Hartree-Fock ground state of the three-dimensional electron gas

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin-density wave state. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the unrestricted HF ground state of the three-dimensional electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the spin-density wave is smaller than 2k(F). The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.     

Exact broken-symmetry states and Hartree–Fock solutions for quantum dots at high magnetic fields

Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree–Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave functions. The broken symmetry states with semi-classical charge density constructed from superpositions of the ED solutions are compared to the UHF results. UHF overlooks the dependence of the few-electron wave functions on the actual relative positions of electrons localized in different charge puddles and partially compensates for this neglect by an exaggerated separation of charge islands which are more strongly localized than in the exact broken-symmetry states.     

Magnetic properties of quantum dots and rings

Exact many-body methods as well as current-spin-density functional theory are used to study the magnetism and electron localization in two-dimensional quantum dots and quasi-one-dimensional quantum rings. Predictions of broken-symmetry solutions within the density functional model are confirmed by exact configuration interaction (CI) calculations: In a quantum ring the electrons localize to form an antiferromagnetic chain which can be described with a simple model Hamiltonian. In a quantum dot the magnetic field localizes the electrons as predicted with the density functional approach. Received 5 December 2000     

A density matrix approach to the dynamical properties of a two-site Holstein model

The two-site Holstein model represents a first non-trivial paradigm for the interaction between an itinerant charge with a quantum oscillator, a very common topic in different ambits. Exact results can be achieved both analytically and numerically, nevertheless it can be useful to compare them with approximate, semi-classical techniques in order to highlight the role of quantum effects. In this paper we consider the adiabatic limit in which the oscillator is slower than the electron. A density matrix approach is introduced for studying the charge dynamics and the exact results are compared with two different approximations: a Born-Oppenheimer-based Static Approximation for the oscillator (SA) and a Quantum-classical (QC) dynamics.     

Exact relaxation in a class of nonequilibrium quantum lattice systems

A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we introduce an experimentally accessible setting where relaxation to a steady state is exact, namely, for the Bose-Hubbard model quenched from a Mott quantum phase to the free strong superfluid regime. We rigorously prove that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments--thus maximizing the entanglement. Remarkably, for this to be true, no time average is necessary. Our argument includes a central limit theorem and exploits the finite speed of information transfer. We also show that for all periodic initial configurations (charge density waves) the system relaxes locally, and identify experimentally accessible signatures in optical lattices as well as implications for the foundations of statistical mechanics.     

Electron waiting times in mesoscopic conductors

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with level spacing statistics and random matrix theory.     

Diagonalizations on a correlated basis

Unsymmetrical quantum-dot systems are generally difficult to study using wave-function techniques, like quantum Monte Carlo (QMC) or exact diagonalization (ED) methods. The initial trial wave function for Monte Carlo methods is difficult to find, and the exact diagonalization method can only handle very few particles.In this article a two-dimensional semiconductor quantum dot containing a non-centered impurity ion is studied, using a new exact wave-function method. Results are analyzed and compared to density-functional-theory calculations. The computational method allows one to relax the commonly used lowest-Landau level (LLL) approximation, and it's effects are studied, e.g., on the charge and current density profiles.The method, which is a combination of QMC and ED methods, is described. It combines the scalability of Monte Carlo methods with the benefits of exact diagonalization, and allows one to accurately obtain the wave function for unsymmetrical quantum dots up to more than ten electrons. Also, excited states are accessible and are analyzed in this article.     

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov’s fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current density correlation function is found to be integrable in space, in both classical and quantum regimes.     

Absolute stability limit for relativistic charged spheres

We find an exact solution for the stability limit of relativistic charged spheres for the case of constant gravitational mass density and constant charge density. We argue that this provides an absolute stability limit for any relativistic charged sphere in which the gravitational mass density decreases with radius and the charge density increases with radius. We then provide a cruder absolute stability limit that applies to any charged sphere with a spherically symmetric mass and charge distribution. We give numerical results for all cases. In addition, we discuss the example of a neutral sphere surrounded by a thin, charged shell.     

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     

Invariants and nonequilibrium density matrices

A new method of calculating nonequilibrium density matrices with the aid of the quantum integrals of motion is proposed. The method is shown to be very effective in the case of systems described by means of quadratic Hamiltonians. The possibility of constructing phenomenological nonstationary Hamiltonians for a wide class of dissipative systems is discussed. The exact formulas for nonequilibrium density matrices of arbitrary quadratic systems are obtained. The quantum problem of the motion of a charged particle in uniform electric and magnetic fields in the presence of a frictional force proportional to the velocity is solved exactly by means of introducing the new phenomenological Hamiltonian.     

Spectral Densities and Partition Functions of Modular Quantum ystems as Derived from a Central Limit Theorem

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite number of subsystems. Even for only small numbers of subsystems we find good accordance with some known, exact results.     

Semi-statistical model for electron densities in positive and negative ions

Electron density for ions from a semi-statistical model has been obtained and used to calculate the potential at the nucleus and the diamagnetic susceptibility. We have taken the quantum mechanical density close to the nucleus and have matched it with the statistical density at some distancer ₀. The electron density is found to be finite close to the nucleus and exponentially decreasing at large distances. Moreover, the kinetic energy density goes to zero close to nucleus in agreement with the Hartree-Fock (HF) result. The potential at the nucleus converges and is in fair agreement with the HF value. The diamagnetic susceptibility increases with increasing atomic number.     

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.     

Nonlinear shielding and electron density enhancement in moderately coupled plasmas

As the plasma coupling grows, the electron density in the vicinity of the central ion increases appreciably, and the atomic reaction rates evaluated with the free Maxwell distribution for weakly coupled plasmas require modifications. The Maxwell–Boltzmann distribution, expressed in terms of the screened ionic potential, provides a simple way to correct for the density change. Several adjustments of the distribution are considered, including the nonlinear shielding, the quantum effect, the charge neutrality condition, and electron–electron correlation. The nonlinear coupling is shown to add to the linearly shielded potential a new component with much stronger shielding and generally reduces the strength of the linear potential. A simple model for the density enhancement is then constructed for moderately coupled plasmas, which may be applied to approximately correct the existing rates which were obtained in the weak coupling limit.     

Spin-filtering and charge- and spin-switching effects in a quantum wire with periodically attached stubs

Spin-dependent electron transport in a periodically stubbed quantum wire in the presence of Rashba spin-orbit interaction (SOI) is studied via the nonequilibrium Green’s function (GF) method combined with the Landauer-Büttiker formalism. By comparing with a straight Rashba quantum wire, the magnitude of spin conductance can be enhanced obviously. In addition, the charge and spin switching can also be found in the considered system. The mechanism of these transport properties is revealed by analyzing the total charge density and spin-polarized density distributions in the stubbed quantum wire. Furthermore, periodic spin-density islands with high polarization are also found inside the stubs, owing to the interaction between the charge density islands and the Rashba SOI-induced effective magnetic field. These interesting findings may be useful in further understanding of the transport properties of low-dimensional systems and in devising an all-electrical multifunctional spintronic device based on the proposed structure.     

Bifurcations and the positiveP-representation

The role of quantum fluctuations in dynamical systems can be described conveniently in terms of quasi-probabilities, since this concept bears a strong but formal analogy to classical statistical mechanics. At a closer look, however, only the method of the positiveP-representation has the potential of associating a classical stochastic process with a nonlinear quantum mechanical problem. The doubling of phase space required by this concept not only introduces new and unphysical dimensions, but also doubles the dimensions of the attractors of the associated deterministic system. A focus of the classical process remains a focus in the extended phase space, but a limit cycle is turned into a two-dimensional manifold, which due to the analytic properties of the method is hyperbolic in nature and extends to infinity. A strange attractor with its broken dimensionality also doubles its dimensions, since the Lyapunov exponents of the deterministic evolution in the extended phase space come in pairs as well. The fluctuating forces distribute the probability density about the attractors. In case of a focus, the probability density remains confined to the neighbourhood of the point of attraction, while for a limit cycle the distribution continues to spread over the entire two-dimensional manifold and a stationary solution for the probability density in the doubled phase space does not exist.     

On the electrostatic potential in crystalline systems where the charge density is expanded in Gaussian functions

Methods for the evaluation of the electrostatic potential in systems which are periodic in three dimensions, where the electronic charge distribution is expanded as a linear combination of Gaussian functions of arbitrary quantum number, are described. An ‘exact’ method based on the Ewald potential function is derived, and an approximate scheme using a distributed point multipole representation of the charge distribution is then presented. Recursion formulae enable Cartesian and thence spherical derivatives (of any order) of the potential to be computed. Related procedures for the evaluation of the Fock matrix elements and the coulombic contribution to the total energy per unit cell are described. Tests of the exact and approximate procedures establish their relative accuracy and cost in the MgO, Si and Si₁₂O₂₄ systems in the rock-salt, diamond and chabazite structures, respectively. Applications include a study of the electric field gradient at the C, N and O sites in urea (crystalline and molecular), and contour mapping of the electrostatic potential in MgO and Si₁₂O₂₄.     

Semiclassical model of a one-dimensional quantum dot

A one-dimensional quantum dot at zero temperature is used as an example for developing a consistent semiclassical method. The method can also be applied to systems of higher dimension that admit separation of variables. For electrons confined by a quartic potential, the Thomas-Fermi approximation is used to calculate the self-consistent potential, the electron density distribution, and the total energy as a function of the electron number and the effective electron charge representing the strength of interaction between electrons. Use is made of scaling with respect to the electron number. An energy quantization condition is derived. The oscillating part of the electron density and both gradient and shell corrections to the total electron energy are calculated by using the results based on the Thomas-Fermi model and analytical expressions derived in this study. The dependence of the shell correction on the interaction strength is examined. Comparisons with results calculated by the density functional method are presented. The relationship between the results obtained and the Strutinsky correction is discussed.     

Correlation-driven heavy-fermion formation in LiV2O4

Optical reflectivity measurements were performed on a single crystal of the d-electron heavy-fermion (HF) metal LiV2O4. Our results evidence the highly incoherent charge dynamics above T* approximately 20 K and the redistribution of the spectral weight of the optical conductivity over broad energy scales ( approximately 5 eV) as the quantum coherence of the charge carriers is recovered. This reveals that LiV2O4 is close to a correlation-driven insulating state and indicates that, in sharp contrast to f-electron HF Kondo-lattice systems, strong electronic correlation effects dominate the heavy quasiparticle formation in LiV2O4.