Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators

We discuss some basic tools for an analysis of one-dimensionalquantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros.Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.Comment: 29 page

Quantum Electrodynamics of the Helium Atom

Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and radiative corrections to the Schr"odinger energy. Average values of these operators can be calculated using a variational Schr"odinger wave function.Comment: 23 pages, revte

Quantitative lower bounds for the full Boltzmann equation, Part I: Periodic boundary conditions

We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some uniform bounds on some hydrodynamic quantities. This lower bound is independent of time and space. When the collision kernel satisfies Grad's cutoff assumption, the lower bound is a global Maxwellian and its asymptotic behavior in velocity is optimal, whereas for non-cutoff collision kernels the lower bound we obtain decreases exponentially but faster than the Maxwellian. Our results cover solutions constructed in a spatially homogeneous setting, as well as small-time or close-to-equilibrium solutions to the full Boltzmann equation in the torus. The constants are explicit and depend on the a priori bounds on the solution.Comment: 37 page

Graphene Rings in Magnetic Fields: Aharonov-Bohm Effect and Valley Splitting

We study the conductance of mesoscopic graphene rings in the presence of a perpendicular magnetic field by means of numerical calculations based on a tight-binding model. First, we consider the magnetoconductance of such rings and observe the Aharonov-Bohm effect. We investigate different regimes of the magnetic flux up to the quantum Hall regime, where the Aharonov-Bohm oscillations are suppressed. Results for both clean (ballistic) and disordered (diffusive) rings are presented. Second, we study rings with smooth mass boundary that are weakly coupled to leads. We show that the valley degeneracy of the eigenstates in closed graphene rings can be lifted by a small magnetic flux, and that this lifting can be observed in the transport properties of the system.Comment: 12 pages, 9 figure

Effects of Fermi energy, dot size and leads width on weak localization in chaotic quantum dots

Magnetotransport in chaotic quantum dots at low magnetic fields is investigated by means of a tight binding Hamiltonian on L x L clusters of the square lattice. Chaoticity is induced by introducing L bulk vacancies. The dependence of weak localization on the Fermi energy, dot size and leads width is investigated in detail and the results compared with those of previous analyses, in particular with random matrix theory predictions. Our results indicate that the dependence of the critical flux Phi_c on the square root of the number of open modes, as predicted by random matrix theory, is obscured by the strong energy dependence of the proportionality constant. Instead, the size dependence of the critical flux predicted by Efetov and random matrix theory, namely, Phi_c ~ sqrt{1/L}, is clearly illustrated by the present results. Our numerical results do also show that the weak localization term significantly decreases as the leads width W approaches L. However, calculations for W=L indicate that the weak localization effect does not disappear as L increases.Comment: RevTeX, 8 postscript figures include

Mesoscopic Electron and Phonon Transport through a Curved Wire

There is great interest in the development of novel nanomachines that use charge, spin, or energy transport, to enable new sensors with unprecedented measurement capabilities. Electrical and thermal transport in these mesoscopic systems typically involves wave propagation through a nanoscale geometry such as a quantum wire. In this paper we present a general theoretical technique to describe wave propagation through a curved wire of uniform cross-section and lying in a plane, but of otherwise arbitrary shape. The method consists of (i) introducing a local orthogonal coordinate system, the arclength and two locally perpendicular coordinate axes, dictated by the shape of the wire; (ii) rewriting the wave equation of interest in this system; (iii) identifying an effective scattering potential caused by the local curvature; and (iv), solving the associated Lippmann-Schwinger equation for the scattering matrix. We carry out this procedure in detail for the scalar Helmholtz equation with both hard-wall and stress-free boundary conditions, appropriate for the mesoscopic transport of electrons and (scalar) phonons. A novel aspect of the phonon case is that the reflection probability always vanishes in the long-wavelength limit, allowing a simple perturbative (Born approximation) treatment at low energies. Our results show that, in contrast to charge transport, curvature only barely suppresses thermal transport, even for sharply bent wires, at least within the two-dimensional scalar phonon model considered. Applications to experiments are also discussed.Comment: 9 pages, 11 figures, RevTe

GENERALIZED CIRCULAR ENSEMBLE OF SCATTERING MATRICES FOR A CHAOTIC CAVITY WITH NON-IDEAL LEADS

We consider the problem of the statistics of the scattering matrix S of a chaotic cavity (quantum dot), which is coupled to the outside world by non-ideal leads containing N scattering channels. The Hamiltonian H of the quantum dot is assumed to be an M x N hermitian matrix with probability distribution P(H) ~ det[lambda^2 + (H - epsilon)^2]^[-(beta M + 2- beta)/2], where lambda and epsilon are arbitrary coefficients and beta = 1,2,4 depending on the presence or absence of time-reversal and spin-rotation symmetry. We show that this ``Lorentzian ensemble'' agrees with microscopic theory for an ensemble of disordered metal particles in the limit M -> infinity, and that for any M >= N it implies P(S) ~ |det(1 - \bar S^{\dagger} S)|^[-(beta M + 2 - beta)], where \bar S is the ensemble average of S. This ``Poisson kernel'' generalizes Dyson's circular ensemble to the case \bar S \neq 0 and was previously obtained from a maximum entropy approach. The present work gives a microscopic justification for the case that the chaotic motion in the quantum dot is due to impurity scattering.Comment: 15 pages, REVTeX-3.0, 2 figures, submitted to Physical Review B

Microscopic Cluster Model for Exotic Nuclei

For a better understanding of the dynamics of exotic nuclei it is of crucial importance to develop a practical microscopic theory easy to be applied to a wide range of masses. Theoretically the basic task consists in formulating an easy solvable theory able to reproduce structures and transitions of known nuclei which should be then used to calculate the sparely known properties of proton- or neutron-rich nuclei. In this paper we start by calculating energies and distributions of A\leq4 nuclei withing a unitary correlation model restricted to include only two-body correlations. The structure of complex nuclei is then calculated extending the model to include correlation effects of higher order.Comment: 10 pages, 4 figures. Final Version to be published in "Progress of Particle and Nuclear Physics (2007

Reflectance Fluctuations in an Absorbing Random Waveguide

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an $N$-mode disordered waveguide with weak absorption $\gamma$ per mean free path. Two distinct regimes are identified. The regime $\gamma N^2\gg1$ shows universal fluctuations. With increasing length $L$ of the waveguide, the variance of the reflectance changes from the value $2/15 N^2$, characteristic for universal conductance fluctuations in disordered wires, to another value $1/8 N^2$, characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value $1/3 N$ to $1/4 N$. In the regime $\gamma N^2\ll1$, the large-$L$ distribution of the reflectance $R$ becomes very wide and asymmetric, $P(R)\propto (1-R)^{-2}$ for $R\ll 1-\gamma N$.Comment: 7 pages, RevTeX, 2 postscript figure

Magnetic Scanning Tunneling Microscopy with a Two-Terminal Non-Magnetic Tip: Quantitative Results

We report numerical simulation result of a recently proposed \{P. Bruno, Phys. Rev. Lett {\bf 79}, 4593, (1997)\} approach to perform magnetic scanning tunneling microscopy with a two terminal non-magnetic tip. It is based upon the spin asymmetry effect of the tunneling current between a ferromagnetic surface and a two-terminal non-magnetic tip. The spin asymmetry effect is due to the spin-orbit scattering in the tip. The effect can be viewed as a Mott scattering of tunneling electrons within the tip. To obtain quantitative results we perform numerical simulation within the single band tight binding model, using recursive Green function method and Landauer-B\"uttiker formula for conductance. A new model has been developed to take into account the spin-orbit scattering off the impurities within the single-band tight-binding model. We show that the spin-asymmetry effect is most prominent when the device is in quasi-ballistic regime and the typical value of spin asymmetry is about 5%.Comment: 5 pages, Late