Coulomb repulsion versus Hubbard repulsion in a disordered chain

We study the difference between on site Hubbard and long range Coulomb repulsions for two interacting particles in a disordered chain. The system size L (in units of the lattice spacing) is of the order of the one particle localization length and the energies are taken near the band center. In the two cases, the limits of weak and strong interactions are characterized by uncorrelated energy levels and are separated by a crossover regime where the states are more extended and the spectra more rigid. U denoting the interaction strength and t the kinetic energy scale, the crossovers take place for interaction energy to kinetic energy ratios U/t and U/(2tL) of order one, for Hubbard and Coulomb repulsions respectively. While Hubbard repulsion can only yield weak critical chaos with intermediate spectral statistics, Coulomb repulsion can drive the two particle system to quantum chaos with Wigner-Dyson spectral statistics. The interaction matrix elements are studied to explain this difference. Received 21 March 2000 and Received in final form 5 February 2001     

Dynamics of collective decoherence and thermalization

We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N², while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.     

1/<Emphasis Type="Italic">Q</Emphasis> expansion for the energy spectrum of quantum dots

A new method is proposed for calculating the energy spectrum and the wave functions of N-electron quantum dots with an arbitrary confining potential. The method consists in expansion with respect to a dimensionless quantum parameter 1/Q, which is expressed in terms of the ratio of the characteristic Coulomb energy of electron-electron interaction to the characteristic energy of one-particle transition in a confining potential. Two-electron quantum dots with a parabolic confining potential in an external magnetic field are considered. Strongly correlated states of the system and the spin rearrangement in a strong magnetic field are analyzed. Analytic expressions are obtained for the energy and the wave functions of the system. It is shown that restriction of the analysis only to the first three terms in the quantum-parameter expansion gives an accuracy of one percent when calculating the energy even for values of Q on the order of unity, i.e., for the presently implementable GaAs quantum dots. The expressions for energy obtained are in a good agreement with the experimental data for quantum dots in a perpendicular magnetic field.     

Cavity‐Photon‐Induced High‐Order Transitions between Ground States of Quantum Dots

It is shown that quantum electromagnetic transitions to high orders are essential to describe the time‐dependent path of a nanoscale electron system in a Coulomb blockade regime when coupled to external leads and placed in a 3D rectangular photon cavity. The electronic system consists of two quantum dots embedded asymmetrically in a short quantum wire. The two lowest in energy spin degenerate electron states are mostly localized in each dot with only a tiny probability in the other dot. In the presence of the leads, a slow high‐order transition between the ground states of the two quantum dots is identified. The Fourier power spectrum for photon–photon correlations in the steady state shows a Fano type of resonance for the frequency of the slow transition. Full account is taken of the geometry of the multilevel electronic system, and the electron–electron Coulomb interactions together with the para‐ and diamagnetic electron–photon interactions are treated with step‐wise exact numerical diagonalization and truncation of appropriate many‐body Fock spaces. The matrix elements for all interactions are computed analytically or numerically exactly.     

Spin Operator Matrix Elements in the Superintegrable Chiral Potts Quantum Chain

We derive spin operator matrix elements between general eigenstates of the superintegrable ℤ _N -symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by Baxter. For each pair of spaces (Onsager sectors) of the irreducible representations of the Onsager algebra, we calculate the spin matrix elements between the eigenstates of the Hamiltonian of the quantum chain in factorized form, up to an overall scalar factor. This factor is known for the ground state Onsager sectors. For the matrix elements between the ground states of these sectors we perform the thermodynamic limit and obtain the formula for the order parameters. For the Ising quantum chain in a transverse field (N=2 case) the factorized form for the matrix elements coincides with the corresponding expressions obtained recently by the Separation of Variables method.     

Donor states in tunnel-coupled quantum wells

We study the energy spectrum of the impurity states in tunnel-coupled double quantum wells for Coulomb and short-range donor potentials. We calculate the impurity contribution and the density of states and detect the transformation of a localized donor state into a resonant state when the binding energy of the donor in an isolated quantum well is less than the separation of the energy levels of the double quantum wells. In the opposite case, where the binding energy is greater than the level separation, there is tunneling repulsion between adjacent impurity levels, with the degree of degeneracy of the levels changing when there is tunneling mixing of the ground and excited impurity states from different wells. Resonant states emerge in an asymmetric double quantum well, while in a symmetric double quantum well the impurity level at the barrier’s center proves to be localized even against the background of the continuum. The calculations are based on a general expression for the impurity contribution to the density of states in terms of a 2-by-2 matrix Green’s function, i.e., only a pair of tunnel-coupled levels of the double quantum wells is taken into account. For an impurity with a short-range potential, we derive a matrix generalization of the Koster-Slater solution, while the impurity with a Coulomb potential is analyzed by using the approximation of a narrow resonance and close arrangement of the repulsive levels. Zh. éksp. Teor. Fiz. 115, 1337–1352 (April 1999)     

Collective electronically excited states of a uniform chain of atoms

Electronically excited states of finite uniform chains of atoms were considered taking into account the influence of the continuous energy spectrum. Traditional quantum-chemical methods for calculating two-electron transitions between neighboring chain atoms were combined with the asymptotic theory of interactions between excited atoms and neutral particles and the mathematical apparatus of the theory of multiple scattering for taking into account intercenter transitions in an ensemble of interacting centers. Recurrence equations for describing energy zones containing symmetrical and antisymmetric excited state levels of chains with an arbitrary length were obtained. Depending on system parameters, different modes of the distribution of the electron density of collective excited states were possible. At a certain ratio between level shifts and exchange integral values, excited states with a uniform electron density distribution over all chain nodes could form for certain solutions. This was a fortuitous circumstance caused by the influence of the continuous spectrum. Such states appeared at small principal quantum number n values, they were similar to one-electron excitations of the type of Frenkel excitons, when an electron was localized near its Coulomb center. These conditions were rapidly disturbed as n increased, and one-electron excitations of a linear molecule were formed in the system (that is, limiting excitations of the type of Wannier-Mott excitons did not form).     

Effect of interdiffusion and magnetic field on two-electron states in Gaussian-shaped double quantum rings

The effects of interdiffusion and electrons' Coulomb interaction on the energy spectrum in Gaussian-shaped single and double quantum rings in the presence of magnetic field has been considered in the framework of exact diagonalization method. The one-electron energies as functions of magnetic field for different values of diffusion parameter have been obtained. The two-electron energies and electron probability density distributions are obtained as well. It is shown that the energy oscillations which are more pronounced for a single quantum ring, smooth out due to the interdiffusion. The Coulomb interaction transforms the crossings of the two-electron levels to anticrossings and can lead to the appearance of an additional level between the anticrossing levels.     

Density of states in the magnetic ground state of the Friedel-Anderson impurity

By applying a magnetic field whose Zeeman energy exceeds the Kondo energy by an order of magnitude the ground state of the Friedel-Anderson impurity is a magnetic state. In recent years the author introduced the FAIR (Friedel Artificially Inserted Resonance) method to investigate the impurity properties. Within this FAIR approach the full excitation spectrum and the composition of the excitations is calculated and numerically evaluated. From the excitation spectrum the electron density of states is calculated. Majority and minority d-resonances are obtained. The width of the resonances is about twice as wide as the mean field theory predicts. This broadening reduces the height of the resonance curve and therefore the density of states by a factor of two. This yields an intuitive understanding for a previous result of the FAIR approach that it requires a much larger Coulomb interaction for the formation of a magnetic moment than the mean field theory.     

Radiative properties of diamagnetic levels in atoms: Dependence of transition probability on magnetic field strength

We study the effect of diamagnetic interaction on the probability of radiative transitions of an atom from states split by a field. We write the analytic expressions for the diamagnetic corrections to the matrix elements of transitions belonging to the Lyman and Balmer series and of transitions between arbitrary nondegenerate states in hydrogen. We also discuss the perturbation theory for transitions from degenerate diamagnetic states. The theory is based on expanding in powers of the field strength the eigenfunctions and eigenvalues of the matrix of diamagnetic interaction in the subspace of states with given principal and magnetic quantum numbers. The field changes the coefficients in both the superposition and the degenerate basis. To derive the analytic expressions for the higher-order matrix elements, we use the Sturm expansion of the reduced Coulomb Green’s function. We also elaborate on the features of the frequency dependence of the corrections to the radiative matrix elements, which correlate with the structure of the diamagnetic spectrum of excited levels. Finally, we establish that the magnetic field acts selectively on the diamagnetic components of emission lines: as the field strength increases, an increase in the intensity of certain lines is accompanied by a decrease in the intensity of the other lines. Zh. éksp. Teor. Fiz. 116, 1161–1183 (October 1999)     

Direct and spatially indirect excitons in GaAs/AlGaAs superlattices in strong magnetic fields

Luminescence and luminescence excitation spectra are used to study the energy spectrum and binding energies of direct and spatially indirect excitons in GaAs/AlaAs superlattices, with different widths of the electron and hole minibands, located in a high magnetic field perpendicular to the heterolayers. It is found that the ground state of the indirect excitons formed by electrons and holes and spatially separated between neighboring quantum wells lies between the ls ground state of the direct excitons and the continuum threshold for dissociated exciton states in the minibands. Indirect excitons in superlattices have a significant oscillator strength when the binding energy of the exciton exceeds the order of the width of the resulting miniband. The behavior of the binding energy of direct and indirect heavy hole excitons during changes in the tunneling coupling between the quantum wells is established. It is shown that a strong magnetic field, which intensifies the Coulomb interaction between the electron and hole in an exciton, weakens the bond in a system of symmetrically bound quantum wells. The spatially indirect excitons studied here are analogous to first order Wannier-Stark localized excitons in superlattices with inclined bands (when an electrical bias is applied), but in the present case the localization is of purely Coulomb origin. Zh. éksp. Teor. Fiz. 112, 1106–1118 (September 1997)     

Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

In this article we study the impact of the spin-orbit interaction on the electron quantum confinement for narrow gap semiconductor quantum dots. The model formulation includes: (1) the effective one-band Hamiltonian approximation; (2) the position- and energy-dependent quasi-particle effective mass approximation; (3) the finite hard wall confinement potential; and (4) the spin-dependent Ben Daniel-Duke boundary conditions. The Hartree-Fock approximation is also utilized for evaluating the characteristics of a two-electron quantum dot system. In our calculation, we describe the spin-orbit interaction which comes from both the spin-dependent boundary conditions and the Rashba term (for two-electron quantum dot system). It can significantly modify the electron energy spectrum for InAs semiconductor quantum dots built in the GaAs matrix. The energy state spin-splitting is strongly dependent on the dot size and reaches an experimentally measurable magnitude for relatively small dots. In addition, we have found the Coulomb interaction and the spin-splitting are suppressed in quantum dots with small height. Received 15 May 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

Signature of symmetry of laterally coupled quantum dots in far-infrared spectrum

We study the effect of structure asymmetry on the energy spectrum and the far-infrared spectrum (FIR) of a lateral coupled quantum dot. The calculated spectrum shows that the parity break of coupled quantum dot results in more coherent superpositions in the low-lying states and exhibits unique anti-crossing in the two-electron FIR spectrum modulated by a magnetic field. We also find that the Coulomb correlation effect can make the FIR spectrum of coupled quantum dot without strict parity deviate greatly from Kohn theorem, which is just contrary to the symmetric case. Our results therefore suggest that FIR spectrum may be used to determine the symmetry of coupled quantum dot and to evaluate the degree of Coulomb interaction.     

Localized charge bifurcation in the coupled quantum dots

We theoretically analyzed localized charge relaxation in a double quantum dot (QD) system coupled with continuous spectrum states in the presence of Coulomb interaction between electrons within a dot. We have found that for a wide range of the system parameters charge relaxation occurs through two stable regimes with significantly different relaxation rates. A certain instant of time exists in the system at which rapid switching between stable regimes takes place. We consider this phenomenon to be applicable for the creation of active elements in nano-electronics based on the fast transition effect between two stable states.     

On the Spatial Density Matrix for the Centre of Mass of a One-Dimensional Perfect Gas

We examine the reduced density matrix of the centre of mass on position basis considering a one-dimensional system of Nnoninteracting distinguishable particles in a infinitely deep square potential well. We find a class of pure states of the system for which the off-diagonal elements of the matrix above go to zero as Nincreases. This property holds also for the state vectors which are factorized in the single particle wave functions. In this last case, if the average energy of each particle is less than a common bound, the diagonal elements are distributed according to the normal law with a mean square deviation which becomes smaller and smaller as Nincreases towards infinity. Therefore when the state vectors are of the type considered we cannot experience spatial superpositions of the centre of mass and we may conclude that position is a preferred basis for the collective variable.     

General Decomposition of Radial Functions on Rn and Applications to N-Body Quantum Systems

We present a generalization of the Fefferman–de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions V on Rⁿ going to zero at infinity. This generalized decomposition can be used to extend previous results on N-body quantum systems with Coulomb interaction to a more general class of interactions. As an example of such an application, we derive the high density asymptotics of the ground state energy of jellium with Yukawa interaction in the thermodynamic limit, using a correlation estimate by Graf and Solovej.     

Energy of exciton in quantum dot for a potential containing Coulomb and quadratic terms

We theoretically study the energy levels of an exciton in a quantum dot. We take in to account both quadratic and Coulomb terms. Next, we use the method of series to solve the Schrödinger equation exactly. Using this formalism, we have calculated the exciton energy in both ground and excited states. The results are comparable to those of variational exact diagonolization, full configuration interaction, Hartree-Fock and 1/N methods. Our approach could be fitted for any desired material.     

S-Matrix formalism for particles interacting with phonon fields: Coherent state representation

We apply the quasiparticle picture to the interaction between a fermion and a boson field using a coherent states representation of theS matrix. Its matrix elements between single particle states are explicitly evaluated in terms of a path integral. The method is extended to include dispersion in the excitation spectrum and applied to the case of a metal with electron-hole symmetry. Its relation with perturbation theory is discussed and the second order perturbative result for polarons in insulators is recovered.     

强场中NO分子回归谱的长程散射矩阵的理论研究

采用半经典散射矩阵方法研究外磁场中高里德伯态双原子分子在能量范围为77010—77050cm^-1的回归谱.通过引进模型势简化强磁场中NO分子的高里德伯电子的势函数,找出其在核转动量子数分别为N=1,3,5的三个通道中的闭合轨道,重点分析了强磁场中NO分子的长程散射矩阵元实部的傅里叶变换谱与闭合轨道之间的一一对应关系.     

Exact wave functions for atomic electron interacting with photon fields

Many nonlinear quantum optical physics phenomena need more accurate wave functions and corresponding energy or quasienergy levels to account for. An analytic expression of wave functions with corresponding energy levels for an atomic electron interacting with a photon field is presented as an exact solution to the Schrödinger-like equation involved with both atomic Coulomb interaction and electron-photon interaction. The solution is a natural generalization of the quantum-field Volkov states for an otherwise free electron interacting with a photon field. The solution shows that an Nlevel atom in light form stationary states without extra energy splitting in addition to the Floquet mechanism. The treatment developed here with computing codes can be conveniently transferred to quantum optics in classical-field version as research tools to benefit the whole physics community.