We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution

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We consider a fermionic system at zero temperature interacting through an effective nonretarded potential of the type introduced by Nozières and Schmitt-Rink, and calculate the phase coherence length phase ͑associated with the spatial fluctuations of the superconducting order parameter͒ by exploiting a functional-integral formulation for the correlation functions and the associated loop expansion. This formulation is especially suited to follow the evolution of the fermionic system from a BCS-type superconductor for weak coupling to a Bose-condensed system for strong coupling, since in the latter limit a direct mapping of the original fermionic system onto an effective system of bosons with a residual boson-boson interaction can be established. Explicit calculations are performed at the one-loop order. The phase coherence length phase is compared with the coherence length pair for two-electron correlation, which is relevant to distinguish the weak-͑k F pair ӷ1͒ from the strong-͑k F pair Ӷ1͒ coupling limits ͑k F being the Fermi wave vector͒ as well as to follow the crossover in between. It is shown that phase coincides with pair down to k F pair Ӎ10, pair in turn coinciding with the Pippard coherence length. In the strong-coupling limit we find instead that phase ӷ pair , with pair coinciding with the radius of the bound-electron pair. From the mapping onto an effective system of bosons in the strong-coupling limit we further relate pair with the ''range'' of the residual boson-boson interaction, which is physically the only significant length associated with the dynamics of the bosonic system. ͓S0163-1829͑96͒02422-8͔

We investigate the adiabatic evolution of a set of nondegenerate eigenstates of a parametrized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for which off-diagonal phases can be determined from published data.

We study the model of a molecular switch comprised of a molecule with a soft vibrational degree of freedom coupled to metallic leads. In the presence of strong electron-ion interaction, different charge states of the molecule correspond to substantially different ionic configurations, which can lead to very slow switching between energetically close configurations ͑Franck-Condon blockade͒. Application of transport voltage, however, can drive the molecule far out of thermal equilibrium and thus dramatically accelerate the switching. The tunneling electrons play the role of a heat bath with an effective temperature dependent on the applied transport voltage. Including the transport-induced "heating" self-consistently, we determine the stationary currentvoltage characteristics of the device and the switching dynamics for symmetric and asymmetric devices. We also study the effects of an extra dissipative environment and demonstrate that it can lead to enhanced nonlinearities in the transport properties of the device and dramatically suppress the switching dynamics.