The Upper Critical Field in Disordered Two-Dimensional Superconductors

We present calculations of the upper critical field in superconducting films as a function of increasing disorder (as measured by the normal state resistance per square). In contradiction to previous work, we find that there is no anomalous low-temperature positive curvature in the upper critical field as disorder is increased. We show that the previous prediction of this effect is due to an unjustified analytical approximation of sums occuring in the perturbative calculation. Our treatment includes both a careful analysis of first-order perturbation theory, and a non-perturbative resummation technique. No anomalous curvature is found in either case. We present our results in graphical form.Comment: 11 pages, 8 figure

Is classical reality completely deterministic?

The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all autonomous classical systems. We give counterexamples of this view. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension shows that the solution to the Cauchy problem with the initial conditions of a particular type is not unique. Therefore, random behavior of closed classical systems is indeed possible. This finding provides a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems.Comment: Replace the paper with a revised versio

Berry phases and pairing symmetry in Holstein-Hubbard polaron systems

We study the tunneling dynamics of dopant-induced hole polarons which are self-localized by electron-phonon coupling in a two-dimensional antiferro- magnet. Our treatment is based on a path integral formulation of the adia- batic approximation, combined with many-body tight-binding, instanton, con- strained lattice dynamics, and many-body exact diagonalization techniques. Our results are mainly based on the Holstein-$tJ$ and, for comparison, on the Holstein-Hubbard model. We also study effects of 2nd neighbor hopping and long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics is mapped onto an effective low-energy Hamiltonian which takes the form of a fermion tight-binding model with occupancy dependent, predominant- ly 2nd and 3rd neighbor tunneling matrix elements, excluded double occupan- cy, and an effective intersite charge interactions. Antiferromagnetic spin correlations in the original many-electron Hamiltonian are reflected by an attractive contribution to the 1st neighbor charge interaction and by Berry phase factors which determine the signs of effective polaron tunneling ma- trix elements. In the two-polaron case, these phase factors lead to polaron pair wave functions of either $d_{x^2-y^2}$-wave symmetry or p-wave symme- try with zero and nonzero total pair momentum, respectively. Implications for the doping dependent isotope effect, pseudo-gap and Tc of a superconduc- ting polaron pair condensate are discussed/compared to observed in cuprates.Comment: 23 pages, revtex, 13 ps figure

Effect of Magnetic Impurities on Suppression of the Transition Temperature in Disordered Superconductors

We calculate the first-order perturbative correction to the transition temperature $T_c$ in a superconductor with both non-magnetic and magnetic impurities. We do this by first evaluating the correction to the effective potential, $\Omega(\Delta)$, and then obtain the first-order correction to the order parameter, $\Delta$, by finding the minimum of $\Omega(\Delta)$. Setting $\Delta=0$ finally allows $T_c$ to be evaluated. $T_c$ is now a function of both the resistance per square, $R_\square$, a measure of the non-magnetic disorder, and the spin-flip scattering rate, $1/\tau_s$, a measure of the magnetic disorder. We find that the effective pair-breaking rate per magnetic impurity is virtually independent of the resistance per square of the film, in agreement with an experiment of Chervenak and Valles. This conclusion is supported by both the perturbative calculation, and by a non-perturbative re-summation technique.Comment: 29 pages, 9 figure

Light Quarks in the Instanton Vacuum at Finite Baryon Density

We consider the finite density, zero-temperature behaviour of quark matter in the instanton picture. Since the instanton-induced interactions are attractive in both $\bar{q}q$ and $qq$ channels, a competition ensues between phases of matter with condensation in either or both. It results in chiral symmetry restoration due to the onset of diquark condensation, a `colour supercondutor', at finite density. Also present is a state with both manners of condensation, however this phase is found to be thermodynamically disfavoured for equilibrium matter. Properties of quark matter in each phase are discussed, with emphasis on the microscopic effects of the effective mass and superconducting energy gap.Comment: 29 pages, 8 figures, LaTeX, minor typos correcte

Anomalous dimensions and phase transitions in superconductors

The anomalous scaling in the Ginzburg-Landau model for the superconducting phase transition is studied. It is argued that the negative sign of the $\eta$ exponent is a consequence of a special singular behavior in momentum space. The negative sign of $\eta$ comes from the divergence of the critical correlation function at finite distances. This behavior implies the existence of a Lifshitz point in the phase diagram. The anomalous scaling of the vector potential is also discussed. It is shown that the anomalous dimension of the vector potential $\eta_A=4-d$ has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling $\sigma(\omega)\sim\xi^{z-2}$. The prediction $z\approx 3.7$ is obtained from existing Monte Carlo data.Comment: RevTex, 20 pages, no figures; small changes; version accepted in PR

White noise and heating of open quantum field Fermi systems

I study the time evolution of the density matrices of quantum Fermi systems interacting with classic external Fermi fields. This interaction either changes the temperature of the system or it affects the density of particles. For relativistic Dirac fermions, variations of temperature lead to creation (annihilation) of particle - antiparticle pairs. The change of the density (or of the chemical potential) indicates the existence of the incoming (outgoing) flux of fermions from (to) the bath. These changes are independent for the different modes and in order to model the thermalization one should adjust the spectrum of the noise. The linear time dependences of the densities of particles are characteristic for all the processes.I study the time evolution of the density matrices of quantum Fermi systems interacting with classic external Fermi fields. This interaction either changes the temperature of the system or it affects the density of particles. For relativistic Dirac fermions, variations of temperature lead to creation (annihilation) of particle - antiparticle pairs. The change of the density (or of the chemical potential) indicates the existence of the incoming (outgoing) flux of fermions from (to) the bath. These changes are independent for the different modes and in order to model the thermalization one should adjust the spectrum of the noise. The linear time dependences of the densities of particles are characteristic for all the processes