Vector Potential and Berry phase-induced Force

We present a general theoretical framework for the exact treatment of a hybrid system that is composed of a quantum subsystem and a classical subsystem. When the quantum subsystem is dynamically fast and the classical subsystem is slow, a vector potential is generated with a simple canonical transformation. This vector potential, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics; on the other hand, it yields a Lorentz-like force in the slow classical dynamics. In this way, the pure phase (Berry phase) of a wavefunction is linked to a physical force.Comment: 4 pages, 1 figur

Anomalous Hall effect in the Co-based Heusler compounds Co2_{2}FeSi and Co2_{2}FeAl

The anomalous Hall effect (AHE) in the Heusler compounds Co$_{2}$FeSi and Co$_{2}$FeAl is studied in dependence of the annealing temperature to achieve a general comprehension of its origin. We have demonstrated that the crystal quality affected by annealing processes is a significant control parameter to tune the electrical resistivity $\rho_{xx}$ as well as the anomalous Hall resistivity $\rho_{ahe}$. Analyzing the scaling behavior of $\rho_{ahe}$ in terms of $\rho_{xx}$ points to a temperature-dependent skew scattering as the dominant mechanism in both Heusler compounds

Gravitational wave energy spectrum of a parabolic encounter

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (~10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ~10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of rp > 20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by LISA.Comment: 5 pages, 3 figures. Minor changes to match published version; figure 1 corrected; references adde

Evidence for the Validity of the Berry-Robnik Surmise in a Periodically Pulsed Spin System

We study the statistical properties of the spectrum of a quantum dynamical system whose classical counterpart has a mixed phase space structure consisting of two regular regions separated by a chaotical one. We make use of a simple symmetry of the system to separate the eigenstates of the time-evolution operator into two classes in agreement with the Percival classification scheme \cite{Per}. We then use a method firstly developed by Bohigas et. al. \cite{BoUlTo} to evaluate the fractional measure of states belonging to the regular class, and finally present the level spacings statistics for each class which confirm the validity of the Berry-Robnik surmise in our model.Comment: 15 pages, 9 figures available upon request, Latex fil

Geometric phase for a dimerized disordered continuum: Topological shot noise

Geometric phase shift associated with an electron propagating through a dimerized-disordered continuum is shown to be 0, or $\pm \pi$ (modulo 2$\pi$), according as the associated circuit traversed in the two-dimensional parameter space excludes, or encircles a certain singularity. This phase-shift is a topological invariant. Its discontinuous dependence on the electron energy and disorder implies a statistical spectral and conductance fluctuation in a corresponding mesoscopic system. Inasmuch as the fluctuation derives from the discreteness of the phase shift, it may aptly be called a topological shot-noise.Comment: 10 pages(LATEX) + 1 figure, (revised version). Will appear in Europhys. Let

Dephasing in matter-wave interferometry

We review different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and neutral particles with permanent dipole moments. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore, be observed. We analyze different trajectories in order to show the dependence of the decoherence factor with the velocity of the particles.Comment: 9 pages, 1 eps-figure. To appear in J. Phys. A: Math. Ge

Quantum effects in the evolution of vortices in the electromagnetic field

We analyze the influence of electron-positron pairs creation on the motion of vortex lines in electromagnetic field. In our approach the electric and magnetic fields satisfy nonlinear equations derived from the Euler-Heisenberg effective Lagrangian. We show that these nonlinearities may change the evolution of vortices.Comment: REVTEX4 and 5 EPS figure

Band Distributions for Quantum Chaos on the Torus

Band distributions (BDs) are introduced describing quantization in a toral phase space. A BD is the uniform average of an eigenstate phase-space probability distribution over a band of toral boundary conditions. A general explicit expression for the Wigner BD is obtained. It is shown that the Wigner functions for {\em all} of the band eigenstates can be reproduced from the Wigner BD. Also, BDs are shown to be closer to classical distributions than eigenstate distributions. Generalized BDs, associated with sets of adjacent bands, are used to extend in a natural way the Chern-index characterization of the classical-quantum correspondence on the torus to arbitrary rational values of the scaled Planck constant.Comment: 12 REVTEX page

Thermodynamics of Finite Quantum Systems: Application to Spin Magnetism II

We extend our study of thermodynamics of a Kubo particle to temperatures smaller than the interlevel spacing. We obtain the distribution functions of spin susceptibility and heat capacity for Poisson and Wigner-Dyson level statistics. We evaluate the line shape of the Knight shift due to spin effects both in a single particle and for the ensemble average and compare it with orbital and spin-orbit contributions.Comment: 20 pages (16 text, 4 figures) uu-encoded, z-compressed PostScript. Latest versions of manuscripts available at http://physuna.phs.uc.edu/professors/serota.html or by e-mail, by request from [email protected]

Vortex lines of the electromagnetic field

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schroedinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schroedinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of Maxwell equations with embedded vortex lines are given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.