Characteristic Potentials for Mesoscopic Rings Threaded by an Aharonov-Bohm Flux

Electro-static potentials for samples with the topology of a ring and penetrated by an Aharonov-Bohm flux are discussed. The sensitivity of the electron-density distribution to small variations in the flux generates an effective electro-static potential which is itself a periodic function of flux. We investigate a simple model in which the flux sensitive potential leads to a persistent current which is enhanced compared to that of a loop of non-interacting electrons. For sample geometries with contacts the sensitivity of the electro-static potential to flux leads to a flux-induced capacitance. This capacitance gives the variation in charge due to an increment in flux. The flux-induced capacitance is contrasted with the electro-chemical capacitance which gives the variation in charge due to an increment in an electro-chemical potential. The discussion is formulated in terms of characteristic functions which give the variation of the electro-static potential in the interior of the conductor due to an increment in the external control parameters (flux, electro-chemical potentials). Paper submitted to the 16th Nordic Semiconductor Meeting, Laugarvatan, Iceland, June 12-15, 1994. The proceedings will be published in Physica Scripta.Comment: 23 pages + 4 figures, revtex, IBM-RC1955

The Origin of Degeneracies and Crossings in the 1d Hubbard Model

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyze in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wave functions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter independent symmetry.Comment: 25 pages, 12 figure

Nonperturbative Coherent Population Trapping: An Analytic Model

Coherent population trapping is shown to occur in a driven symmetric double-well potential in the strong-field regime. The system parameters have been chosen to reproduce the $0^{-}\leftrightarrow 3^{+}$ transition of the inversion mode of the ammonia molecule. For a molecule initially prepared in its lower doublet we find that, under certain circumstances, the $3^{+}$ level remains unpopulated, and this occurs in spite of the fact that the laser field is resonant with the $0^{-}\leftrightarrow 3^{+}$ transition and intense enough so as to strongly mix the $0^{+}$ and $0^{-}$ ground states. This counterintuitive result constitutes a coherent population trapping phenomenon of nonperturbative origin which cannot be accounted for with the usual models. We propose an analytic nonperturbative model which accounts correctly for the observed phenomenon.Comment: 5 pages, 2 figure

Dynamic response of mesoscopic metal rings and thermodynamics at constant particle number

We show by means of simple exact manipulations that the thermodynamic persistent current $I ( \phi , N )$ in a mesoscopic metal ring threaded by a magnetic flux $\phi$ at constant particle number $N$ agrees even beyond linear response with the dynamic current $I_{dy} ( \phi , N )$ that is defined via the response to a time-dependent flux in the limit that the frequency of the flux vanishes. However, it is impossible to express the disorder average of $I_{dy} ( \phi , N )$ in terms of conventional Green's functions at flux-independent chemical potential, because the part of the dynamic response function that involves two retarded and two advanced Green's functions is not negligible. Therefore the dynamics cannot be used to map a canonical average onto a more tractable grand canonical one. We also calculate the zero frequency limit of the dynamic current at constant chemical potential beyond linear response and show that it is fundamentally different from any thermodynamic derivative.Comment: 19 pages, postscript (uuencoded, compressed

Effective-field-theory approach to persistent currents

Using an effective-field-theory (nonlinear sigma model) description of interacting electrons in a disordered metal ring enclosing magnetic flux, we calculate the moments of the persistent current distribution, in terms of interacting Goldstone modes (diffusons and cooperons). At the lowest or Gaussian order we reproduce well-known results for the average current and its variance that were originally obtained using diagrammatic perturbation theory. At this level of approximation the current distribution can be shown to be strictly Gaussian. The nonlinear sigma model provides a systematic way of calculating higher-order contributions to the current moments. An explicit calculation for the average current of the first term beyond Gaussian order shows that it is small compared to the Gaussian result; an order-of-magnitude estimation indicates that the same is true for all higher-order contributions to the average current and its variance. We therefore conclude that the experimentally observed magnitude of persistent currents cannot be explained in terms of interacting diffusons and cooperons.Comment: 12 pages, no figures, final version as publishe

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunneling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunneling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics. Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions. In applying all of the above models to physical situations, the need for an exact analysis of small scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.Comment: 49 pages, 1 figure, invited review for J. Phys. A., published version available at http://stacks.iop.org/JPhysA/36/R6

Current-spin-density functional study of persistent currents in quantum rings

We present a numerical study of persistent currents in quantum rings using current spin density functional theory (CSDFT). This formalism allows for a systematic study of the joint effects of both spin, interactions and impurities for realistic systems. It is illustrated that CSDFT is suitable for describing the physical effects related to Aharonov-Bohm phases by comparing energy spectra of impurity-free rings to existing exact diagonalization and experimental results. Further, we examine the effects of a symmetry-breaking impurity potential on the density and current characteristics of the system and propose that narrowing the confining potential at fixed impurity potential will suppress the persistent current in a characteristic way.Comment: 7 pages REVTeX, including 8 postscript figure

Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlev\'e equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.Comment: AMS-Tex Us