Aharonov-Bohm System Research Articles

Non-Abelian gauge field optics

The concept of gauge field is a cornerstone of modern physics and the synthetic gauge field has emerged as a new way to manipulate particles in many disciplines. In optics, several schemes of Abelian synthetic gauge fields have been proposed. Here, we introduce a new platform for realizing synthetic SU(2) non-Abelian gauge fields acting on two-dimensional optical waves in a wide class of anisotropic materials and discover novel phenomena. We show that a virtual non-Abelian Lorentz force arising from material anisotropy can induce light beams to travel along Zitterbewegung trajectories even in homogeneous media. We further design an optical non-Abelian Aharonov–Bohm system which results in the exotic spin density interference effect. We can extract the Wilson loop of an arbitrary closed optical path from a series of gauge fixed points in the interference fringes. Our scheme offers a new route to study SU(2) gauge field related physics using optics.

Geometric phase of a classical Aharonov–Bohm Hamiltonian

Abstract We present a gauge-invariant approach for associating a geometric phase with the phase space trajectory of a classical dynamical system. As an application, we consider the classical analog of the quantum Aharonov–Bohm (AB) Hamiltonian for a charged particle orbiting around a current carrying long thin solenoid. We compute the classical geometric phase of a closed phase space trajectory, and also determine its dependence on the magnetic flux enclosed by the orbit. We study the similarities and differences between this classical geometric phase and the AB phase acquired by the wave function of the quantum AB Hamiltonian. We suggest an experiment to measure the geometric phase for the classical AB system, by using an appropriate optical fiber ring interferometer.

Hidden superconformal symmetry of the spinless Aharonov–Bohm system

A hidden supersymmetry is revealed in the spinless Aharonov–Bohm problem. The intrinsic supersymmetric structure is shown to be intimately related to the scale symmetry. As a result, a bosonized superconformal symmetry is identified in the system. Different self-adjoint extensions of the Aharonov–Bohm problem are studied in the light of this superconformal structure and interacting anyons. The scattering problem of the original Aharonov–Bohm model is discussed in the context of the revealed supersymmetry.

Levinson theorem for Aharonov-Bohm scattering in two dimensions

We apply the recently generalized Levinson theorem for potentials with inverse-square singularities [Sheka et al., Phys. Rev. A 68, 012707 (2003)] to Aharonov-Bohm systems in two dimensions (2D). By this theorem, the number of bound states in a given mth partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.

Elementary Aharonov-Bohm system in three space dimensions: Quantum attraction with no classical force

As a consequence of the Aharonov-Bohm effect, there is a quantum-induced attraction between a charged particle and a rigid, impenetrable hoop made from an arbitrarily thin tube containing a superconductor quantum of magnetic flux. This is remarkable because in classical physics there is no force between the two objects, and quantum-mechanical effects (associated with uncertainty-principle energy) generally are repulsive rather than attractive. For an incident spinless charged particle in a P wave (in a configuration with total angular momentum zero) we verify a resonance just above threshold using the Kohn variational principle in its S-matrix form. Even if optimistic choices of parameters describing a model system with these properties were feasible, the temperature required to observe the resonance would be far lower than has yet been attained in the laboratory.

Path integrals for boundaries and topological constraints: A white noise functional approach

Using the Streit–Hida formulation where the Feynman path integral is realized in the framework of white noise analysis, we evaluate the quantum propagator for systems with boundaries and topological constraints. In particular, the Feynman integrand is given as generalized white noise functionals for systems with flat wall boundaries and periodic constraints. Under a suitable Gauss–Fourier transform of these functionals the quantum propagator is obtained for: (a) the infinite wall potential; (b) a particle in a box; (c) a particle constrained to move in a circle; and (d) the Aharonov–Bohm system. The energy spectrum and eigenfunctions are obtained in all four cases.

Spectral and transport properties of quantum wires with bond disorder

Systems with bond disorder are defined through lattice Hamiltonians that are of pure nearest neighbour hopping type, i.e., do not contain on-site contributions. They stand representative for the general family of disordered systems with chiral symmetries. Application of the Dorokhov–Mello–Pereyra–Kumar transfer matrix technique P.W. Brouwer et al. [Phys. Rev. Lett 81 (1998) 862; Phys. Rev. Lett. 84 (2000) 1913] has shown that both spectral and transport properties of quasi one-dimensional systems belonging to this category are highly unusual. Most notably, regimes with absence of exponential Anderson localization are observed, the single particle density of states exhibits singular structure in the vicinity of the band centre, and the manifestation of these phenomena depends in an apparently topological manner on the even- or oddness of the channel number. In this paper we re-consider the problem from the complementary perspective of the nonlinear σ -model. Relying on the standard analogy between one-dimensional statistical field theories and zero-dimensional quantum mechanics, we will relate the problem to the behaviour of a quantum point particle subject to an Aharonov–Bohm flux. We will build on this analogy to re-derive earlier DMPK results, identify a new class of even/odd staggering phenomena (now dependent on the total number of sites in the system) and trace back the anomalous behaviour of the bond disordered system to a simple physical mechanism, viz. the flux periodicity of the quantum Aharonov–Bohm system. We will also touch upon connections to the low energy physics of other lattice systems, notably disordered chiral systems in 0 and 2 dimensions and antiferromagnetic spin chains.

Quantum oscillations in superconductors in magnetic field

The Aharonov–Bohm oscillations (ABO) of the free energy, the critical temperature, and the magnetic susceptibility in a stack of hollow mesoscopic cylinders are calculated. It is shown that sinusoidal (in flux) ABO crosses over to the parabolic Little–Parks oscillations (LPO) when the diameter of cylinders exceeds the coherence length. The exponential temperature behaviour of the magnetic susceptibility is like that found in Ag cylinders with thin Nb coating [Czech. J. Physics 46 (1996) 2317]. The formal analogy between oscillations of the free energy in the Aharonov–Bohm system in question and the de Haas–van Alphen oscillations (dHvAO) in layered superconductors is discussed.

Quantum Mechanics of an Electron in a Homogeneous Magnetic Field and a Singular Magnetic Flux Tube

The eigenvalue problem of the Hamiltonian of an electron confined to a plane and sub- jected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux tube, i.e., of zero width, is investigated. Since both a direct approach based on distribution-valued operators and a limit process starting from a non-singular flux tube, i.e., of finite size, fail, an alternative method is applied leading to consistent results. An essential feature is quantum mechanical supersymmetry at g=2 which imposes, by proper representation, the correct choice of “boundary conditions.” The corresponding representation of the Hilbert space in coordinate space differs from the usual space of square-integrable 2-spinors, entailing other unusual properties. The analysis is extended to g≠2 so that supersymmetry is explicitly broken. Finally, the singular Aharonov–Bohm system with the same amount of singular flux is analyzed by making use of the fact that the Hilbert space must be the same.

Green’s-function approach to two- and three-dimensional delta-function potentials and application to the spin-1/2 Aharonov–Bohm problem

Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by incorporating the self-adjoint extension method within the Green’s-function method. The energy-dependent Green’s functions for free particle plus delta-function potential systems are explicitly determined and similar calculations are carried out for the spin-1/2 Aharonov–Bohm system. It is found that the time-dependent propagator for the latter cannot be evaluated analytically except for a particular value of the self-adjoint extension parameter. It corresponds to the case in which the singular solution alone contributes for the partial wave defined by ‖m+α‖<1.

Parity violation in Aharonov-Bohm systems: The spontaneous Hall effect.

We show how macroscopic manifestations of $P$ (and $T$) symmetry breaking can arise in a simple system subject to Aharonov-Bohm interactions. Specifically, we study the conductivity of a gas of charged particles moving through a dilute array of flux tubes. The interaction of the electrons with the flux tubes is taken to be of a purely Aharonov-Bohm type. We find that the system exhibits a non-zero transverse conductivity, i.e., a spontaneous Hall effect. This is in contrast with the fact that the cross sections for both scattering and bremsstrahlung (soft photon emission) of a single electron from a flux tube are invariant under reflections. We argue that the asymmetry in the conductivity coefficients arises from many-body effects. On the other hand, the transverse conductivity has the same dependence on universal constants that appears in the Quantum Hall Effect, a result that we relate to the validity of the Mean Field approximation.

Scattering States in Conformally Invariant Quantum Mechanics

We present a general algebraic analysis of scattering in conformally invariant quantum mechanical systems. The dynamical group is the most elementary non-Abelian noncompact Lie group, SU(1, 1). The Hamiltonians we investigate Contain the noncompact generators of SU(1, 1) and hence possess a purely continuous spectrum. We diagonalize these generators showing that their generalized eigenvectors (the scattering states) have an elegant representation in terms of SU(1, 1) coherent states. We revisit the well-known examples of the nonrelativistic point particle in an inverse square potential and the Aharonov-Bohm system. We discuss the connection of our algebraic approach with previous studies.

Quantum effects of electric fluxes in multiparticle systems

The electric Aharonov-Bohm single-particle phase shift is derived in the quasi-classical approximation by an analysis of the multiparticle closed system constituted by an incident particle and the source particles for the electric space-time flux. An explicit multiparticle wave function is given representing an electric Aharonov-Bohm system.