44 research outputs found
Light localization signatures in backscattering from periodic disordered media
The backscattering line shape is analytically predicted for thick disordered
medium films where, remarkably, the medium configuration is periodic along the
direction perpendicular to the incident light. A blunt triangular peak is found
to emerge on the sharp top. The phenomenon roots in the coexistence of quasi-1D
localization and 2D extended states.Comment: 5 pages, 3 figures. accepted for publication in JETP Let
Hydrodynamic and field-theoretic approaches of light localization in open media
Many complex systems exhibit hydrodynamic (or macroscopic) behavior at large
scales characterized by few variables such as the particle number density,
temperature and pressure obeying a set of hydrodynamic (or macroscopic)
equations. Does the hydrodynamic description exist also for waves in complex
open media? This is a long-standing fundamental problem in studies on wave
localization. Practically, if it does exist, owing to its simplicity
macroscopic equations can be mastered far more easily than sophisticated
microscopic theories of wave localization especially for experimentalists. The
purposes of the present paper are two-fold. On the one hand, it is devoted to a
review of substantial recent progress in this subject. We show that in random
open media the wave energy density obeys a highly unconventional macroscopic
diffusion equation at scales much larger than the elastic mean free path. The
diffusion coefficient is inhomogeneous in space; most strikingly, as a function
of the distance to the interface, it displays novel single parameter scaling
which captures the impact of rare high-transmission states that dominate
long-time transport of localized waves. We review aspects of this novel
macroscopic diffusive phenomenon. On the other hand, it is devoted to a review
of the supersymmetric field theory of light localization in open media. In
particular, we review its application in establishing a microscopic theory of
the aforementioned unconventional diffusive phenomenon.Comment: 49 pages, 13 figures, review article invited by editors of Physica
Planck's quantum-driven integer quantum Hall effect in chaos
The integer quantum Hall effect (IQHE) and chaos are commonly conceived as
being unrelated. Contrary to common wisdoms, we find in a canonical chaotic
system, the kicked spin- rotor, a Planck's quantum()-driven
phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically,
the rotor's energy growth is unbounded ('metallic' phase) for a discrete set of
critical -values, but otherwise bounded ('insulating' phase). The latter
phase is topological in nature and characterized by a quantum number
('quantized Hall conductance'). The number jumps by unity whenever
decreases passing through each critical value. Our findings, within the reach
of cold-atom experiments, indicate that rich topological quantum phenomena may
emerge from chaos.Comment: Fig. 1 and 2 modifie
The Ehrenfest Oscillations in The Level Statistics of Chaotic Quantum Dots
We study a crossover from classical to quantum picture in the electron energy
statistics in a system with broken time-reversal symmetry. The perturbative and
nonperturbative parts of the two level correlation function, are
analyzed. We find that in the intermediate region, , where and are the Ehrenfest and
ergodic times, respectively, consists of a series of oscillations
with the periods depending on , deviating from the universal Wigner-Dyson
statistics. These Ehrenfest oscillations have the period dependence as
in the perturbative part. [For systems with time-reversal symmetry,
this oscillation in the perturbative part of was studied in an
earlier work (I. L. Aleiner and A. I. Larkin, Phys. Rev. E {\bf 55}, R1243
(1997))]. In the nonperturbative part they have the period dependence as
with a universal numerical factor. The
amplitude of the leading order Ehrenfest oscillation in the nonperturbative
part is larger than that of the perturbative part.Comment: 20 pages, 4 figures, submitted to Phys. Rev.
Symmetry and dynamics universality of supermetal in quantum chaos
Chaotic systems exhibit rich quantum dynamical behaviors ranging from
dynamical localization to normal diffusion to ballistic motion. Dynamical
localization and normal diffusion simulate electron motion in an impure crystal
with a vanishing and finite conductivity, i.e., an "Anderson insulator" and a
"metal", respectively. Ballistic motion simulates a perfect crystal with
diverging conductivity, i.e., a "supermetal". We analytically find and
numerically confirm that, for a large class of chaotic systems, the
metal-supermetal dynamics crossover occurs and is universal, determined only by
the system's symmetry. Furthermore, we show that the universality of this
dynamics crossover is identical to that of eigenfunction and spectral
fluctuations described by the random matrix theory.Comment: 10 pages, 8 figure
Wave thermalization and its implications for nonequilibrium statistical mechanics
Understanding the rich spatial and temporal structures in nonequilibrium
thermal environments is a major subject of statistical mechanics. Because
universal laws, based on an ensemble of systems, are mute on an individual
system, exploring nonequilibrium statistical mechanics and the ensuing
universality in individual systems has long been of fundamental interest. Here,
by adopting the wave description of microscopic motion, and combining the
recently developed eigenchannel theory and the mathematical tool of the
concentration of measure, we show that in a single complex medium, a universal
spatial structure - the diffusive steady state - emerges from an overwhelming
number of scattering eigenstates of the wave equation. Our findings suggest a
new principle, dubbed "the wave thermalization", namely, a propagating wave
undergoing complex scattering processes can simulate nonequilibrium thermal
environments, and exhibit macroscopic nonequilibrium phenomena.Comment: 10 pages, 7 figure
Many-body eigenstate thermalization from one-body quantum chaos: emergent arrow of time
A profound quest of statistical mechanics is the origin of irreversibility -
the arrow of time. New stimulants have been provided, thanks to unprecedented
degree of control reached in experiments with isolated quantum systems and
rapid theoretical developments of manybody localization in disordered
interacting systems. The proposal of (many-body) eigenstate thermalization (ET)
for these systems reinforces the common belief that either interaction or
extrinsic randomness is required for thermalization. Here, we unveil a quantum
thermalization mechanism challenging this belief. We find that, provided
one-body quantum chaos is present, as a pure many-body state evolves the arrow
of time can emerge, even without interaction or randomness. In times much
larger than the Ehrenfest time that signals the breakdown of quantum-classical
correspondence, quantum chaotic motion leads to thermal [Fermi-Dirac (FD) or
Bose-Einstein (BE)] distributions and thermodynamics in individual eigenstates.
Our findings lay dynamical foundation of statistical mechanics and
thermodynamics of isolated quantum systems.Comment: 6.1 pages, 3 figures, 7-page supplementary materia
Self-duality triggered dynamical transition
A basic result about the dynamics of spinless quantum systems is that the
Maryland model exhibits dynamical localization in any dimension. Here we
implement mathematical spectral theory and numerical experiments to show that
this result does not hold, when the 2-dimensional Maryland model is endowed
with spin 1/2 -- hereafter dubbed spin-Maryland (SM) model. Instead, in a
family of SM models, tuning the (effective) Planck constant drives dynamical
localization{delocalization transitions of topological nature. These
transitions are triggered by the self-duality, a symmetry generated by some
transformation in the parameter -- the inverse Planck constant -- space. This
provides significant insights to new dynamical phenomena such as what occur in
the spinful quantum kicked rotor.Comment: 18 pages, 6 figure
Concentration-of-measure theory for structures and fluctuations of waves
The emergence of nonequilibrium phenomena in individual complex wave systems
has long been of fundamental interests. Its analytic studies remain notoriously
difficult. Using the mathematical tool of the concentration of measure (CM), we
develop a theory for structures and fluctuations of waves in individual
disordered media. We find that, for both diffusive and localized waves,
fluctuations associated with the change in incoming waves ("wave-to-wave"
fluctuations) exhibit a new kind of universalities, which does not exist in
conventional mesoscopic fluctuations associated with the change in disorder
realizations ("sample-to-sample" fluctuations), and originate from the
coherence between the natural channels of waves -- the transmission
eigenchannels. Using the results obtained for wave-to-wave fluctuations, we
find the criterion for almost all stationary scattering states to exhibit the
same spatial structure such as the diffusive steady state. We further show that
the expectations of observables at stationary scattering states are independent
of incoming waves and given by their averages with respect to eigenchannels.
This suggests the possibility of extending the studies of thermalization of
closed systems to open systems, which provides new perspectives for the
emergence of nonequilibrium statistical phenomena.Comment: 7 pages, 4 figures, Supplemental Materials(13 pages, 6 figures
The spectral form factor near the Ehrenfest-time
We calculate the Ehrenfest-time dependence of the leading quantum correction
to the spectral form factor of a ballistic chaotic cavity using periodic orbit
theory. For the case of broken time-reversal symmetry, our result differs from
that previously obtained using field-theoretic methods [Tian and Larkin, Phys.
Rev. B 70, 035305 (2004)]. The discrepancy shows that short-time regularization
procedures dramatically affect physics near the Ehrenfest-time.Comment: 6 pages, 1 figur