One discusses the validity and equivalence of various perturbative approaches for the Aharonov-Bohm and Anyon models.

This paper is concerned with the diffusive Nicholson’s blowflies model with nonlocal (or spatiotemporal) delay. When the spatial variable is one-dimensional, we establish the existence of travelling wave-front solutions by using the approach developed by Wang, Li, and Ruan (J. Differ. Equ. 222, 185–232, 2006) on the existence of travelling front solutions of reaction–diffusion systems with nonl...

We study the inverse boundary value problems for the Schrödinger equations with Yang-Mills potentials in a bounded domain Ω 0 ⊂ R n containing finite number of smooth obstacles Ω j , 1 ≤ j ≤ r. We prove that the Dirichlet-to-Neumann opeartor on ∂Ω 0 determines the gauge equivalence class of the Yang-Mills potentials. We also prove that the metric tensor can be recovered up to a diffeomorphism t...

We study the proximity effect in superconductor metallic or ferromagnetic Aharonov Bohm loop hybrid structures self consistently using the BogoliubovdeGennes formalism within the two dimensional extended Hubbard model. We calculate the local density of states, the pair amplitude, and persistent currents as a function of several modulation parameters, the position around the loop, the exchange f...

In this paper, we prove existence results for singular problem( x(t) + f(t, x(t), . . . , x(n−2)(t)) = 0, 0 < t < 1, x(0) = 0, 0 ≤ i ≤ n− 2, x(n−2)(1) = R 1 0 x (n−2)(s)dg(s). Here the positive Carathédory function f may be singular at the zero value of all its phase variables. Proofs are based on the Leray-Schauder degree and Vitali’s convergence theorem.

In 1985, Matteucci and Pozzi (1985 Phys. Rev. Lett. 54 2469) demonstrated the presence of a quantum mechanical phase shift for electrons passing a pair of oppositely charged biprism wires. For this experimental arrangement no forces deflect the electrons. Consequently, the result was reported as a non-local type-2 Aharonov–Bohm effect. Boyer (2002 Found. Phys. 32 41–50; 1987 Nuovo Cimento B 100...

Solutions of relativistic wave equations in superpositions of Aharonov-Bohm, magnetic, and electric fields. Abstract We present new exact solutions (in 3 + 1 and 2 + 1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some additional electric and magnetic field...

Electromagnetic duality between the Aharonov-Bohm and the Aharonov-Casher quantum mechanical phases predicts the existence of a new collective state of matter which can be regarded as a spin dual to the fractional quantum Hall effect. The state, induced by electric fields, is driven by effective spin-spin interactions. We derive experimental and materials conditions of spin-spin interactions an...

We show that black holes can posses a long range quantum mechanical hair associated with a massive spin-2 field, which can be detected by a stringy generalization of the Aharovon-Bohm effect, in which a string loop lassoes the black hole. The long distance effect persist for arbitrarily high mass of the spin-2 field. An analogous effect is exhibited by a massive antisymmetric two-form field. We...

This note collects, classifies and evaluates common criticism against the deBroglie-Bohm theory, including Ockham’s razor, asymmetry in the deBroglie-Bohm theory, the “surreal trajectory” problem and relativistic generalizations. This controversy highlights that even in science theories can not solely be evaluated based on their empirical confirmation.