Critical transport in weakly disordered semiconductors and semimetals.

Motivated by Weyl semimetals and weakly doped semiconductors, we study transport in a weakly disordered semiconductor with a power-law quasiparticle dispersion ξ_{k}∝k^{α}. We show, that in 2α dimensions short-correlated disorder experiences logarithmic renormalization from all energies in the band. We study the case of a general dimension d using a renormalization group, controlled by an ϵ=2α-d expansion. Above the critical dimensions, conduction exhibits a localization-delocalization phase transition or a sharp crossover (depending on the symmetries of the Hamiltonian) as a function of disorder strength. We utilize this analysis to compute the low-temperature conductivity in Weyl semimetals and weakly doped semiconductors near and below the critical disorder point.

Topological invariant for the orbital spin of the electrons in the quantum Hall regime and Hall viscosity.

Hall conductance of noninteracting fermions filling a certain number of Landau levels can be written as a topological invariant. A particular version of this invariant when expressed in terms of the single particle Green's functions directly generalizes to cases when interactions are present including those of fractional Hall states, although in those cases this invariant no longer corresponds to Hall conductance. We argue that when evaluated for both integer and fractional Hall states this invariant gives twice the total orbital spin of fermions which in turn is closely related to the Hall viscosity, a quantity characterizing the integer and fractional Hall states which recently received substantial attention in the literature.

Reentrant BCS-BEC crossover and a superfluid-insulator transition in optical lattices.

We study the thermodynamics of a two-species Feshbach-resonant atomic Fermi gas in a periodic potential, focusing in a deep optical potential where a tight binding model is applicable. We show that for a more than half-filled band the gas exhibits a reentrant crossover with decreased detuning (increased attractive interaction), from a paired BCS superfluid to a Bose-Einstein condensate (BEC) of molecules of holes, back to the BCS superfluid, and finally to a conventional BEC of diatomic molecules. This behavior is associated with the nonmonotonic dependence of the chemical potential on detuning and the concomitant Cooper-pair or molecular size, larger in the BCS and smaller in the BEC regimes. For a single filled band we find a quantum phase transition from a band insulator to a BCS-BEC superfluid, and map out the corresponding phase diagram.

Nonequilibrium dynamics of weakly and strongly paired superconductors.

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 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 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. Finally, we interpret the result in the strongly paired superconductor as the probability of the molecular decay as a function of time.

Excitations of one-dimensional Bose-Einstein condensates in a random potential.

We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as l(omega) approximately 1/omega(alpha). We show that the well-known result alpha=2 applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, alpha starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, alpha=1. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.

Collapse and revivals of the photon field in a Landau-Zener process.

We consider the evolution of a two-level system coupled to a photon field initially in a coherent state, as the energy of the two-level system is linearly varied through resonance with the photon field. At a fixed time after the resonance, the amplitude of the photon field is found to show a collapse and subsequent revivals as a function of rate of energy variation. Including decay of the photon field, we find that the observation of such collapse and revivals is near the technological limit of current cavity QED experiments but should be achievable.

Many body generalization of the Landau-Zener problem.

We formulate and approximately solve a specific many body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems. Our solution can be used to understand, for example, the behavior of two-level systems coupled to an electromagnetic field, as realized in cavity QED experiments.

Strongly resonant p-wave superfluids.

We study theoretically a dilute gas of identical fermions interacting via a p-wave resonance. We show that, depending on the microscopic physics, there are two distinct regimes of p-wave resonant superfluids, which we term "weak" and "strong." Although expected naively to form a paired superfluid, a strongly resonant p-wave superfluid is in fact unstable toward the formation of a gas of fermionic trimers. We examine this instability and estimate the lifetime of the p-wave molecules due to the collisional relaxation into trimers. We discuss consequences for the experimental achievement of p-wave superfluids in both weakly and strongly resonant regimes.

Quantum phase transitions across a p-wave Feshbach resonance.

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.

Nonequilibrium dynamics and thermodynamics of a degenerate fermi gas across a feshbach resonance.

We consider a two-species degenerate Fermi gas coupled by a diatomic Feshbach resonance. We show that the resulting superfluid can exhibit a form of coherent BEC-to-BCS oscillations in response to a nonadiabatic change in the system's parameters, such as, for example, a sudden shift in the position of the Feshbach resonance. In the narrow resonance limit, the resulting solitonlike collisionless dynamics can be calculated analytically. In equilibrium, the thermodynamics can be accurately computed across the full range of BCS-BEC crossover, with corrections controlled by the ratio of the resonance width to the Fermi energy.

Some generic aspects of bosonic excitations in disordered systems.

We consider noninteracting bosonic excitations in disordered systems, emphasizing generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes established for fermionic systems. We examine the density rho(omega) of excitation frequencies omega, showing how the universal behavior rho(omega) approximately omega(4) for small omega can be obtained both from general arguments and by detailed calculations for one-dimensional models.