Abstract:
We study small oscillations of the order parameter in weakly and strongly paired superconductors driven slightly out of equilibrium, in the collisionless approximation. While it was known for quite some time that the amplitude of the oscillations in a weakly paired superconductor decays as 1/t^(1/2), we show that in a superconductor sufficiently strongly paired so that its fermions form bound states usually referred to as molecules, these oscillations decay as 1/t^(3/2). The transition between these two regimes happens when the chemical potential of the superconductor vanishes, thus the behavior of the oscillations can be used to distinguish weakly and strongly paired superconductors. These results are obtained in the mean field approximation which may not be reliable in the crossover region between the strong and weak pairing, so we also obtain identical results within the two-channel model, which can be tuned to be reliable throughout the entire crossover, although it then describes a special type of interactions between the fermions which may be difficult to observe experimentally. Finally, we interpret the result in the strongly paired superconductor as the probability of the molecular decay as a function of time.

Abstract:
We complete the program outlined in the paper of the author with A. Migdal and sum up exactly all the fluctuations around the instanton solution of the randomly large scale driven Burgers equation. We choose the force correlation function $\kappa$ to be exactly quadratic function of the coordinate difference. The resulting probability distribution satisfy the differential equation proposed by Polyakov without an anomaly term. The result shows that unless the anomaly term is indeed absent it must come from other possible instanton solutions, and not from the fluctuations.

Abstract:
We develop an exact solution to the problem of one dimensional chiral bosons interacting via an s-wave Feshbach resonance. This problem is integrable, being the quantum analog of a classical two-wave model solved by the inverse scattering method thirty years ago. Its solution describes one or two branches of dressed chiral right moving molecules depending on the chemical potential (particle density). We also briefly discuss the possibility of experimental realization of such a system.

Abstract:
We study the phenomenon of turbulence from the point of view of statistical physics. We discuss what makes the turbulent states different from the thermodynamic equilibrium and give the turbulent analog of the partition function. Then, using the soluble theory of turbulence of waves as an example, we construct the turbulent action and show how one can compute the turbulent correlation functions perturbatively thus developing the turbulent Feynman diagrams. And at last, we discuss which part of what we learnt from the turbulence of waves can be used in other types of turbulence, in particular, the hydrodynamic turbulence of fluids. This paper is based on the talk delivered at SMQFT (1993) conference at the University of Southern California.

Abstract:
We apply the methods of Field Theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate them explicitly and study their properties. Using those densities we show how one can in principle calculate any correlation function in this theory by means of direct perturbative expansion in powers of the interaction. Then we give the general form of the corrections to the kinetic equation and develop an appropriate diagrammatic technique. This technique, while resembling that of $\varphi^4$ theory, has many new distinctive features. The role of the $\epsilon=d-4$ parameter is played here by the parameter $\kappa=\beta + d - \alpha - \gamma$ where $\beta$ is the dimension of the interaction, $d$ is the space dimension, $\alpha$ is the dimension of the energy spectrum and $\gamma$ is the ``classical'' wave density dimension. If $\kappa > 0$ then the Kolmogorov index is exact, and if $\kappa < 0$ then we expect it to be modified by the interaction. For $\kappa$ a small negative number, $\alpha<1$ and a special form of the interaction we compute this modification explicitly with the additional assumption of the irrelevance of the IR divergencies which still needs to be verified.

Abstract:
This paper examines the problem of molecule production in an atomic fermionic gas close to an s-wave Feshbach resonance by means of a magnetic field sweep through the resonance. The density of molecules at the end of the process is derived for narrow resonance and slow sweep.

Abstract:
When heavy nuclei collide, a quark-gluon plasma is formed. The plasma is subject to strong electric field due to the charge of the colliding nuclei. The electric field can influence the behavior of the quark-gluon plasma. In particular, we might observe an increased number of quarks moving in the direction of that field, as we do in the standard electron-ion plasma. In this paper we show that this phenomenon, called the runaway quarks, does not exist.

Abstract:
Conformal field theories with correlation functions which have logarithmic singularities are considered. It is shown that those singularities imply the existence of additional operators in the theory which together with ordinary primary operators form the basis of the Jordan cell for the operator $L_{0}$. An example of the field theory possessing such correlation functions is given.

Abstract:
We find an analog of Zamolodchikov's c-theorem for disordered two dimensional noninteracting systems in their supersymmetric representation. For this purpose we introduce a new parameter b which flows along the renormalization group trajectories much like the central charge for unitary two dimensional field theories. However, it is not known yet if this flow is irreversible. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the physical free energy of the disordered system defined on a cylinder. We discuss possible applications by computing b for two dimensional Dirac fermions with random gauge potential.

Abstract:
This paper studies the 1D pressureless turbulence (the Burgers equation). It shows that reliable numerics in this problem is very easy to produce if one properly discretizes the Burgers equation. The numerics it presents confirms the 7/2 power law proposed for probability of observing large negative velocity gradients in this problem. It also suggests that the entire probability function for the velocity gradients could be universal, perhaps in some approximate sense. In particular, the probability that the velocity gradient is negative appears to be $p \approx 0.21 \pm 0.01$ irrespective of the details of the random force. Finally, I speculate that the theory initially proposed by Polyakov, with a particular value of the "anomaly" parameter, may indeed be exact, at least as far as velocity gradients are concerned.