Aharonov-Bohm effects in entangled molecules

Molecules which are magnetic and conducting, if suitably entangled (e.g., catenanes and knots) could exhibit Aharonov-Bohm effects which can be viewed as particular examples of a Berry phase. The corrections to the quantum energy levels reflect the entangled geometry of the molecules and, while small (they are proportional to the square of the fine structure constant), may be observable. We illustrate these corrections for a number of catenated and knotted structures. For couplings between the components of a catenane (link), the Aharonov-Bohm corrections are determined by integer-valued linking numbers. For knots, the Aharonov-Bohm correction is proportional to the geometric writhe of the knot.     

Dynamics of quantum zeno and anti-zeno effects in an open system

We provide a general dynamical approach for the quantum Zeno and anti-Zeno efects in an open quantum system under repeated non-demolition measurements.In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation.Based on that model,we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements,and derive the measurement-modified decay rates of the excited state.In the cases with frequent ideal measurements at zero-temperature,we re-obtain the same decay rate as that from the wave function collapse postulation(Nature,2000,405:546).The correction to the ideal decay rate is also obtained under the non-ideal measurements.Especially,we find that the quantum Zeno and anti-Zeno efects are possibly enhanced by the non-ideal natures of measurements.For the open system under measurements with arbitrary period,we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum,and show that in the long-time evolution the noise spectrum is efectively tuned by the repeated measurements.Our approach is also able to describe the quantum Zeno and anti-Zeno efects given by the phase modulation pulses,as well as the relevant quantum control schemes.     

Bound states in the continuum in open Aharonov-Bohm rings

Using the formalism of the effective Hamiltonian, we consider bound states in a continuum (BIC). They are nonhermitian effective Hamiltonian eigenstates that have real eigenvalues. It is shown that BICs are orthogonal to open channels of the leads, i.e., disconnected from the continuum. As a result, BICs can be superposed to a transport solution with an arbitrary coefficient and exist in a propagation band. The one-dimensional Aharonov-Bohm rings that are opened by attaching single-channel leads to them allow exact consideration of BICs. BICs occur at discrete values of the energy and magnetic flux; however, it’s realization strongly depends on the way to the BIC point. The text was submitted by the authors in English.     

Inelastic effects in Aharonov-Bohm molecular interferometers

Inelastic effects arising from electron-phonon coupling in molecular Aharonov-Bohm (AB) interferometers are studied using the nonequilibrium Green's function method. Results for the magnetoconductance are compared for different values of the electron-phonon coupling strength. At low-bias voltages, the coupling to the phonons does not change the lifetime and leads mainly to scattering phase shifts of the conducting electrons. As a result of these dephasing processes, the magnetoconductance of the molecular AB interferometer becomes more sensitive to the threading magnetic flux as the electron-phonon coupling is increased, opposite to the behavior of an electric gate.     

Aharonov-Casher and scalar Aharonov-Bohm topological effects

We reexamine the topological and nonlocal natures of the Aharonov-Casher and scalar Aharonov-Bohm phase effects. The underlying U(1) gauge structure is exhibited explicitly. And the conditions for developing topological Aharonov-Casher and scalar Aharonov-Bohm phases are clarified. We analyze the arguments of M. Peshkin and H.?J. Lipkin [Phys. Rev. Lett. 74, 2847 (1995)] in detail and show that they are based on the wrong Hamiltonian which yields their conclusion incorrect.     

Non-Markovian relaxation in an open quantum system

Non-Markovian dynamics in open quantum systems is characterized by a time-non-locality in the equation of motion valid for the reduced density operator. An expansion of this density matrix equation with respect to Laguerre polynomials is used to tackle the time-non-locality. The applicability and the numerical limitations of the method are discussed in detail. In order to illuminate the characteristics of non-Markovian dynamics the reference example is studied of a single quantum degree of freedom moving in a harmonic potential and being embedded in a heat bath. If interpreted as the photoinduced dynamics of nuclear motion in polyatomic molecules we can suggest two clear signatures of non-Markovian dynamics observable in ultrafast optical experiments, firstly a pronounced and somewhat irregular oscillatory behavior of the vibrational level populations, and secondly a separation of the vibrational wavepacket into a double-structure. Received 12 April 2000 and Received in final form 2 September 2000     

Vacuum polarization around an Aharonov-Bohm solenoid

The quantisation of a charged scalar field in an externally specified electromagnetic field, described by the vector potentialA _i=∂_if withf(t,r,θ,z)=Bθ is discussed. The electromagnetic field is zero everywhere except at the origin; a singular magnetic field (Aharonov-Bohm field) exists at the origin. The vacuum polarization around such a magnetic field is computed and the non-local behaviour is discussed.     

Scattering of spin-polarized electron in an Aharonov-Bohm potential

The scattering of spin-polarized electrons in an Aharonov-Bohm vector potential is considered. We solve the Pauli equation in 3 + 1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment of electron and magnetic field. Expressions for the scattering amplitude and the cross section are obtained for spin-polarized electron scattered off a flux tube of small radius. It is also shown that bound electron states cannot occur in this quantum system. The scattering problem for the model of a flux tube of zero radius in the Born approximation is briefly discussed.     

Detection of Majorana fermions in an Aharonov–Bohm interferometer

By using the non-equilibrium Green's function technique, we investigate the electronic transport properties in an Aharonov–Bohm interferometer coupling with Majorana fermions. We find a fixed unit conductance peak which is independent of the other factors when the topological superconductor is grounded. Especially, an additional phase appears when the topological superconductor is in the strong Coulomb regime, which induces a new conductance resonant peak compared with the structure of replacing the topological superconductor by a quantum dot, and the conductance oscillation with the magnetic flux reveals a 2π phase shift by raising(lowering) a charge on the capacitor.     

Anyonic strings and membranes in anti-de Sitter space and dual Aharonov-Bohm effects

It is observed that strings in AdS(5) x S(5) and membranes in AdS(7) x S(4) exhibit long range phase interactions. Two well separated membranes dragged around one another in anti-de Sitter space (AdS) acquire phases of 2 pi/N. The same phases are acquired by a well separated F and D string dragged around one another. The phases are shown to correspond to both the standard and a novel type of Aharonov-Bohm effect in the dual field theory.     

Zero modes in a periodic system of Aharonov-Bohm solenoids

The existence of infinitely degenerate zero modes is proved for a quantum-mechanical two-dimensional charged particle with spin 1/2 moving in the field of an infinite system of Aharonov-Bohm solenoids. The condition for appearance of these modes is found and their explicit form is obtained.     

Kondo-assistant Aharonov-Bohm transport in a quantum dot-Majorana wire system

We investigate the Kondo-assistant Aharonov-Bohm (AB) transport in a Quantum dot (QD) coupled with a topological Majorana wire. We noted that the conductance exhibits sensitive dependence on the phase factor of AB ring when the wire-QD coupling strength changes. The DOS resonance split when the coupling strength changes from small to large. The current is determined by the Kondo transport characteristics presented by the quantum dots (QDs). Also, the transport results show different p-dependence properties under parallel and anti-parallel leads alignment. We believe that these results can be helpful for understanding the Majorana-QD coupling properties as well as the detection of the Majorana bound states.     

Non-adiabatic geometric phases and dephasing in an open quantum system

We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases of both weak short-correlated noise and slow quasi-stationary noise. Motivated by recent experiments, we find the leading non-adiabatic corrections to the results, known for the adiabatic limit.     

Conductance in an Aharonov-Bohm Interferometer with Parallel-Coupled Double Dots

We present a theoretical study of the conductance in an Aharonov-Bohm interferometer containing two coupled quantum dots. The interdot tunneling divides the interferometer into two coupled subrings, where opposite magnetic fluxes are threaded separately while the net flux is kept zero. Using the Green function technique we derive the expression of the linear conductance. It is found that the Aharonov-Bohm effect still exists, and when the level of each dot is aligned, the exchange of the Fano and Breit-Wigner resonances in the conductance can be achieved by tuning the magnetic flux. When the two levels are mismatched the exchange may not happen. Further, for some specific asymmetric systems where the coupling strengths between the two dots and the leads are not equal, the flux can change the Fano resonance into an antiresonance, which is absent in symmetric systems.