[en] Short communication

[en] An algebraic approach to the Aharonov-Bohm effect is considered. The constructed mathematical scheme agrees with experimental data and provides a clear physical interpretation of this effect that does not contradict classical concepts.

[en] Short communication

[en] We propose an atom-interferometry experiment based on the scalar Aharonov-Bohm effect which detects an atom charge at the 10^-28 e level, and improves the current laboratory limits by 8 orders of magnitude. This setup independently probes neutron charges down to 10²⁸ e, 7 orders of magnitude below current bounds

[en] We present a theory of the transmission of guided matter-waves through Sagnac interferometers. Interferometer configurations with only one input and one output port have a property similar to the phase rigidity observed in the transmission through Aharonov-Bohm interferometers in coherent mesoscopic electronics. This property enables their operation with incoherent matter-wave sources. High rotation sensitivity is predicted for high finesse configurations

[en] A two-step measurement protocol of a quantum system, known as the weak value (WV), was introduced more than two decades ago by Aharonov et al (1988 Phys. Rev. Lett. 60 1351) and has since then been studied in various contexts. In this paper, we discuss another two-step measurement protocol that we dub the null weak value (NWV). The protocol consists of a partial-collapse measurement followed by quantum manipulation on the system and finally a strong measurement. The first step is a strong measurement which takes place with a small probability. The second strong measurement is used as a postselection on the outcome of the earlier step. Not being measured in the partial-collapse stage (null outcome) leads to a nontrivial correlation between the two measurements. The NVW protocol, first defined for a two-level system (Zilberberg et al 2012 arXiv:1205.3877), is then generalized to a multi-level system and compared with the standard-WV protocol.

[en] A mesoscopic oscillator in U-shape has been proposed and studied. Making use of a magnetic flux together with a potential of confinement, the electron contained in the oscillator has been localized initially and an amount of energy has been thereby stored. Then a sudden cancellation of both the potential and the flux may cause an initial current which initiates a periodic motion of the electron from one end of the U-oscillator to the opposite end, and repeatedly. The period is adjustable. The current associated with the periodic motion can be tuned very strong (say, more than two orders larger than the current of the usual Aharonov-Bohm oscillation). Related theory and numerical results are presented.

[en] The spectral analysis of Aharonov-Bohm Hamiltonians with flux 1/2 leads surprisingly to a new insight on some questions of isospectrality appearing for example in Jakobson et al (2006 J. Comput. Appl. Math. 194 141-55) and Levitin et al (J. Phys. A: Math. Gen. 39 2073-82) and of minimal partitions (Helffer et al 2009 Ann. Inst. H. Poincare Anal. Non Lineaire 26 101-38). We will illustrate this point of view by discussing the question of spectral minimal 3-partitions for the rectangle. It has been observed in Helffer et al (2009 Ann. Inst. H. Poincare Anal. Non Lineaire 26 101-38) that the minimal 3-partition is obtained by the three nodal domains of the third eigenfunction corresponding to the three rectangles. We will describe a possible mechanism of transition for increasing a/b between these nodal minimal 3-partitions and non-nodal minimal 3-partitions at the value √3/8 and discuss the existence of symmetric candidates for giving minimal 3-partitions when √3/8< a/b≤1. Numerical analysis leads very naturally to nice questions of isospectrality which are solved by the introduction of Aharonov-Bohm Hamiltonians or by going on the double covering of the punctured rectangle

[en] The generation of the new forms of the consistency condition in the framework of the consistent history approach to quantum mechanics is presented. Further, the consistency condition is analyzed in the limit of an infinite number of intermediate events. It is shown that under assumptions, which do not destroy the nature of the problem, the decoherence does not appear

[en] There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.