Diffraction and quasiclassical limit of the Aharonov--Bohm effect

Since the Aharonov-Bohm effect is the purely quantum effect that has no analogues in classical physics, its persistence in the quasiclassical limit seems to be hardly possible. Nevertheless, we show that the scattering Aharonov-Bohm effect does persist in the quasiclassical limit owing to the diffraction, i.e. the Fraunhofer diffraction in the case when space outside the enclosed magnetic flux is Euclidean, and the Fresnel diffraction in the case when the outer space is conical. Hence, the enclosed magnetic flux can serve as a gate for the propagation of short-wavelength, almost classical, particles. In the case of conical space, this quasiclassical effect which is in principle detectable depends on the particle spin.Comment: 12 pages, minor changes, references update

Re-parameterization Invariance in Fractional Flux Periodicity

We analyze a common feature of a nontrivial fractional flux periodicity in two-dimensional systems. We demonstrate that an addition of fractional flux can be absorbed into re-parameterization of quantum numbers. For an exact fractional periodicity, all the electronic states undergo the re-parameterization, whereas for an approximate periodicity valid in a large system, only the states near the Fermi level are involved in the re-parameterization.Comment: 4 pages, 1 figure, minor changes, final version to appear in J. Phys. Soc. Jp

Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure

The Locality Problem in Quantum Measurements

The locality problem of quantum measurements is considered in the framework of the algebraic approach. It is shown that contrary to the currently widespread opinion one can reconcile the mathematical formalism of the quantum theory with the assumption of the existence of a local physical reality determining the results of local measurements. The key quantum experiments: double-slit experiment on electron scattering, Wheeler's delayed-choice experiment, the Einstein-Podolsky-Rosen paradox, and quantum teleportation are discussed from the locality-problem point of view. A clear physical interpretation for these experiments, which does not contradict the classical ideas, is given.Comment: Latex, 40 pages, 7 figure

Nonlocal Phases of Local Quantum Mechanical Wavefunctions in Static and Time-Dependent Aharonov-Bohm Experiments

We show that the standard Dirac phase factor is not the only solution of the gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials), apart from Dirac phases also contains terms of classical fields that act nonlocally (in spacetime) on the local solutions of the time-dependent Schr\"odinger equation: the phases of wavefunctions in the Schr\"odinger picture are affected nonlocally by spatially and temporally remote magnetic and electric fields, in ways that are fully explored. These contributions go beyond the usual Aharonov-Bohm effects (magnetic or electric). (i) Application to cases of particles passing through static magnetic or electric fields leads to cancellations of Aharonov-Bohm phases at the observation point; these are linked to behaviors at the semiclassical level (to the old Werner & Brill experimental observations, or their "electric analogs" - or to recent reports of Batelaan & Tonomura) but are shown to be far more general (true not only for narrow wavepackets but also for completely delocalized quantum states). By using these cancellations, certain previously unnoticed sign-errors in the literature are corrected. (ii) Application to time-dependent situations provides a remedy for erroneous results in the literature (on improper uses of Dirac phase factors) and leads to phases that contain an Aharonov-Bohm part and a field-nonlocal part: their competition is shown to recover Relativistic Causality in earlier "paradoxes" (such as the van Kampen thought-experiment), while a more general consideration indicates that the temporal nonlocalities found here demonstrate in part a causal propagation of phases of quantum mechanical wavefunctions in the Schr\"odinger picture. This may open a direct way to address time-dependent double-slit experiments and the associated causal issuesComment: 49 pages, 1 figure, presented in Conferences "50 years of the Aharonov-Bohm effect and 25 years of the Berry's phase" (Tel Aviv and Bristol), published in Journ. Phys. A. Compared to the published paper, this version has 17 additional lines after eqn.(14) for maximum clarity, and the Abstract has been slightly modified and reduced from the published 2035 characters to the required 1920 character

Driven depinning of strongly disordered media and anisotropic mean-field limits

Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the driving force and that slip along at least one of the directions transverse to the motion. A realization of such a model is a collection of elastic channels with transverse viscous couplings. In the infinite range limit this model has a tricritical point separating a region where the depinning is continuous, in the universality class of elastic depinning, from a region where depinning is hysteretic. Many of the collective transport models discussed in the literature are special cases of the generic model.Comment: 4 pages, 2 figure

An interferometric complementarity experiment in a bulk Nuclear Magnetic Resonance ensemble

We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability $D$ quantifying the amount of which-way (WW) information to the fringe visibility $V$ characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We propose a quantitative measure of $D$ by an alternative geometric strategy and investigate the relation between $D$ and entanglement. By measuring $D$ and $V$ independently, it turns out that the duality relation $D^{2}+V^{2}=1$ holds for pure quantum states of the markers.Comment: 13 page, 5 PS figure

Stokes' Drift of linear Defects

A linear defect, viz. an elastic string, diffusing on a planar substrate traversed by a travelling wave experiences a drag known as Stokes' drift. In the limit of an infinitely long string, such a mechanism is shown to be characterized by a sharp threshold that depends on the wave parameters, the string damping constant and the substrate temperature. Moreover, the onset of the Stokes' drift is signaled by an excess diffusion of the string center of mass, while the dispersion of the drifting string around its center of mass may grow anomalous.Comment: 14 pages, no figures, to be published in Phys.Rev.

New method to simulate quantum interference using deterministic processes and application to event-based simulation of quantum computation

We demonstrate that networks of locally connected processing units with a primitive learning capability exhibit behavior that is usually only attributed to quantum systems. We describe networks that simulate single-photon beam-splitter and Mach-Zehnder interferometer experiments on a causal, event-by-event basis and demonstrate that the simulation results are in excellent agreement with quantum theory. We also show that this approach can be generalized to simulate universal quantum computers.Comment: J. Phys. Soc. Jpn. (in press) http://www.compphys.net/dl