(−ih̄D)2 2m ψ = ih̄D0ψ, using the “altered” (covariant) derivative Dμ = ∂μ − ieAμ/h̄c, (1) which is gauge invariant only if the gauge transformation of the potentials, Aμ(xν) → Aμ + ∂μΩ(xν), is accompanied by a phase change of the wavefunction, ψ(xν) → e−ieΩ(xν )/h̄c ψ. Yang and Mills (1954) [4, 5] may have been the first to point out that Fock’s argument can be inverted such that a requirement of ...

Synchrotron radiation of a charged particle in a constant uniform magnetic field and in the presence of the Aharonov-Bohm solenoid field is studied in the frame of the relativistic quantum theory. First, to this end exact solutions of the Klein-Gordon and Dirac equations are found. Using such solutions, all characteristics of one photon spontaneous irradiation, such as its intensity and angular...

We study theoretically nonequilibrium noise in the fractional quantum Hall regime for an Aharonov-Bohm ring with a third contact in the middle of the ring. Because of their fractional statistics the tunneling of Laughlin quasiparticles between the inner and outer edges of the ring changes the effective Aharonov-Bohm flux experienced by quasiparticles going around the ring, leading to a change i...

Resorting to a Gedankenexperiment which is very similar to the famous Aharonov–Bohm proposal it will be shown that, in the case of a Minkowskian spacetime, we may use a nonrelativistic quantum particle and a noninertial coordinate system and obtain geometric information of regions that are, to this particle, forbidden. This shows that the outcome of a nonrelativistic quantum process is determin...

We study theoretically the exciton absorption on a ring shreded by a magnetic flux. For the case when the attraction between electron and hole is short-ranged we get an exact solution of the problem. We demonstrate that, despite the electrical neutrality of the exciton, both the spectral position of the exciton peak in the absorption, and the corresponding oscillator strength oscillate with mag...

We study a nonlocal diffusion equation approximating the dynamics of coupled phase oscillators on large graphs. Under appropriate assumptions, the model has a family of steady state solutions called twisted states. We prove a sufficient condition for stability of twisted states with respect to perturbations in the Sobolev and BV spaces. As an application, we study the stability of twisted state...

For the nonlocal T-periodic Gross–Pitaevsky operator, formal solutions of the Floquet problem asymptotic in small parameter , → 0, up to O(3/2) have been constructed. The quasi-energy spectral series found correspond to the closed phase trajectories of the Hamilton–Ehrenfest system which are stable in the linear approximation. The monodromy operator of this equation has been constructed to with...

We consider the existence of at least one positive solution of the problem –D0+u(t) = f (t,u(t)), 0 < t < 1, under the circumstances that u(0) = 0, u(1) = H1(φ(u)) + ∫ E H2(s,u(s))ds, where 1 < α < 2, D α 0+ is the Riemann-Liouville fractional derivative, and u(1) = H1(φ(u)) + ∫ E H2(s,u(s))ds represents a nonlinear nonlocal boundary condition. By imposing some relatively mild structural condit...