Nonadiabatic Phase Research Articles

Spin precession and time-reversal symmetry breaking in quantum transport of electronsthrough mesoscopic rings

We consider the motion of electrons through a mesoscopic ring in the presence of spin-orbit interaction, Zeeman coupling, and magnetic flux. The coupling between the spin and the orbital degrees of freedom results in the geometric and the dynamical phases associated with a cyclic evolution of spin state. Using a non-adiabatic Aharonov-Anandan phase approach, we obtain the exact solution of the system and identify the geometric and the dynamical phases for the energy eigenstates. Spin precession of electrons encircling the ring can lead to various interference phenomena such as oscillating persistent current and conductance. We investigate the transport properties of the ring connected to current leads to explore the roles of the time-reversal symmetry and its breaking therein with the spin degree of freedom being fully taken into account. We derive an exact expression for the transmission probability through the ring. We point out that the time-reversal symmetry breaking due to Zeeman coupling can totally invalidate the picture that spin precession results in effective, spin-dependent Aharonov-Bohm flux for interfering electrons. Actually, such a picture is only valid in the Aharonov-Casher effect induced by spin-orbit interaction only. Unfortunately, this point has not been realized in prior works on the transmission probability in the presence of both SO interaction and Zeeman coupling. We carry out numerical computation to illustrate the joint effects of spin-orbit interaction, Zeeman coupling and magnetic flux. By examining the resonant tunneling of electrons in the weak coupling limit, we establish a connection between the observable time-reversal symmetry breaking effects manifested by the persistent current and by the transmission probability. For a ring formed by two-dimensional electron gas, we

Persistent currents from the competition between Zeeman coupling and spin-orbit interaction

Applying the non-adiabatic Aharonov-Anandan phase approach to a mesoscopic ring with non-interacting many electrons in the presence of the spin-orbit interaction, Zeeman coupling and magnetic flux, we show that the time-reversal symmetry breaking due to Zeeman coupling is intrinsically different from that due to magnetic flux. We find that the direction of the persistent currents induced by the Zeeman coupling changes periodically with the particle number, while the magnetic flux determines the direction of the induced currents by its sign alone.

Non-Abelian geometric phase and generalized invariant method.

We quantitatively formulate the nonadiabatic non-Abelian geometric phase by generalizing the Lewis invariant method to a degenerate case, which is reduced to Wilczek and Zee's [Phys. Rev. Lett. 52, 2111 (1984)] non-Abelian geometric phase in the adiabatic limit. We also derive the effective propagator accommodating the nonadiabatic non-Abelian geometric phase and the semiclassical quantization rule in the adiabatic limit.

Application of strong-coupling asymptotic expansions to the complex Nikitin model of atomic collisions

We consider a phase integral interpretation of the two-state time-dependent exponential model of Nikitin. We generalize to complex energies and complex interactions following previous workers (Krstić & Janev 1988). Applying the method of steepest descent to the Whittaker functions for which all three parameters are large and complex we obtain the adiabatic semi-classical scattering matrix of non-adiabatic transitions. The matrix elements which are expressed in terms of phase integrals taken over physical potentials, are shown to reduce correctly in known limiting cases. These include the Demkov, Rosen-Zener and parabolic models and also the case of symmetric and non-symmetric resonance. It has been previously shown by Coveney et al . that the elastic Stueckelberg non-adiabatic phase may be interpreted as arising from adiabatic parallel transport of the state vector round a closed contour or circuit in the complex time ( t ) plane, even though the hamiltonian is real hermitian on the real t -axis. For a hamiltonian matrix which is complex hermitian on the real t -axis, it has been shown by Berry that anholonomy results in a non-integrable real geometric phase in adiabatic parallel transport around a circuit in real space. It is shown that the Berry phase interpretation also applies to the generalized Whittaker model and all of the above mentioned models, and that it involves contributions from both real and complex closed-circuit adiabatic phases.

Nonadiabatic Berry phase in rotating systems.

The time-dependent Schr\odinger equation for a particle in general rotating systems is solved analytically, and the exact solutions are used to study the nonadiabatic Berry phase. It is shown that the nonadiabatic Berry topological phase appears in general rotating systems for purely mechanical reasons and is observable. An alternative expression for the nonadiabatic Berry phase is given and discussed.

Strong Non-Adiabatic Interactions and Phase Transitions in Conductive Jahn-Teller Crystals

A model of a conducting crystal composed of quasi-molecules with D4h symmetry and with nearly degenerate A1g and B1g states is considered. The model Hamiltonian includes intramolecular strong non-adiabatic interactions, which are non-diagonal with respect to the electronic quantum numbers and linear (Jahn-Teller type) and quadratic (Renner-type) in the vibrational coordinates. The model Hamiltonian is analysed with the help of the mean field method. It is shown that the non-adiabatic electron-phonon interaction causes a structural phase transition which splits the degenerate vibrational mode involved in the interaction, the minimum frequency of the lower branch decreasing when the temperature decreases. For the electrons the two-band BCS equation follows from the calculation, the interaction constant being multiplied by the average number of low-frequency phonons. [Russian Text Ignored].