Albert Schmid

On a quasiclassical Langevin equation

It is shown that the motion of a quantum mechanical particle coupled to a dissipative environment can be described by a Langevin equation where the stochastic force is generalized such that its power spectrum is in accordance with the fluctuation-dissipation theorem. This generalized Langevin equation has an interesting range of applicability. It includes the quasiclassical regime provided that the damping, that is, the coupling of the particle to its environment, is sufficiently strong.

Quasiclassical wave function in multidimensional quantum decay problems

Abstract The quantum decay rate of metastable state is calculated in quasiclassical accuracy. Specifically, the calculation is based entirely on the standard quasiclassical ansatz, where the wave function is put equal to exp-(action)/ħ, and where the action is expanded in powers of ħ. Such a calculation is well known in the case of one-dimensional systems, and not so well known for multidimensional systems. Therefore, this paper intends to give a comprehensive presentation of the quasiclassical method. A straightforward procedure leads to a decay rate which agrees with the one obtained by the instanton technique. However, a calculation of the entire wave function shows that the procedure is consistent only if the metastable state is dominated by an internal degree of freedom which is slow in comparison with the remaining degrees of freedom.

Persistent Currents of Single Mesoscopic Rings

We study the stochastic fluctuations (from sample to sample) in the persistent current I() of mesoscopic rings threaded by a flux . We find that it is necessary to include the Coulomb interaction between the electrons. Then we obtain I21/2 ~ (L/l)I ~ evF/L; and h/e for the dominant period in . This agrees well with a recent experiment on single gold rings. Furthermore, we predict that the persistent currents have a Gaussian probability distribution, since the total electron number of a typical ring is still very large.

Stability of superconducting states out of thermal equilibrium

Quasiparticles of superconductors can be manipulated either by irradiation or tunnel injection such that substantial changes of the gap (order parameter) occur which are most pronounced close to the transition temperature. These phenomena are investigated by a theory which is based on the combined system of the Boltzmann equation and the BCS gap equation. Several stationary, spatially homogeneous states are found in some range of temperatures. A linear stability analysis reveals two types of behavior, depending, essentially, on whether quasiparticle diffusion increases or decreases the stability. In a representative situation of the first type, two states turn out to be locally stable. An investigation of a nonlinear equation of motion for the order parameter leads to the conclusion that a first-order phase transition between these two states occurs at a given temperature. In a situation of the second type, one finds that fluctuations of a definite wave vector destroy the spatially homogeneous state and lead to a stable state of layered structure.

Quantum creep of vortices in granular superconductors

Abstract Recent experimental and theoretical studies of granular superconducting systems have attracted great attention. In general, the superconducting grains are only weakly coupled, and therefore at low temperatures the order parameter has a fixed modulus which is independent of any super current flow. It is the phase of the order parameter only which remains a degree of freedom for each grain. In such a case there exist vortex configurations and one expects minima in the potential energy when the center of the vortex is situated in the free space between the grains. We consider here the case where the energy barrier which separates the adjacent minima is sufficiently well developed. Then, a vortex may change its position by thermal activation over the top of the barrier or by quantum tunneling between neighboring minima. In this paper we study this quantum tunneling which, in the presence of a transport current, leads to a creep-like flow of vortices.

Anomalous magnetoconductance beyond the diffusion limit

The weak localization contribution to the conductance depends sensitively on the applied magnetic field. This anomalous magnetoconductance provides a unique tool for the identification of weak localization and other phenomena associated with it. The standard theory of the anomalous magnetoconductance is based on the diffusion approximation, which applies to the case where the number of elastic scattering events is very large during a time of phase coherence in the electronic wave. For a strictly two-dimensional film, an arbitrary number of scattering events is considered and marked deviations are found from the standard theory if this number is not large.

The quasiclassical Langevin equation and its application to the decay of a metastable state and to quantum fluctuations

We report on investigations on the consequences of the quasiclassical Langevin equation. This Langevin equation is an equation of motion of the classical type where, however, the stochastic Langevin force is correlated according to the quantum form of the dissipation-fluctuation theorem such that ultimately its power spectrum increases linearly with frequency. Most extensively, we have studied the decay of a metastable state driven by a stochastic force. For a particular type of potential well (piecewise parabolic), we have derived explicit expressions for the decay rate for an arbitrary power spectrum of the stochastic force. We have found that the quasiclassical Langevin equation leads to decay rates which are physically meaningful only within a very restricted range. We have also studied the influence of quantum fluctuations on a predominantly deterministic motion and we have found that there the predictions of the quasiclassical Langevin equations are correct.

On the influence of lattice vibrations on the tunnel-current in normal metals

The tunnel-current in normal metals should show a fine structure due to the dynamical electron-phonon interaction and the momentum dependence of the tunneling matrix elements. This structure reflects the peaks of the density of phonon states and is smaller than that one observed in superconductors by one order of magnitude.

Kinetic Equations for Dirty Superconductors

In this lecture, I will first derive from the Gorkov-Eliashberg theory a system of kinetic equations and then, I will show that these equations allow an adequate and convenient calculation of nonequilibrium phenomena in superconductors.

The approach to equilibrium in a pure superconductor the relaxation of the Cooper pair density

AbstractElectron-phonon and electron-electron collisions are the processes which determine the relaxation timeτR of the Cooper pair density. The case is considered for which the deviation of the pair density from equilibrium is small and where the equilibrium state is homogeneous. Starting from the Eliashberg equation, one is able to reduce the problem to a quadrature once the equilibrium Green functions are known. If the deviation is constant in space, andT/Tc≳0.5, we find