level, is satisfied. These findings may be useful in the study of interacting electronic pumping devices, and serve to clarify the connection between current conservation (beyond the mean value level) and real-time nonlinear response theory.     

Coarsening in inhomogeneous systems

This article is a brief review of coarsening phenomena occurring in systems where quenched features—such as random field, varying coupling constants or lattice vacancies—spoil homogeneity. We discuss the current understanding of the problem in ferromagnetic systems with a non-conserved scalar order parameter by focusing primarily on the form of the growth law of the ordered domains and on the scaling properties.     

Linear response theory for systems obeying the master equation

Linear response theory is developed for systems whose time dependence is described by a master equation. The fluctuation dissipation theorem expressing the linear response of the system in terms of fluctuation properties of the system in equilibrium is derived. The time-dependent Ising spin system in interaction with a heat bath, the Glauber model, is discussed as a particular case of the formalism.The work of one of the authors (D.B.) was supported in part by the National Science Foundation under Contract GP 10536.On leave of absence from the Institute of Physics, Belgrade, Yugoslavia.     

Interface response theory of composite systems

A short account of a new unified interface response theory of composite systems is given. This theory applies as well to discrete as to continuous d-dimensional spaces and enables one to calculate the response function for any composite system from a new simple and general equation. With the help of this response function all the properties associated to a given operator and a composite system can be obtained. A short review of a few physical properties obtained with the help of response functions will be given for vibrational, electronic, magnetic, electromagnetic problems associated with surfaces, interfaces, adsorbates, superlattices,… As an illustration, it will be shown how the interface response theory enables one to solve the Schrödinger equation for free electrons in any composite material, and in particular superlattices.     

Linear response theory in stochastic many-body systems revisited

The Green–Kubo relation, the Einstein relation, and the fluctuation–response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these universal relations for stochastic many-body systems. Through these simple proofs, we characterize the three relations as follows. The Green–Kubo relation is a direct result of the local detailed balance condition, the fluctuation–response relation represents the dynamic extension of both the Green–Kubo relation and the fluctuation relation in equilibrium statistical mechanics, and the Einstein relation can be understood by considering thermodynamics. We also clarify the interrelationships among the universal relations.     

非均匀量子等离子体中的非线性波

本文探讨具有温度和密度梯度的非均匀量子等离子体系统, 获得了该系统在离子与中子碰撞频率较低情况下的二维非线性流体动力学方程． 求得了非均匀量子等离子体中的电势的冲击、爆炸和旋涡解．分析讨论了在致密天体物理环境中静电势的变化, 结果表明电势的冲击波的幅度和爆炸波的宽度,都随密度的增大(即随无维量子参量的减小)而增大, 但随漂移速度的增大(即随密度和温度梯度的增大)而减小; 静电势随时空相位的增大而趋向于稳定值, 系统最后达到稳定的状态． 旋涡解表明,旋涡静电势的时空分布呈现稳定的周期性的旋涡流．     

Nonlinear plasma resonance in inhomogeneous relativistic plasma

We present a theoretical study of relativistic electron plasma oscillations in the plasma resonance region based on the renormalization group symmetry method. A steady-state solution to equations describing the electron dynamics in the vicinity of the plasma resonance is found and spatial-temporal and spectral characteristics of the potential electric field are discussed.     

The equivalence of ensembles for classical systems of particles

For systems of particles in classical phase space with standard Hamiltonian, we consider (spatially averaged) microcanonical Gibbs distributions in finite boxes. We show that infinite-volume limits along suitable subsequences exist and are grand canonical Gibbs measures. On the way, we establish a variational formula for the thermodynamic entropy density, as well as a variational characterization of grand canonical Gibbs measures.