Resistance due to vortex motion in the ν=1\nu=1 bilayer quantum Hall superfluid

The longitudinal and Hall resistances have recently been measured for quantum Hall bilayers at total filling $\nu=1$ in the superfluid state with interlayer pairing, both for currents flowing parallel to one another and for "counterflowing" currents in the two layers. Here I examine the contribution to these resistances from the motion of unpaired vortices in these systems, developing some possible explanations of various qualitative features of these data.Comment: 4 pages, slightly revised, accepted to PR

Localization of interacting fermions at high temperature

We suggest that if a localized phase at nonzero temperature $T>0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and $T$ is very high. We show that in this high-$T$ regime the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero $T$

Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

We treat the nonequilibrium motion of a single impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as $\sim t^{d/(d+1)}$ for the $d$-dimensional system with $d\geq 2$. For nonzero temperature $T$, this crosses over to diffusive motion at long times with diffusivity $D\sim T^{-(d-1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.Comment: 5 pages, 1 figure, to appear in Phys. Rev.

Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit

The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus to define the phase transition one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called "avalanche" instability due to rare thermalizing regions in the MBL phase for quenched-random systems in more than one spatial dimension, finding an unconventional way of scaling the systems so that they do have a type of phase transition. These arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension is a transition where entanglement in the eigenstates begins to spread in to some typical regions: the transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.Comment: 10 pages, 2 figure

Ballistic spreading of entanglement in a diffusive nonintegrable system

We study the time evolution of the entanglement entropy of a one-dimensional nonintegrable spin chain, starting from random nonentangled initial pure states. We use exact diagonalization of a nonintegrable quantum Ising chain with transverse and longitudinal fields to obtain the exact quantum dynamics. We show that the entanglement entropy increases linearly with time before finite-size saturation begins, demonstrating a ballistic spreading of the entanglement, while the energy transport in the same system is diffusive. Thus we explicitly demonstrate that the spreading of entanglement is much faster than the energy diffusion in this nonintegrable system.Comment: 7 pages, 7 figures. Published version. Supplementary material adde

Many body localization and thermalization in quantum statistical mechanics

We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the `Eigenstate Thermalization Hypothesis' (ETH), and the resulting `single-eigenstate statistical mechanics'. We then focus on a class of systems which fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can locally remember forever information about their local initial conditions, and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL), and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveals dynamically-stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality where equilibrium ordering is forbidden.Comment: Updated to reflect recent development

Dissipation peak as an indicator of sample inhomogeneity in solid 4^4He oscillator experiments

A simple phenomenological model is developed for the recent torsional oscillator experiments on solid $^4$He. Within this model, for a homogeneous sample there is a specific quantitative relation between the change in the oscillator's frequency and its maximum damping at the apparent supersolid transition. Much of the published data do not satisfy this relation, indicating that the dissipation peaks in those samples are strongly inhomogeneously broadened.Comment: 2 page

Evaporative depolarization and spin transport in a unitary trapped Fermi gas

We consider a partially spin-polarized atomic Fermi gas in a high-aspect-ratio trap, with a flux of predominantly spin-up atoms exiting the center of the trap. We argue that such a scenario can be produced by evaporative cooling, and we find that it can result in a substantially non-equilibrium polarization pattern for typical experimental parameters. We offer this as a possible explanation for the quantitative discrepancies in recent experiments on spin-imbalanced unitary Fermi gases.Comment: 6 pages, 3 figures; published versio