Emil A. Yuzbashyan

Influence of topology on bacterial social interaction

The environmental topology of complex structures is used by Escherichia coli to create traveling waves of high cell density, a prelude to quorum sensing. When cells are grown to a moderate density within a confining microenvironment, these traveling waves of cell density allow the cells to find and collapse into confining topologies, which are unstable to population fluctuations above a critical threshold. This was first observed in mazes designed to mimic complex environments, then more clearly in a simpler geometry consisting of a large open area surrounding a square (250 × 250 μm) with a narrow opening of 10–30 μm. Our results thus show that under nutrient-deprived conditions bacteria search out each other in a collective manner and that the bacteria can dynamically confine themselves to highly enclosed spaces.

Eigenfunction fractality and pseudogap state near the superconductor-insulator transition.

We develop a theory of a pseudogap state appearing near the superconductor-insulator (SI) transition in strongly disordered metals with an attractive interaction. We show that such an interaction combined with the fractal nature of the single-particle wave functions near the mobility edge leads to an anomalously large single-particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.

Dynamical Vanishing of the Order Parameter in a Fermionic Condensate

We analyze the dynamics of a condensate of ultracold atomic fermions following an abrupt change of the pairing strength. At long times, the system goes to a nonstationary steady state, which we determine exactly. The superfluid order parameter asymptotes to a constant value. We show that the order parameter vanishes when the pairing strength is decreased below a certain critical value. In this case, the steady state of the system combines properties of normal and superfluid states -- the gap and the condensate fraction vanish, while the superfluid density is nonzero.

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 nonadiabatic 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 multifrequency 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.

Bardeen-Cooper-Schrieffer Theory of Finite-Size Superconducting Metallic Grains

Antonio M. Garćıa-Garćıa, Juan Diego Urbina, 3 Emil A. Yuzbashyan, Klaus Richter, and Boris L. Altshuler 7 Physics Department, Princeton University, Princeton, New Jersey 08544, USA Institut Für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany Department of Physics, Universidad Nacional de Colombia, Cll45 Cra 30, Bogota, Colombia Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA Institut Für Theoretische Physik, Universität Regensburg, 93047 Regensburg, Germany Physics Department, Columbia University, 538 West 120th Street, New York, NY 10027, USA NEC-Laboratories America, Inc., 4 Independence Way, Princeton, NJ 085540, USA

Integrable dynamics of coupled Fermi-Bose condensates

We study the mean-field dynamics of a fermionic condensate interacting with a single bosonic mode (a generalized Dicke model). This problem is integrable and can be mapped onto a corresponding BCS problem. We derive the general solution and a full set of integrals of motion for the time evolution of coupled Fermi-Bose condensates. The present paper complements our earlier study of the dynamics of the BCS model. Here we provide a self-contained introduction to the variable separation method, which enables a complete analytical description of the evolution of the generalized Dicke, BCS, and other similar models.

Finite-size corrections for the pairing Hamiltonian

We study the effects of superconducting pairing in small metallic grains. We show that in the limit of large Thouless conductance one can explicitly determine the low-energy spectrum of the problem as an expansion in the inverse number of electrons on the grain. The expansion is based on the formal exact solution of the Richardson model. We use this expansion to calculate finite-size corrections to the ground-state energy, Matveev-Larkin parameter, and excitation energies.

Strong-coupling expansion for the pairing Hamiltonian for small superconducting metallic grains

The paper is devoted to the study of the effects due to superconducting pairing in small metallic grains. We explicitly determine the low-energy spectrum of the problem at strong superconducting coupling and in the limit of large Thouless conductance. We start with the strong-coupling limit and develop a systematic expansion in powers of the inverse coupling constant for the many-particle spectrum of the system. The strong- coupling expansion is based on the formal exact solution of the Richardson model and converges for realistic values of the coupling constant. We use this expansion to study the low-energy excitations of the system, in particular energy and spin gaps in the many-body spectrum.

Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium

We study the non-adiabatic dynamics of a 2D p+ip superfluid following an instantaneous quantum quench of the BCS coupling constant. The model describes a topological superconductor with a non-trivial BCS (trivial BEC) phase appearing at weak (strong) coupling strengths. We extract the exact long-time asymptotics of the order parameter �(t) by exploiting the integrability of the classical p-wave Hamiltonian, which we establish via a Lax construction. Three different types of asymptotic behavior can occur depending upon the strength and direction of the interaction quench. We refer to these as the non-equilibrium phases {I, II, III}, characterized as follows. In phase I, the order parameter asymptotes to zero due to dephasing. In phase II, � → �∞, a nonzero constant. Phase III is characterized by persistent oscillations of �(t). For quenches within phases I and II, we determine the topological character of the asymptotic states. We show that two different formulations of the bulk topological winding number, although equivalent in the BCS or BEC ground states, must be regarded as independent out of equilibrium. The first winding number Q characterizes the Anderson pseudospin texture of the initial state; we show that Q is generically

BCS superconductivity in metallic nanograins: Finite-size corrections, low-energy excitations, and robustness of shell effects.

We combine the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements to describe analytically how the superconducting gap depends on the size and shape of a two- and three-dimensional superconducting grain. In chaotic grains mesoscopic fluctuations of the matrix elements lead to a smooth dependence of the order parameter on the excitation energy. In the integrable case we find shell effects; i.e., for certain values of the electron number N a small change in N leads to large changes in the energy gap. With regard to possible experimental tests we provide a detailed analysis of the dependence of the gap on the coherence length and the robustness of shell effects under small geometrical deformations.