43 research outputs found
Classical and quantum systems: transport due to rare events
We review possible mechanisms for energy transfer based on 'rare' or
'non-perturbative' effects, in physical systems that present a many-body
localized phenomenology. The main focus is on classical systems, with or
without quenched disorder. For non-quantum systems, the breakdown of
localization is usually not regarded as an issue, and we thus aim at
identifying the fastest channels for transport. Next, we contemplate the
possibility of applying the same mechanisms in quantum systems, including
disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized
systems with mobility edges at energies below the edge, and strongly disordered
lattice systems in . For quantum mechanical systems, the relevance of
these considerations for transport is currently a matter of debate.Comment: Review paper. To appear on the special issue on Many-body
Localization in Annalen der Physi
Random walk driven by the simple exclusion process
We prove a strong law of large numbers and an annealed invariance principle
for a random walk in a one-dimensional dynamic random environment evolving as
the simple exclusion process with jump parameter . First, we establish
that if the asymptotic velocity of the walker is non-zero in the limiting case
"", where the environment gets fully refreshed between each
step of the walker, then, for large enough, the walker still has a
non-zero asymptotic velocity in the same direction. Second, we establish that
if the walker is transient in the limiting case , then, for
small enough but positive, the walker has a non-zero asymptotic
velocity in the direction of the transience. These two limiting velocities can
sometimes be of opposite sign. In all cases, we show that the fluctuations are
normal.Comment: v2 -> v3: Figures and heuristic comments added. Various typos
correcte
Asymptotic quantum many-body localization from thermal disorder
We consider a quantum lattice system with infinite-dimensional on-site
Hilbert space, very similar to the Bose-Hubbard model. We investigate many-body
localization in this model, induced by thermal fluctuations rather than
disorder in the Hamiltonian. We provide evidence that the Green-Kubo
conductivity , defined as the time-integrated current
autocorrelation function, decays faster than any polynomial in the inverse
temperature as . More precisely, we define approximations
to by integrating the current-current
autocorrelation function up to a large but finite time and we rigorously
show that vanishes as , for
any such that is sufficiently large.Comment: 53 pages, v1-->v2, revised version accepted in Comm.Math.Phys. We
added an extensive outline of proofs, a glossary of symbols and more
explanations in Section
Glassy dynamics in strongly anharmonic chains of oscillators
We review the mechanism for transport in strongly anharmonic chains of
oscillators near the atomic limit where all oscillators are decoupled. In this
regime, the motion of most oscillators remains close to integrable, i.e.
quasi-periodic, on very long time scales, while a few chaotic spots move very
slowly and redistribute the energy across the system. The material acquires
several characteristic properties of dynamical glasses: intermittency, jamming
and a drastic reduction of the mobility as a function of the thermodynamical
parameters. We consider both classical and quantum systems, though with more
emphasis on the former, and we discuss also the connections with quenched
disordered systems, which display a similar physics to a large extent.Comment: Review paper. Invited submission to the CRAS (special issue on
Fourier's legacy). 16 pages, 3 figure
Asymptotic localization of energy in non-disordered oscillator chains
We study two popular one-dimensional chains of classical anharmonic
oscillators: the rotor chain and a version of the discrete non-linear
Schr\"odinger chain. We assume that the interaction between neighboring
oscillators, controlled by the parameter , is small. We rigorously
establish that the thermal conductivity of the chains has a non-perturbative
origin, with respect to the coupling constant , and we provide strong
evidence that it decays faster than any power law in as . The weak coupling regime also translates into a high
temperature regime, suggesting that the conductivity vanishes faster than any
power of the inverse temperature.Comment: v1 -> v2: minor corrections, references added. 33 pages, 1 figure. To
appear in Comm. Pure Appl. Mat
Energy fluctuations in simple conduction models
We introduce a class of stochastic weakly coupled map lattices, as models for
studying heat conduction in solids. Each particle on the lattice evolves
according to an internal dynamics that depends on its energy, and exchanges
energy with its neighboors at a rate that depends on its internal state. We
study energy fluctuations at equilibrium in a diffusive scaling. In some cases,
we derive the hydordynamic limit of the fluctuation field.Comment: 18 pages, some formulas and misprints correcte
Exponentially slow heating in periodically driven many-body systems
We derive general bounds on the linear response energy absorption rates of
periodically driven many-body systems of spins or fermions on a lattice. We
show that for systems with local interactions, energy absorption rate decays
exponentially as a function of driving frequency in any number of spatial
dimensions. These results imply that topological many-body states in
periodically driven systems, although generally metastable, can have very long
lifetimes. We discuss applications to other problems, including decay of highly
energetic excitations in cold atomic and solid-state systems.Comment: v1 to v2: several typos corrected. 5 page