Vinay Ambegaokar

Effect of friction on electron transfer in biomolecules

In biological and chemical electron transfer, a nuclear reaction coordinate is coupled to other nuclear and/or ‘‘solvent’’ coordinates. This coupling, or friction, if strong enough, may substantially slow down motion along the reaction coordinate, and thus vitiate the assumption of electron transfer being nonadiabatic with respect to the nuclei. Here, a simple, fully quantum mechanical model for electron transfer using a one mode treatment which incorporates this coupling is studied. Path integral methods are used to study the dependence of the reaction rate on friction, and the limits of the moderate and the high friction are analyzed in detail. The first limit will prevail if the reaction coordinate is, e.g., an underdamped nuclear vibration, whereas the second limit will prevail if it corresponds to a slow or diffusive degree of freedom. In the high‐friction limit, the reaction rate is explicitly shown to vary between the nonadiabatic and adiabatic expressions as the tunneling matrix element and/or the friction are varied. Starting from a path integral expression for the time evolution of the reduced density matrix for the electron and reaction coordinate, a Fokker–Planck equation is obtained which reduces in the high‐friction limit to a Smoluchowski equation similar to one solved by Zusman.

Charge pumping and photovoltaic effect in open quantum dots

We propose a random matrix theory to describe the influence of a time-dependent external field on electron transport through open quantum dots. We describe the generation of the current by an oscillating field for the dot, connected to two leads with equal chemical potentials. For low-frequency fields, our results correspond to adiabatic charge pumping. Finite current can be produced if the system goes along a closed loop in parameter space, which covers a finite area. At high frequency, a finite current is produced even if the loop is a line in parameter space. This result can be explained in the same way as adiabatic pumping, but considering the evolution of the system in phase space rather than in parametric space.

Effect of Level Statistics on Superconductivity in Ultrasmall Metallic Grains.

We examine the destruction of superconducting pairing in metallic grains as their size is decreased for both even and odd numbers of electrons. This occurs when the average level spacing {ital d} is of the same order as the BCS order parameter {Delta}. The energy levels of these grains are randomly distributed according to random matrix theory, and we must work statistically. We find that the average value of the critical level spacing is larger than that for the model of equally spaced levels for both parities, and derive numerically the probability densities {ital P}{sub {ital o},{ital e}}({ital d}) that a grain of mean level spacing {ital d} shows pairing. {copyright} {ital 1996 The American Physical Society.}

BCS SUPERCONDUCTIVITY WITH FIXED NUMBER PARITY

We investigate superconductivity in a grand canonical ensemble with [ital fixed] [ital number] [ital parity] (even or odd). In the low-temperature limit we find small corrections to the BCS gap equation and dispersion [ital E]([ital k]). The even-odd free-energy difference in the same limit decreases linearly with temperature, in accordance with the behavior observed experimentally and previously arrived at from a quasiparticle model. The theory yields deviations from the BCS predictions for the specific heat, ultrasound attenuation, nucleon spin-relaxation rate, and electromagnetic absorption.

Loss ofπ-junction behavior in an interacting impurity Josephson junction

Using a generalization of the non-crossing approximation which incorporates Andreev reflection, we study the properties of an infinite-U Anderson impurity coupled to two superconducting leads. In the regime where

Electromagnetic properties of superconductors

\Delta

Andreev scattering and the Kondo effect

and

Theory of hopping conductivity in disordered systems

T_K

Universal gap fluctuations in the superconductor proximity effect.

are comparable, we find that the position of the sub-gap resonance in the impurity spectral function develops a strong anomalous phase dependence-- its energy is a minimum when the phase difference between the superconductors is equal to

Nonlinear Diamagnetic Response in Mesoscopic Rings of Superconductors above Tc

\pi