Fermi Edge Resonances in Non-equilibrium States of Fermi Gases

We formulate the problem of the Fermi Edge Singularity in non-equilibrium states of a Fermi gas as a matrix Riemann-Hilbert problem with an integrable kernel. This formulation is the most suitable for studying the singular behavior at each edge of non-equilibrium Fermi states by means of the method of steepest descent, and also reveals the integrable structure of the problem. We supplement this result by extending the familiar approach to the problem of the Fermi Edge Singularity via the bosonic representation of the electronic operators to non-equilibrium settings. It provides a compact way to extract the leading asymptotes.Comment: Accepted for publication, J. Phys.

Hofstadter butterfly as Quantum phase diagram

The Hofstadter butterfly is viewed as a quantum phase diagram with infinitely many phases, labelled by their (integer) Hall conductance, and a fractal structure. We describe various properties of this phase diagram: We establish Gibbs phase rules; count the number of components of each phase, and characterize the set of multiple phase coexistence.Comment: 4 prl pages 1 colored figure typos corrected, reference [26] added, "Ten Martini" assumption adde

Pairing in High Temperature Superconductors and Berry Phase

The topological approach to the understanding of pairing mechanism in high $T_c$ superconductors analyses the relevance of the Berry phase factor in this context. This also gives the evidence for the pairing mechanism to be of magnetic origin.Comment: 6 page

Magnetic properties of the Anderson model: a local moment approach

We develop a local moment approach to static properties of the symmetric Anderson model in the presence of a magnetic field, focussing in particular on the strong coupling Kondo regime. The approach is innately simple and physically transparent; but is found to give good agreement, for essentially all field strengths, with exact results for the Wilson ratio, impurity magnetization, spin susceptibility and related properties.Comment: 7 pages, 3 postscript figues. Latex 2e using the epl.cls Europhysics Letters macro packag

Raman Scattering and Anomalous Current Algebra: Observation of Chiral Bound State in Mott Insulators

Recent experiments on inelastic light scattering in a number of insulating cuprates [1] revealed a new excitation appearing in the case of crossed polarizations just below the optical absorption threshold. This observation suggests that there exists a local exciton-like state with an odd parity with respect to a spatial reflection. We present the theory of high energy large shift Raman scattering in Mott insulators and interpret the experiment [1] as an evidence of a chiral bound state of a hole and a doubly occupied site with a topological magnetic excitation. A formation of these composites is a crucial feature of various topological mechanisms of superconductivity. We show that inelastic light scattering provides an instrument for direct measurements of a local chirality and anomalous terms in the electronic current algebra.Comment: 18 pages, TeX, C Version 3.

Tunneling and orthogonality catastrophe in the topological mechanism of superconductivity

We compute the angular dependence of the order parameter and tunneling amplitude in a model exhibiting topological superconductivity and sketch its derivation as a model of a doped Mott insulator. We show that ground states differing by an odd number of particles are orthogonal and the order parameter is in the d-representation, although the gap in the electronic spectrum has no nodes. We also develop an operator algebra, that allowes one to compute off-diagonal correlation functions.Comment: 4 pages, Revtex, psfig; some references are correcte

Mate Choice and the Evolutionary Stability of a Fixed Threshold in a Sequential Search Strategy

The sequential search strategy is a prominent model of searcher behavior, derived as a rule by which females might sample and choose a mate from a distribution of prospective partners. The strategy involves a threshold criterion against which prospective mates are evaluated. The optimal threshold depends on the attributes of prospective mates, which are likely to vary across generations or within the lifetime of searchers due to stochastic environmental events. The extent of this variability and the cost to acquire information on the distribution of the quality of prospective mates determine whether a learned or environmentally canalized threshold is likely to be favored. In this paper, we determine conditions on cross-generational perturbations of the distribution of male phenotypes that allow for the evolutionary stability of an environmentally canalized threshold. In particular, we derive conditions under which there is a genetically determined threshold that is optimal over an evolutionary time scale in comparison to any other unlearned threshold. These considerations also reveal a simple algorithm by which the threshold could be learned

Tunneling in the topological mechanism of superconductivity

We compute the two-particle matrix element and Josephson tunneling amplitude in a two-dimensional model of topological superconductivity which captures the physics of the doped Mott insulator. The hydrodynamics of topological electronic liquid consists of the compressible charge sector and the incompressible chiral topological spin liquid. We show that ground states differing by an odd number of particles are orthogonal and insertion of two extra electrons is followed by the emission of soft modes of the transversal spin current. The orthogonality catastrophe makes the physics of superconductivity drastically different from the BCS-theory but similar to the physics of one-dimensional electronic liquids. The wave function of a pair is dressed by soft modes. As a result the two particle matrix element forms a complex d-wave representation (i.e., changes sign under $90^o$ degree rotation), although the gap in the electronic spectrum has no nodes. In contrast to the BCS-theory the tunneling amplitude has an asymmetric broad peak (much bigger than the gap) around the Fermi surface. We develop an operator algebra, that allows one to compute other correlation functions.Comment: 18 pages, 2 eps figures, revtex, psfig, significant changes have been mad

Raman scattering and anomalous current algebra in Mott insulators

We present a theory of large shift Raman scattering in Mott insulators and show that inelastic light scattering provides information about electronic current algebra. We argue that the recent experiment where a new excitation below the optical absorption threshold was observed in crossed polarizations gives evidence of anomalous terms in the current alegebra. We show that it suggests there exists an exciton bound state with a topological magnetic excitation with odd parity with respect to a spatial reflection

Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas

A semiclassical wave-packet propagating in a dissipationless Fermi gas inevitably enters a "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes a dramatic shock wave phenomenon. The non-linear effects in electronic transport are due to the curvature of the electronic spectrum at the Fermi surface. They can be probed by a sudden switching of a local potential. In equilibrium, this process produces a large number of particle-hole pairs, a phenomenon closely related to the Orthogonality Catastrophe. We study a generalization of this phenomenon to the non-equilibrium regime and show how the Orthogonality Catastrophe cures the Gradient Catastrophe, providing a dispersive regularization mechanism. We show that a wave packet overturns and collapses into modulated oscillations with the wave vector determined by the height of the initial wave. The oscillations occupy a growing region extending forward with velocity proportional to the initial height of the packet. We derive a fundamental equation for the transition rates (MKP-equation) and solve it by means of the Whitham modulation theory.Comment: 5 pages, 1 figure, revtex4, pr