A calculation of the Aharonov-Bohm wave function is presented. The result is a series of confluent hypergeometric functions which is finite at the forward direction. MIT–CTP–2473 October 1995 hep-th/9510085 Submitted to Physical Review D This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under cooperative research agreement #DE-FC02-94ER40818. Email: mar...

We determine the |p|/m expansion of the two body scattering amplitude of the quantum theory of a Chern-Simons field minimally coupled to a scalar field with quartic self-interaction. It is shown that the existence of a critical value of the self-interaction parameter for which the 2-particle amplitude reduces to the Aharonov-Bohm one is restricted to the leading, nonrelativistic, order. The sub...

In this article, we investigate the decay rate of the solutions of two water wave models with a nonlocal viscous term written in the KdV form ut + ux + βuxxx + √ ν √ π ∫ t 0 ut(s) √ t− s ds+ uux = νuxx. and ut + ux − βutxx + √ ν √ π ∫ t 0 ut(s) √ t− s ds+ uux = νuxx. in the BBM form. In order to realize this numerical study, a numerical scheme based of the Gα-scheme is developed.

We deal with symmetry properties for solutions of nonlocal equations of the type (−∆) s v = f (v) in R n , where s ∈ (0, 1) and the operator (−∆) s is the so-called fractional Laplacian. The study of this nonlocal equation is made via a careful analysis of the following degenerate elliptic equation −div (x α ∇u) = 0 on R

The theory of weak measurement, proposed by Aharonov and coworkers, has been applied by Steinberg to the long-discussed traversal time problem. The uncertainty and ambiguity that characterize this concept from the perspective of von Neumann measurement theory apparently vanish, and joint probabilities and conditional averages become meaningful concepts. We express the Larmor clock and some othe...

The nonlocal vacuum condensates or vacuum correlators describe the distribution of quarks and gluons in the nonperturbative QCD vacuum [1]. Physically, it means that vacuum quarks and gluons can flow through the vacuum with nonzero momentum. Nonlocal condensates play an important role in hadron physics. The nonlocal properties of the vacuum condensates are of principle importance in the study o...

In a previous work, it is shown that a set of path equations,in Absolute Parallelism (AP) geometry, is naturally quantized. Generalizing the Lagrangian used in that work, by inserting a term containing the basic vector of the AP-geometry, we have obtained a new class of path equations with a geometric term similar to Lorentz force term. The new class of path equations is still preserving the qu...

Classical and quantum aspects of fluctuations are reviewed in a discussion on the universality of the second law. Consideration is given to the need of information and the requirement of a ratchet and pawl-type mechanism for the utilization of energy from fluctuations. Some aspects of the quantum theory of the Copenhagen school are compared to those of Bohm within the discussion.

Using the theory of self-adjoint extensions, we construct all the possible hamiltonians describing the non relativistic Aharonov-Bohm effect. In general the resulting hamiltonians are not rotationally invariant so that the angular momentum is not a constant of motion. Using an explicit formula for the resolvent, we describe the spectrum and compute the generalized eigenfunctions and the scatter...

We discuss the Γ-convergence, under the appropriate scaling, of the energy functional ‖u‖Hs(Ω) + ∫ Ω W (u) dx, with s ∈ (0, 1), where ‖u‖Hs(Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential. When s ∈ [1/2, 1), we show that the energy Γ-converges to the classical minimal surface functional – while, when s ∈ (0, 1/2), it is easy to see that the functio...