Indirect optical cooperative excitation of two-particle electronic excitations in doped organic molecular crystals

A theory on the indirect optical cooperative excitation of a two-particle electronic excitation composed of one host exciton and one guest-molecule one-particle electronic excitation through one electric dipole-moment active singlet guest molecule one-particle electronic excitation is developed by considering the nonradiative coupling bstween one- and two-particle electronic excitations.The complex dielectric tensor and the corresponding absorption coefficient are found out, which are expressed in terms of the Fourier-transform of the retarded Green function: The derived formulas are discussed in an explicit form for the one-dimensional model of the doped organic molecular crystal. Within the framework of ths one-dimensional model also the conditions for the existence of the host exciton-guest molecule one-particle electronic excitation bound states are established and discussed.     

Gauge invariance of relativistic two-particle bound-state energies (I)

The gauge invariance of relativistic two-particle energy levels in quantum electrodynamics is demonstrated for both covariant and non-covariant gauges, by considering infinitesimal gauge transformations from a fixed gauge. The proof is carried out by expressing the bound-state energies in terms of ratios of contour integrals involving four-point Green functions in the neighborhood of their poles in the energy plane. The generalized Ward-Takahashi identities are then used to help reduce the Green functions which appear into forms which make the singularity structure of the four-point function apparent. The formalism is illustrated for the special cases of one- and two-photon exchange in perturbation theory.     

Single-site theory for the random Hubbard alloy

A new theory for the random system with electron correlation is presented, which is an extension of the Hubbard's theory for the random system and also an extension of the CPA for the interacting electron system. The equation of motion for the Green function is solved by the same decoupling method used by Hubbard. The self-consistent relations for the Green function, the self-energy and the effective occupation number are derived. It is predicted in the binary alloy system that tails or satellites of the state density are produced by the combined effect of the randomness and electron correlation. The origin of the tail is the inelastic scattering of the electron byA — B atomic pairs, whose electronic configuration is changed during the scattering. Numerical calculations are reported for a simple model.     

The two-dimensional one-component plasma at Γ=2: The semiperiodic strip

The one-component two-dimensional plasma is studied in a strip of finite width, replicated periodically parallel to the long axis of the strip. Exact results for the one- and two-particle distribution functions are found at coupling =q ²/kT =2. The system is inhomogeneous: the one- and two-particle distribution functions show long-range order.     

Correlated motion of a pair of electrons in a random alloy

A theory of dynamical electron-electron correlation in a random A_xB_1?x alloy is developed as an extension to the Kanamori model: two electrons in a narrow band, interacting via randomly varying contact pair interaction are considered. The exact theory, including exact moments and localization theorems, is derived. A coherent potential approximation in the space of two-particle states, describing the effect of the pair interaction quite exactly, is then developed. The case with randomness in the pair interaction only is discussed in detail. Results of numerical analysis for a simple model based on the scaling-factor approximation are given to illustrate the essential features of the CPA solution.     

自旋梯可积模型的研究

通过对自旋梯可积模型的研究,求出该模型的能量本征值和两体散射矩阵.用可积模型中的坐标Bethe Ansatz方法,首先由薛定谔方程求得能量的本征方程.设定波函数的具体形式,求出本征能量,然后利用能量本征方程和波函数的连续性求出两体散射矩阵.求出单粒子、双粒子和N₀个粒子的本征能量,同时求得粒子的两体散射矩阵.自旋梯可积模型的本征能量和两体散射矩阵可通过Bethe Ansatz的方法求得.     

On the self-consistent theory of localization

A modification of W. Götze's self-consistent approach is proposed, which predicts a complete localization in the one- and two-dimensional cases. The modification is based on a choice of such a form of the time dependence for the two-particle Green function, which takes an apparent account of time-reversal invariance.     

Kinetics of exciton-exciton annihilation in molecular crystals

The theoretical investigation of the time dependence of the concentration of incoherent excitons formed by pulsed pumping is carried out. The basis of this investigation is a system of an infinite number of coupled equations for multiparticle distribution functions. Using the Kirkwood method of uncoupling, this system is reduced to a system of differetial equations for one- and two-particle distribution functions. The algorithm for calculating these equations by means of an electronic computer is developed.A simple phenomenological differential equation for exciton density has been obtained. The solution of this phenomenological equation coincides with good accuracy with the solution obtained by numerical integration of the above-mentioned system of differential equations for one- and two-particle distribution functions.     

Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

Exactly solvable toy model for the pseudogap state

We present an exactly solvable toy model which describes the emergence of a pseudogap in an electronic system due to a fluctuating off-diagonal order parameter. In one dimension our model reduces to the fluctuating gap model (FGM) with a gap that is constrained to be of the form , where A and Q are random variables. The FGM was introduced by Lee, Rice and Anderson [Phys. Rev. Lett. 31, 462 (1973)] to study fluctuation effects in Peierls chains. We show that their perturbative results for the average density of states are exact for our toy model if we assume a Lorentzian probability distribution for Q and ignore amplitude fluctuations. More generally, choosing the probability distributions of A and Q such that the average of vanishes and its covariance is , we study the combined effect of phase and amplitude fluctuations on the low-energy properties of Peierls chains. We explicitly calculate the average density of states, the localization length, the average single-particle Green's function, and the real part of the average conductivity. In our model phase fluctuations generate delocalized states at the Fermi energy, which give rise to a finite Drude peak in the conductivity. We also find that the interplay between phase and amplitude fluctuations leads to a weak logarithmic singularity in the single-particle spectral function at the bare quasi-particle energies. In higher dimensions our model might be relevant to describe the pseudogap state in the underdoped cuprate superconductors. Received 15 March 2000     

Melt-crystal phase transition in a two-component system

The melt-crystal phase transition in a two-component system is described by a generalized Ornstein-Zernicke equation for one- and two-particle distribution functions. The jump in the density δn under melt crystallization is a small parameter. The desired distribution functions are found as δn power series. The two-particle distribution function for the melt along its crystallization line is chosen as a zeroth approximation. Institute of Applied Physics at the Irkutsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 54–61, February 2000.     

无序合金中相干势近似的另一种推导——紧束缚模型

本文用Matsubara和Toyozawa的locator展开方法重新推导单粒子和双粒子格林函数的相干势近似(CPA)方程,文中不采用对累积量做自洽处理的方法来考虑原子之间的体积排斥效应,而采用Yonezawa早先提出的一种图形法,本文的重点是提出一个可以用来生成单格点图形自洽方程的系统方法,并用在处理双粒子平均格林函数上,这种处理方法可以推广到处理包括液态金属或非晶态金属等具有短程序系统电导率的CPA方程。 关键词：     

Random patterns generated by random permutations of natural numbers

We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time n, whose moves to the right or to the left are prescribed by the rise-and-descent sequence associated with a given random permutation. We determine exactly the probability of finding the trajectory of such a permutation-generated random walk at site X at time n, obtain the probability measure of different excursions and define the asymptotic distribution of the number of “U-turns" of the trajectories - permutation “peaks" and “through". In the second part, we focus on some statistical properties of surfaces obtained by randomly placing natural numbers 1,2,3, ...,L on sites of a 1d or 2d lattices containing L sites. We calculate the distribution function of the number of local “peaks" - sites the number at which is larger than the numbers appearing at nearest-neighboring sites - and discuss surprising collective behavior emerging in this model.     

Dilute limit of a strongly-interacting model of spinless fermions and hardcore bosons on the square lattice

In our model, spinless fermions (or hardcore bosons) on a square lattice hop to nearest neighbor sites, and also experience a hard-core repulsion at the nearest neighbor separation. This is the simplest model of correlated electrons and is more tractable for exact diagonalization than the Hubbard model. We study systematically the dilute limit of this model by a combination of analytical and several numerical approaches: the two-particle problem using lattice Green functions and the t-matrix, the few-fermion problem using a modified t-matrix (demonstrating that the interaction energy is well captured by pairwise terms), and for bosons the fitting of the energy as a function of density to Schicks analytical result for dilute hard disks. We present the first systematic study for a strongly-interacting lattice model of the t-matrix, which appears as the central object in older theories of the existence of a two-dimensional Fermi liquid for dilute fermions with strong interactions. For our model, we can (Lanczos) diagonalize the 7 x 7 system at all fillings and the 20 x 20 system with four particles, thus going far beyond previous diagonalization works on the Hubbard model.Received: 8 May 2003, Published online: 28 May 2004PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) - 05.30.Jp Boson systems - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.)N.G. Zhang: Present address: Dept. of Physics, George Washington University, Washington, DC 20052     

Real‐space multiple‐scattering Hubbard model calculations for d‐ and f‐state materials

Calculations are presented of the electronic structure and X‐ray spectra of materials with correlated d‐ and f‐electron states based on the Hubbard model, a real‐space multiple‐scattering formalism and a rotationally invariant local density approximation. Values of the Hubbard parameter are calculated ab initio using the constrained random‐phase approximation. The combination of the real‐space Green's function with Hubbard model corrections provides an efficient approach to describe localized correlated electron states in these systems, and their effect on core‐level X‐ray spectra. Results are presented for the projected density of states and X‐ray absorption spectra for transition metal‐ and lanthanide‐oxides. Results are found to be in good agreement with experiment.     

Density and current response functions in strongly disordered electron systems: diffusion,electrical conductivity and Einstein relation

We study noninteracting quantum charged particles (electron gas) subject to a strong random potential and perturbed by a weak classical electromagnetic field. We examine consequences of gauge invariance and charge conservation in the space of Bloch waves. We use two specific forms of the Ward identity between the one- and two-particle averaged Green functions to establish exact relations between the density and current response functions. In particular, we find precise conditions under which we can extract the current-current from the density-density correlation functions and vice versa. We use these results to prove a formula relating the density response and the electrical conductivity in strongly disordered systems. We introduce quantum diffusion as a response function that reduces to the diffusion constant in the static limit. We then derive Ficks law, a quantum version of the Einstein relation and prove the existence of the diffusion pole in the quasistatic limit of the zero-temperature electron-hole correlation function. We show that the electrical conductivity controls the long-range spatial fluctuations of the electron-hole correlation function only in the static limit.Received: 10 June 2003, Published online: 22 September 2003PACS: 72.10.Bg General formulation of transport theory - 72.15.Eb Electrical and thermal conduction in crystalline metals and alloys - 72.15.Qm Scattering mechanisms and Kondo effect     

Faddeev random phase approximation applied to molecules

The Faddeev Random Phase Approximation (FRPA) is a Green’s function method which couples collective degrees of freedom to the single particle motion by resumming an infinite number of Feynman diagrams. The Faddeev technique is applied to describe the two-particle-one-hole (2p1h) and two-hole-one-particle (2h1p) Green’s function in terms of non-interacting propagators and kernels for the particle-particle (pp) and particle-hole (ph) interactions. This results in an equal treatment of the intermediary pp and ph channels. In FRPA both the pp and ph phonons are calculated on the random phase approximation (RPA) level. In this work the equations that lead to the FRPA eigenvalue problem are derived. The method is then applied to atoms, small molecules and the Hubbard model, for which the ground state energy and the ionization energies are calculated. Special attention is directed to the RPA instability in the dissociation limit of diatomic molecules and in the Hubbard model. Several solutions are proposed to overcome this problem.     

Electrical conductivity of electrons in a model binary disordered alloy with long range order

The CPA d. c. electrical conductivity for a bcc based random binary substitutional alloy with long range ordering is determined for a single band model with diagonal disorder and arbitrary alloy parameters. The CPA vertex corrections to vanish, off-diagonal elements of the Green function are most important. The conductivity obeys general symmetries with respect to alloy parameters and can be brought to closed form resembling the standard expression = ne²/m. To interpret various terms in correctly, limits with available Boltzmann equation solutions are analyzed in detail.     

Phase-space density in heavy-ion collisions revisited

We derive the phase space density of bosons from a general boson interferometry formula. We find that the phase space density is connected with the two-particle and the single-particle density distribution functions. If the boson density is large, the two-particle density distribution function cannot be expressed as a product of two single-particle density distributions. However, if the boson density is so small that the two-particle density distribution function can be expressed as a product of two single-particle density distributions, then Bertsch's formula is recovered. For a Gaussian model, the effects of multi-particles Bose-Einstein correlations on the mean phase space density are studied.Received: 10 July 2002, Revised: 18 June 2003, Published online: 5 September 2003