Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an alg...

We present a unified treatment of the Aharonov-Bohm (AB) effect for two-dimensional multiband electronic systems possessing isotropic band structures. propose an integral representation AB scattering state electron scattered by infinitely thin solenoid. Moreover, we derive asymptotic form and obtain differential cross section from that. found remarkable result, namely, that this is same all agr...

We analyze a Hanbury Brown-Twiss geometry in which particles are injected from two independent sources into a mesoscopic conductor in the quantum Hall regime. All partial waves end in different reservoirs without generating any single-particle interference; in particular, there is no single-particle Aharonov-Bohm effect. However, exchange effects lead to two-particle Aharonov-Bohm oscillations ...

The two main features of the Aharonov-Bohm effect are the topological dependence of accumulated phase on the winding number around the magnetic fluxon, and nonlocality-local observations at any intermediate point along the trajectories are not affected by the fluxon. The latter property is usually regarded as exclusive to quantum mechanics. Here we show that both the topological and nonlocal fe...

In a Ramsey atom interferometer excited by two electromagnetic fields, if atoms are under a time-varying scalar potential during the interrogation time, the phase of the Ramsey fringes shifts owing to the scalar Aharonov–Bohm effect. The phase shift was precisely examined using a Ramsey atom interferometer with a two-photon Raman transition under the second-order Zeeman potential, and a formula...

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...

The role of Aharonov-Bohm effect in quantum tunneling is examined when a potential is defined on the S1 and has N -fold symmetry. We show that the low-lying energy levels split from the N -fold degenerate ground state oscillate as a function of the Aharonov-Bohm phase, from which general degeneracy conditions depending on the magnetic flux is obtained. We apply these results to the spin tunneli...

A simple classical probabilistic system (a simple card game) classically exemplifies Aharonov and Vaidman’s “Three-Box ‘paradox’ ” [J. Phys. A 24, 2315 (1991)], implying that the Three-Box example is neither quantal nor a paradox and leaving one less difficulty to busy the interpreters of quantum mechanics. An ambiguity in the usual expression of the retrodiction formula is shown to have misled...