Strong coupling of electronic and vibrational degrees of freedom entails a low-bias suppression of the current through single-molecule devices, termed Franck-Condon blockade. In the limit of slow vibrational relaxation, transport in the Franck-Condon-blockade regime proceeds via avalanches of large numbers of electrons, which are interrupted by long waiting times without electron transfer. The avalanches consist of smaller avalanches, leading to a self-similar hierarchy which terminates once the number of transferred electrons per avalanche becomes of the order of unity. Experimental signatures of self-similar avalanche transport are strongly enhanced current (shot) noise, as expressed by giant Fano factors, and a power-law noise spectrum. We develop a theory of the Franck-Condonblockade regime with particular emphasis on effects of electron cotunneling through highly excited vibrational states. As opposed to the exponential suppression of sequential tunneling rates for low-lying vibrational states, cotunneling rates suffer only a power-law suppression. This leads to a regime where cotunneling dominates the current for any gate voltage. Including cotunneling within a rate-equation approach to transport, we find that both the Franck-Condon blockade and self-similar avalanche transport remain intact in this regime. We predict that cotunneling leads to absorptioninduced vibrational sidebands in the Coulomb-blockaded regime as well as intrinsic telegraph noise near the charge degeneracy point.

Under a strong ac drive the zero-frequency linear response dissipative resistivity rho(d)(j=0) of a homogeneous state is allowed to become negative. We show that such a state is absolutely unstable. The only time-independent state of a system with a rho(d)(j=0)<0 is characterized by a current which almost everywhere has a magnitude j(0) fixed by the condition that the nonlinear dissipative resistivity rho(d)(j(2)(0))=0. As a result, the dissipative component of the dc-electric field vanishes. The total current may be varied by rearranging the current pattern appropriately with the dissipative component of the dc-electric field remaining zero. This result, together with the calculation of Durst et al., indicating the existence of regimes of applied ac microwave field and dc magnetic field where rho(d)(j=0)<0, explains the zero-resistance state observed by Mani et al. and Zudov et al.

We develop a field theory formalism for the disordered interacting electron liquid in the dynamical Keldysh formulation. This formalism is an alternative to the previously used replica technique. In addition it naturally allows for the treatment of non-equilibrium effects. Employing the gauge invariance of the theory and carefully choosing the saddle point in the Q-matrix manifold, we separate purely phase effects of the fluctuating potential from the ones that change quasi-particle dynamics. As a result, the cancellation of super-divergent diagrams (double logarithms in d = 2) is automatically build in the formalism. As a byproduct we derive a non-perturbative expression for the single particle density of states. The remaining low-energy σ-model describes the quantum fluctuations of the electron distribution function. Its saddle point equation appears to be the quantum kinetic equation with an appropriate collision integral along with collisionless terms. Altshuler-Aronov corrections to conductivity are shown to arise from the one-loop quantum fluctuation effects.

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.

We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, κ. This is in striking contrast to the Stokes flow, in which the resistance is independent of κ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magnetoresistance.

Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the Heisenberg time. We find that the singularities (present for random matrix ensembles) are washed out in a grain with a finite conductance. The results are nonuniversal (they depend on the shape of the grain and on its conductance), though they suggest a generalization for any system with finite Heisenberg time.

The Bohigas-Giannoni-Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory is proved. For this purpose a new semiclassical field theory for individual chaotic systems is constructed in the framework of the non-linear σ-model. The low lying modes are shown to be associated with the Perron-Frobenius spectrum of the underlying irreversible classical dynamics. It is shown that the existence of a gap in the Perron-Frobenius spectrum results in a RMT behavior. Moreover, our formalism offers a way of calculating system specific corrections beyond RMT.The theory of random matrices [1] emerged from the need to characterize complex quantum systems in which knowledge of the Hamiltonian is minimal, e.g. complex nuclei. The basic hypothesis is that the Hamiltonian may be treated as one drawn from an ensemble of random matrices with appropriate symmetries. It has been proposed by invoking the complexity of systems which have many degrees of freedom with unknown interaction coupling among them.The study of the statistical quantum properties of systems with small number of degrees of freedom, within the framework of random matrix theory (RMT), has developed along two parallel lines. The first was by considering an ensemble of random systems such as disordered metallic grains [2]. Randomness in this case is introduced on the level of the Hamiltonian itself, e.g. as a consequence of the unknown impurity configuration. In the second approach, RMT was used in order to understand the level statistics of non-stochastic systems which are chaotic in their classical limit such as the Sinai or the stadium billiards [3]. Here "randomness" is generated by the underlying deterministic classical dynamics itself. Nevertheless, it has been conjectured [3] that "spectrum fluctuations of quantal time-reversal invariant systems whose classical analogues are strongly chaotic have the Gaussian Orthogonal Ensembles pattern".Despite being supported by extensive numerical studies, the origin of the success of RMT as well as its domain of validity are still not completely resolved. In this letter we show that, in the semiclassical limit, this conjecture is indeed valid for systems with exponential decay of classical correlation functions in time. Moreover, the formalism which we introduce below offers a way of calculating system specific corrections beyond RMT.So far, the main attempts to establish the relationship between non-stochastic chaotic systems and RMT, have been based on periodic orbit theory [4]. Gutzwiller's trace formula expresses the semiclassical density of states as an infinite sum over the classical periodic orbits of the system. However, the number of periodic orbits is exponentially large and clearly contains information that is redundant from quantum mechanical point of view. This detailed information conceals the way of drawing a connection between the quantum behavior of chaotic systems and RMT. Indeed, the success of the periodic...

We demonstrate that in a wide range of temperatures Coulomb drag between two weakly coupled quantum wires is dominated by processes with a small interwire momentum transfer. Such processes, not accounted for in the conventional Luttinger liquid theory, cause drag only because the electron dispersion relation is not linear. The corresponding contribution to the drag resistance scales with temperature as T2 if the wires are identical, and as T5 if the wires are different.