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The Greens functions of the two and three-dimensional relativistic Aharonov-Bohm (A-B) systems are given by the path integral approach. In addition the exact radial Greens functions of the spherical A-B quantum billiard system in two and three-dimensional are obtained via the perturbation techanique of $delta $-function.
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We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum $hbar c/e$ as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the double-qubit controlled operations (conditional bit flip). We suggest a tentative realization of the mechanism as either the mesoscopic structure of three quantum dots coherently coupled by mesoscopic tunnelling in crossed magnetic and electric fields, or as a nanoscopic structure of triple anionic vacancy (similar to $F_3$ centers in alkali halides) with one trapped electron in one spin projection state.
Aharonov-Bohm oscillations have been observed in a lattice formed by a two dimensional rhombus tiling. This observation is in good agreement with a recent theoretical calculation of the energy spectrum of this so-called T3 lattice. We have investigated the low temperature magnetotransport of the T3 lattice realized in the GaAlAs/GaAs system. Using an additional electrostatic gate, we have studied the influence of the channel number on the oscillations amplitude. Finally, the role of the disorder on the strength of the localization is theoretically discussed.
We show that the Aharonov-Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labeling charged superselection sectors. In the present paper we show that this topological quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov-Bohm effect. To confirm these abstract results we quantize the Dirac field in presence of a background flat potential and show that the Aharonov-Bohm phase gives an irreducible representation of the fundamental group of the spacetime labeling the charged sectors of the Dirac field. We also show that non-Abelian generalizations of this effect are possible only on space-times with a non-Abelian fundamental group.
Experimental study of quantum Hall corrals reveals Aharonov-Bohm-Like (ABL) oscillations. Unlike the Aharonov-Bohm effect which has a period of one flux quantum, $Phi_{0}$, the ABL oscillations possess a flux period of $Phi_{0}/f$, where $f$ is the integer number of fully filled Landau levels in the constrictions. Detection of the ABL oscillations is limited to the low magnetic field side of the $ u_{c}$ = 1, 2, 4, 6... integer quantum Hall plateaus. These oscillations can be understood within the Coulomb blockade model of quantum Hall interferometers as forward tunneling and backscattering, respectively, through the center island of the corral from the bulk and the edge states. The evidence for quantum interference is weak and circumstantial.
The consequences of microreversibility for the linear and nonlinear transport properties of systems subjected to external magnetic fields are systematically investigated in Aharonov-Bohm rings connected to two, three, and four terminals. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is expressed in terms of the scattering matrix of these circuits. The time-reversal symmetry relations up to the third responses of the currents and the fourth cumulants are analytically investigated and numerically tested as a function of the magnetic flux. The validity of such relations is thus firmly confirmed in this class of open quantum systems.
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