Bipartite composite fermion States

We study a class of ansatz wave functions in which composite fermions form two correlated "partitions." These "bipartite" composite fermion states are demonstrated to be very accurate for electrons in a strong magnetic field interacting via a short-range 3-body interaction potential over a broad range of filling factors. Furthermore, this approach gives accurate approximations for the exact Coulomb ground state at 2+3/5 and 2+4/7 and is thus a promising candidate for the observed fractional quantum Hall states at the hole conjugate fractions at 2+2/5 and 2+3/7.     

Spectral properties of quantum dots influenced by a confining potential model

We obtain the exact energy spectra and corresponding wave functions of the spherical quantum dots for any (n,l) state in the presence of a combination of pseudo-harmonic, Coulomb and linear confining potential terms within the exact analytical iteration method (EAIM). The interaction potential model under consideration is labeled as the Cornell modified-plus-harmonic (CMpH) type which is a correction form to the harmonic, Coulomb and linear confining potential terms.     

Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation

The impact of the strongly attractive electromagnetic field of heavy nuclei on electrons in quasi-elastic (e, e') scattering is often accounted for by the effective momentum approximation. This method is a plane wave Born approximation which takes the twofold effect of the attractive nucleus on initial- and final-state electrons into account, namely the modification of the electron momentum in the vicinity of the nucleus, and the focusing of electrons towards the nuclear region leading to an enhancement of the corresponding wave function amplitudes. The focusing effect due to the attractive Coulomb field of a homogeneously charged sphere on a classical ensemble of charged particles incident on the field is calculated in the highly relativistic limit and compared to results obtained from exact solutions of the Dirac equation. The result is relevant for the theoretical foundation of the effective momentum approximation and describes the high-energy behavior of the amplitude of continuum Dirac waves in the potential of a homogeneously charged sphere. Our findings indicate that the effective momentum approximation is a useful approximation for the calculation of Coulomb corrections in (e, e') scattering off heavy nuclei for sufficiently high electron energies and momentum transfer.     

Edge excitations and non-Abelian statistics in the moore-read state: A numerical study in the presence of coulomb interaction and edge confinement

We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at a filling fraction nu = 5/2, with Coulomb interaction and a background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge +e/4 quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.     

Superconductivity in weakly correlated electron systems

We study the influence of the short-ranged Hubbard correlation U between the conduction electrons on the Cooper pair formation in normal (s-wave) superconductors. The Coulomb correlation is considered within the standard second order perturbation theory, which becomes exact in the weak coupling limit but goes beyond the simple Hartree-Fock treatment by yielding a finite lifetime of the quasiparticles at finite temperature. An attractive pairing interaction V, which may be mediated by the standard electron-phonon mechanism, is considered between nearest neighbor sites. A critical value for the attractive interaction is required to obtain a superconducting state. For finite temperature a gapless superconductivity is obtained due to the finite lifetime of the quasiparticles, i.e. the Coulomb correlation has a pair-breaking influence. The energy gap and depend very sensitively on U, V and band filling n and develop a maximum away from half filling as function of n. The ratio varies with n, being higher than the BCS value near half filling and reaching the BCS value for lower n. Received 17 February 1999     

Magnetoexcitons in nanostructures exhibiting cylindrical symmetry

The problem of an exciton in the cylindrical nanostructure exposed to an external static magnetic field is investigated. The theoretical model assumes anisotropic masses which are different inside and outside the nanostructure. The confinement potential has finite value at the boundaries and magnetic field is parallel to the axis of the cylinder. The screened Coulomb interaction between an electron and a hole is assumed. The consistent mathematical procedure is developed to calculate the magnetoexciton eigenfunctions and eigenenergies. Our method applies to the systems exhibiting cylindrical symmetry where, due to confinement effects accompanied by the e-h Coulomb interaction, the separation of relative- and center-of-mass motion is not possible. Numerical calculations have been performed for the quantum disk, the cylinder and the quantum rod. The magnetic field dependent energy spectrum and corresponding wave functions, expressed in terms of known one-particle electron and hole eigenfunctions, are calculated. Additionally, we point out the different role of Coulomb interaction in every case.     

Disorder and interaction-induced pairing in the addition spectra of quantum dots

We have numerically investigated the electron addition spectra in quantum dots containing a small number (N相似文献   

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.     

扩展哈伯德模型中原子团簇的结构和热力学性质研究

采用数值精确对角化方法,在加入了近邻电子库仑排斥作用的扩展哈伯德模型中对原子数N=5和N=6的原子团簇进行了研究.首先得到了对应于不同强度的电子在位库仑作用能U、近邻排斥作用能V,以及不同电子填充数的团簇的优化结构和相应的总自旋S.研究结果表明,电子的近邻排斥能V的引入会使团簇向成键数目减少的链状或星状结构改变.然后结合团簇的能级特征,分析了团簇的热容和磁化率等热力学特性,其中热容曲线的峰值位置可由团簇的低能激发给出合理的解释.     

Exact results for systems of electrons in the fractional quantum Hall regime

There has been a great deal of interest over the last two decades on the fractional quantum Hall effect, a novel quantum many-body liquid state of strongly correlated two-dimensional electronic systems in a strong perpendicular magnetic field. The most pronounced fractional quantum Hall states occur at odd denominator filling factors of the lowest Landau level and are described by the Laughlin wave function. It is well known that exact closed-form solutions for many-body wave functions, including the Laughlin wave function, are generally very rare and hard to obtain. In this work we present some exact results corresponding to small systems of electrons in the fractional quantum Hall regime at odd denominator filling factors. Use of Jacobi coordinates is the key tool that facilitates the exact calculation of various quantities. Expressions involving integrals over many variables are considerably simplified with the help of Jacobi coordinates allowing us to calculate exactly various quantities corresponding to systems with several electrons.     

Energy-transfer rate in a double-quantum-well system due to Coulomb coupling

We study the energy-transfer rate for electrons in a double-quantum-well structure, where the layers are coupled through screened Coulomb interactions. The energy-transfer rate between the layers (similar to the Coulomb drag effect in which the momentum-transfer rate is considered) is calculated as functions of electron densities, interlayer spacing, the temperature difference of the 2DEGs, and the electron drift velocity in the drive layer. We employ the full wave vector and frequency-dependent random-phase approximation at finite temperature to describe the effective interlayer Coulomb interaction. We find that the collective modes (plasmons) of the system play a dominant role in the energy-transfer rates.     

Equilibrium properties of two-component classical plasmas

Two-component overall neutral classical Coulomb Gas is considered in the canonical ensemble for any value of the space dimensionality ν. The equilibrium properties, i.e. pair correlations and thermodynamic functions are investigated in two complementary ways. The first one is adequate in considering the low temperature range and uses the “molecular” interaction within a pair of unlike charges as a zero order starting point. On the other hand, the high-temperature fully ionized and translation-invariant plasma is considered within the nodal expression with respect to the classical plasma parameter. These two ways are possible through the use of effective temperature-dependent classical interaction for ν > 2. As a by-product, we obtain a unified treatment of the Coulomb Gas thermal properties with respect to dimensionality (integer or real). We also obtain a contrasting comparison with corresponding properties of the one component plasma model which are already known. In this analysis the ν = 2 two-component Coulomb Gas seems to be a landmark for the other TCP'₈. I do not consider degeneracy effects. I consider diffraction corrections in a first order expansion with respect to the Coulomb interaction, in the high-temperature range. The “Hydrogen atom” spectrum is explained for all ν. The long-range hypernetted chain resummation of the pair correlation functions asymptotic behavior does not hold for symmetrical (Z₁ = ?Z₂) plasmas; the corresponding onset of short-range order disappears when the plasma parameter increases. The modified long- and short-range behaviors of the pair correlation functions are then displayed with the canonical thermodynamics.     

Approximate scattering solutions of the dirac equation for electron-nucleus processes in light nuclei

Scattering solutions of the second-order Dirac equation for the case of the Coulomb potential and which are correct to first order in the coupling constantZe ²/hc are investigated and found to describe pure Coulomb scattering equally well as the Sommerfeld-Maue wave functions. Errors introduced by the use of these solutions are studied in a numerical calculation of cross sections for nuclear electric-quadrupole excitation by high-energy electrons. The use of these wave functions is suggested for simplified calculations of lowest-order Coulomb corrections to Born approximation results for various electron-nucleus processes.     

Ferromagnetism in the Hubbard model

Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrödinger equation hasN _d-fold degenerate ground states. The degeneracyN _d is proportional to the total number of sites ||. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to=N _d/(2||), and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.     

Localization of a pair of bound particles in a random potential

We study the localization length l_c of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle. For a pair with many bound states N the localization length is proportional to N, independently of the form of the two particle interaction. For the case of two bound states, we present an exact solution for the corresponding Fokker–Planck equation and demonstrate that l_c depends sensitively on the shape of the interaction potential and the symmetry of the bound state wave functions.     

The influence of Coulomb interaction on transport through mesoscopic two-barrier structures

We investigate the influence of the Coulomb interaction on the energy spectrum of a finite number of electrons in a geometrically confined quantum mechanical system. The spectrum is calculated numerically using the Slater determinants of the one-electron states as basis set. It is found to be dominated by the Coulomb repulsion when the system is large. Coulomb and exchange matrix elements for a given combination of four one-electron states are of the same order of magnitude. As a consequence, the energy difference between the ground states of the (N+1)- and theN-electron system is an order of magnitude smaller than each of the matrix elements, although being much larger than the separation of the one-electron energy levels. We discuss the importance of the interaction effects for the explanation of the recently observed resonant behavior of the electronic transport through quantum dots.     

Long-range Coulomb forces in DIS: missed radiative corrections?

The Born approximation, one photon exchange, used for DIS (deep inelastic scattering) is subject to virtual radiative corrections which are related to the long-range Coulomb forces. They may be sizeable for heavy nuclei since Zα is not a small parameter. So far, these corrections are known only for two processes, elastic scattering and bremsstrahlung on the Coulomb field of a point-like target. While the former amplitude acquires only a phase, in the latter case also the cross-section is modified. Although the problem of Coulomb corrections for DIS on nuclei is extremely difficult, it should be challenged rather than “swept under the carpet”. The importance of these radiative corrections is questioned in the present paper. We show that, in the simplest case of a constant hadronic current, the Coulomb corrections provide a phase to the Born amplitude, therefore the cross-section remains the same. Inclusion of more realistic hadronic dynamics changes this conclusion. The example of coherent production of vector mesons off nuclei reveals large effects. So far a little progress has been made deriving lepton wave functions in the Coulomb field of an extended target. Employing available results based on the first-order approximation in Zα, we conclude that the Coulomb corrections are still important for heavy nuclei. We also consider an alternative approach for extended nuclear targets, the eikonal approximation, which we demonstrate to reproduce the known exact results for Coulomb corrections. Calculating electroproduction of vector mesons, we again arrive at a large deviation from the Born approximation. We conclude that one should accept with caution the experimental results for nuclear effects in DIS based on analyses done in the Born approximation. Received: 16 May 2001 / Accepted: 4 July 2001     

Molecular dynamics study of a classical two-dimensional electron system: positional and orientational orders

Molecular dynamics simulation is used to investigate the crystallization of a classical two-dimensional electron system, in which electrons interact with the Coulomb repulsion. From the positional and the orientational correlation functions, we have found an indication that the solid phase has a quasi-long-range (power-law correlated) positional order and a long-range orientational order. This implies that the long-range 1/r system shares the absence of the true long-range crystalline order at finite temperatures with short-range ones to which Mermin's theorem applies. We also discuss the existence of the “hexatic” phase predicted by the Kosterlitz–Thouless–Halperin–Nelson–Young theory.     

Finite clusters of fast-rotating spinless bosons in a harmonic trap

Rapidly rotating two-dimensional ultracold Bose–Einstein condensates of spinless bosons in a harmonic trap have attracted considerable interest during the recent years. It is expected that, in the fast-rotation limit, the system of bosons will exhibit collective behavior similar to that of two-dimensional electrons in the fractional quantum Hall effect regime. It is predicted that the most robust correlated bosonic state in this regime will be the Bose Laughlin state at a half filling factor. An exact treatment of such a state is generally a formidable task due to the inherent many-particle nature of the wave function. We report in this work that a transformation to Jacobi coordinates allows one to obtain much desirable exact analytic closed-form expressions for various quantities of interest corresponding to a Bose Laughlin wave function for various finite systems of particles.