arXiv subjects

Frank Gaitan

Publications and source records attributed to Frank Gaitan.

23 records · Page 2Linked to original sources

arXiv1998

Berry's Phase in the Presence of a Stochastically Evolving Environment: A Geometric Mechanism for Energy-Level Broadening

The generic Berry phase scenario in which a two-level system is coupled to a second system whose dynamical coordinate is slowly-varying is generalized to allow for stochastic evolution of the slow system. The stochastic behavior is produced by coupling the slow system to a heat resevoir which is modeled by a bath of harmonic oscillators initially in equilibrium at temperature T, and whose spectral density has a bandwidth which is small compared to the energy-level spacing of the fast system. The well-known energy-level shifts produced by Berry's phase in the fast system, in conjunction with the stochastic motion of the slow system, leads to a broadening of the fast system energy-levels. In the limit of strong damping and sufficiently low temperature, we determine the degree of level-broadening analytically, and show that the slow system dynamics satisfies a Langevin equation in which Lorentz-like and electric-like forces appear as a consequence of geometrical effects. We also determine the average energy-level shift produced in the fast system by this mechanism.

quant-ph↗

arXiv1995

Berry's Phase, Josephson's Equation, and the Dynamics of Weak Link Superconductors and Their Vortices

We examine the dynamical consequences of Berry's phase for Josephson junctions, junction arrays, and their vortices. Josephson's equation and the related phase slip voltages are shown to be uneffected by Berry's phase. In an annular Josephson junction, Berry's phase is seen to generate a new current drive on a vortex. In the continuum limit, vortex dynamics in a 2D array is shown to map onto that of a 2D film. A Hall sign anomaly is expected in arrays; and the merits of arrays for studies of disorder on vortex motion is discussed.

cond-mat↗

arXiv1994

Microscopic Analysis of the Non-Dissipative Force on a Line Vortex in Superconductor

A microscopic analysis of the non-dissipative force F_nd acting on a line vortex in a type-II superconductor at T=0 is given. All work assumes a charged BCS superconductor. We first examine the Berry phase induced in the BCS ground state by movement of the vortex and show how this phase enters into the hydrodynamic action S_hyd of the condensate. Appropriate variation of S_hyd gives F_nd and variation of the Berry phase term is seen to contribute the Magnus force of classical hydrodynamics to F_nd. This analysis confirms in detail the arguments of Ao and Thouless within the context of the BCS model. Our Berry phase, in the limit e -> 0, reproduces the Berry phase they obtain for a neutral superfluid. A second independent determination of F_nd is given through a microscopic derivation of the continuity equation for the condensate linear momentum. This yields the acceleration equation for the superflow. The vortex is seen to act as a momentum sink and the rate of momentum loss yields F_nd. Both calculations yield the same F_nd and show that the Magnus force contribution to F_nd is a consequence of the vortex motion and topology.

cond-mat↗

arXiv1994

Microscopic Analysis of the Non-Dissipative Force on a Line Vortex in a Superconductor: Berry's Phase, Momentum Flows and the Magnus Force

A microscopic analysis of the non-dissipative force ${\bf F}_{nd}$ acting on a line vortex in a type-II superconductor at $T=0$ is given. We first examine the Berry phase induced in the true superconducting ground state by movement of the vortex and show how this induces a Wess-Zumino term in the hydrodynamic action $S_{hyd}$ of the superconducting condensate. Appropriate variation of $S_{hyd}$ gives ${\bf F}_{nd}$ and variation of the Wess-Zumino term is seen to contribute the Magnus (lift) force of classical hydrodynamics to ${\bf F}_ {nd}$. This first calculation confirms and strengthens earlier work by Ao and Thouless which was based on an ansatz for the many-body ground state. We also determine ${\bf F}_{nd}$ through a microscopic derivation of the continuity equation for the condensate linear momentum. This equation yields the acceleration equation for the superflow and shows that the vortex acts as a sink for the condensate linear momentum. The rate at which momentum is lost to the vortex determines ${\bf F}_{nd}$ and the result obtained agrees with the Berry phase calculation. The Magnus force contribution to ${\bf F}_{nd}$ is seen to be a consequence of the vortex topology. Preliminary remarks are made regarding finite temperature extensions, with emphasis on its relevance to the sign anomaly occurring in Hall effect experiments done in the flux flow regime.

cond-mat↗

arXiv1993

On the Observability of Meso- and Macro-scopic Quantum Coherence of Domain Walls in Magnetic Insulators

Results are presented of a numerical calculation of the tunneling gap for a domain wall moving in the double well potential of a pair of voids in a magnetic insulator. Both symmetric and asymmetric double well potentials are considered. It is found that, even in the absence of dissipation, the prospects for observing quantum coherence on a meso- or macro-scopic scale appears unlikely.

cond-mat↗