The dynamics of developing Cooper pairing at finite temperatures

We study the time evolution of a system of fermions with pairing interactions at a finite temperature. The dynamics is triggered by an abrupt increase of the BCS coupling constant. We show that if initially the fermions are in a normal phase, the amplitude of the BCS order parameter averaged over the Boltzman distribution of initial states exhibits damped oscillations with a relatively short decay time. The latter is determined by the temperature, the single-particle level spacing, and the ground state value of the BCS gap for the new coupling. In contrast, the decay is essentially absent when the system was in a superfluid phase before the coupling increase.Comment: 4 pages, figure fixe

Electron localization in sound absorption oscillations in the quantum Hall effect regime

The absorption coefficient for surface acoustic waves in a piezoelectric insulator in contact with a GaAs/AlGaAs heterostructure (with two-dimensional electron mobility $\mu= 1.3\times 10^5 cm^2/V\cdot s)$ at T=4.2K) via a small gap has been investigated experimentally as a function of the frequency of the wave, the width of the vacuum gap, the magnetic field, and the temperature. The magnetic field and frequency dependencies of the high-frequency conductivity (in the region 30-210 MHz) are calculated and analyzed. The experimental results can be explained if it assumed that there exists a fluctuation potential in which current carrier localization occurs. The absorption of the surface acoustic waves in an interaction with two-dimensional electrons localized in the energy "tails" of Landau levels is discussed.Comment: RevTeX 6 pages+6 EPS pic

Dissipationless BCS Dynamics with Large Branch Imbalance

In many situations a BCS-type superconductor will develop an imbalance between the populations of the holelike and electronlike spectral branches. This imbalance suppresses the gap. It has been noted by Gal'perin et al. [Sov. Phys. JETP 54, 1126 (1981)] that at large imbalance, when the gap is substantially suppressed, an instability develops. The analytic treatment of the system beyond the instability point is complicated by the fact that the Boltzmann approach breaks down. We study the short-time behavior following the instability, in the collisionless regime, using methods developed by Yuzbashyan et al. [J. Phys. A 38, 7831 (2005); Phys. Rev. B 72, 220503(R) (2005)].Comment: 12 pages, 3 figure

Nonequilibrium Cooper pairing in the nonadiabatic regime

We obtain a complete solution for the mean-field dynamics of the BCS paired state with a large, but finite number of Cooper pairs in the non-adiabatic regime. We show that the problem reduces to a classical integrable Hamiltonian system and derive a complete set of its integrals of motion. The condensate exhibits irregular multi-frequency oscillations ergodically exploring the part of the phase-space allowed by the conservation laws. In the thermodynamic limit however the system can asymptotically reach a steady state.Comment: 4 pages, no figure

Normal and anomalous solitons in the theory of dynamical Cooper pairing

We obtain multi-soliton solutions of the time-dependent Bogoliubov-de Gennes equations or, equivalently, Gorkov equations that describe the dynamics of a fermionic condensate in the dissipationless regime. There are two kinds of solitons - normal and anomalous. At large times, normal multi-solitons asymptote to unstable stationary states of the BCS Hamiltonian with zero order parameter (normal states), while the anomalous ones tend to eigenstates characterized by a nonzero anomalous average. Under certain circumstances, multi-soliton solutions break up into sums of single solitons. In the linear analysis near the stationary states, solitons correspond to unstable modes. Generally, they are nonlinear extensions of these modes, so that a stationary state with $k$ unstable modes gives rise to a $k$-soliton solution. We relate parameters of the multi-solitons to those of the asymptotic stationary state, which determines the conditions necessary for exciting solitons. We further argue that the dynamics in many physical situations is multi-soliton.Comment: 41 pages, 14 figure

Vortex mediated microwave absorption in superclean layered superconductors

In the superclean case the spectrum of vortex core excitations in the presence of disorder is not random but consists of two series of equally-spaced levels. The I-V characteristics of such superconductors displays many interesting phenomena. A series of resonances is predicted at frequencies commensurate with the spacing of the vortex excitations. These resonances reveal an even-odd anomaly. In the presence of one weak impurity the excitation levels can approach each other and almost cross. Absorption at very low frequencies is identified with the resonances arising in this case. The results of such microscopic theory coincide up to the order of magnitude with both the theory employing kinetic equation and the experiment. The non-linear effects associated with Zener transitions in such crossings are studied. These phenomena can be used as a probe of vortex core excitations.Comment: 11 pages, 2 Postscript figure

Molecular random walks and invariance group of the Bogolyubov equation

Statistics of molecular random walks in a fluid is considered with the help of the Bogolyubov equation for generating functional of distribution functions. An invariance group of solutions to this equation as functions of the fluid density is discovered. It results in many exact relations between probability distribution of the path of a test particle and its irreducible correlations with the fluid. As the consequence, significant restrictions do arise on possible shapes of the path distribution. In particular, the hypothetical Gaussian form of its long-range asymptotic proves to be forbidden (even in the Boltzmann-Grad limit). Instead, a diffusive asymptotic is allowed which possesses power-law long tail (cut off by ballistic flight length).Comment: 23 pages, no figures, LaTeX AMSART, author's translation from Russian of the paper accepted to the TMPh (``Theoretical and mathematical physics''

Bi-stability in voltage-biased NISIN structures

As a generic example of a voltage-driven superconducting structure we study a short superconductor connected to normal leads by means of low transparency tunnel junctions, with a voltage bias $V$ between the leads. The superconducting order parameter $\Delta$ is to be determined self-consistently. We study the stationary states of the system as well as the dynamics after a perturbation. We find a region in parameter space where there are two stable stationary states at a given voltage. These bi-stable states are distinguished by distinct values of the superconducting order parameter $\Delta$ and of the current between the leads. We have evaluated (1) the multi-valued superconducting order parameter $\Delta$ at given $V$; (2) the current between the leads at a given V; and (3) the critical voltage at which superconductivity in the island ceases. With regards to dynamics, we find numerical evidence that the stationary states are stable and that no complicated non-stationary regime can be induced by changing the voltage. This result is somewhat unexpected and by no means trivial, given the fact that the system is driven out of equilibrium. The response to a change in the voltage is always gradual, even in the regime where changing the interaction strength induces rapid anharmonic oscillations of the order parameter.Comment: 15 pages, 11 figures, submitted to Phys. Rev.

Thermodynamics of Nonstoichiometric Nickel Tellurides. I. Heat Capacity and Thermodynamic Functions of the δ Phase from 5 to 350°K

Heat capacities of the nickel tellurides were measured at compositions NiTe1.1 and NiTe2.0 (near limits of homogeneity of the δ phase) and at one intermediate composition, NiTe1.5, from 5 to 350°K. Heat capacity values and entropy and enthalpy increments are tabulated. No evidence of order‐disorder transitions, or thermal anomalies, or of contributions to the thermal properties from the anisotropy or phonon scattering by the holes in the structure on approaching the composition NiTe2 was observed. Although simple additivity of the heat capacities of the constituent elements failed to represent that of the solution compositions adequately, a Kopp‐Neumann treatment in terms of the limiting compositions of the δ phase gives good agreement with the experimental heat capacity and entropy of NiTe1.5 and hence is useful in interpolating to other intermediate compositions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70090/2/JCPSA6-28-3-497-1.pd