11,700 research outputs found
Superballistic wavepacket spreading in double kicked rotors
We investigate possible ways in which a quantum wavepacket spreads. We show
that in a general class of double kicked rotor systems, a wavepacket may
undergo superballistic spreading; i.e., its variance increases as the cubic of
time. The conditions for the observed superballistic spreading and two related
characteristic time scales are studied. Our results suggest that the symmetry
of the studied model and whether it is a Kolmogorov-Arnold-Moser system are
crucial to its wavepacket spreading behavior. Our study also sheds new light on
the exponential wavepacket spreading phenomenon previously observed in the
double kicked rotor systems.Comment: 10 pages, 5 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
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
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
Lie-point symmetries of the Lagrangian system on time scales
This letter investigates the Lie point symmetries and conserved quantities of
the Lagrangian systems on time scales, which unify the Lie symmetries of the
two cases for the continuous and the discrete Lagrangian systems. By defining
the infinitesimal transformations' generators and using the invariance of
differential equations under infinitesimal transformations, the determining
equations of the Lie symmetries on time scales are established. Then the
structure equations and the form of conserved quantities with delta derivatives
are obtained. The letter also gives brief discussion on the Lie symmetries for
the discrete systems. Finally, several examples are designed to illustrate
these results.Comment: 14 pages,0 figure
On deep-holes of Gabidulin codes
In this paper, we determine the covering radius and a class of deep holes for
Gabidulin codes with both rank metric and Hamming metric. Moreover, we give a
necessary and sufficient condition for deciding whether a word is not a deep
hole for Gabidulin codes, by which we study the error distance of a special
class of words to certain Gabidulin codes.Comment: Published in Finite Fields and Their Application
Domain resource integration system
Domain Resource Integrated System (DRIS) is introduced in this paper. DRIS is
a hierarchical distributed Internet information retrieval system. This system
will solve some bottleneck problems such as long update interval, poor coverage
in current web search system. DRIS will build the information retrieval
infrastructure of Internet, but not a commercial search engine. The protocol
series of DRIS are also detailed in this paper.Comment: 6 pages,4 figure
Approximated seventh order calculation of vacuum wave function of 2+1 dimensional SU(2) lattice gauge theory
Using the coupled cluster expansion with the random phase approximation, we
calculate the long wavelength vacuum wave function and the vacuum energy of 2+1
dimensional Hamiltonian SU(2) lattice gauge theory (LGT) up to the seventh
order. The coefficients , of the vacuum wave function show good
scaling behavior and convergence in high order calculations
Identifying two-photon high-dimensional entanglement in transverse patterns
We propose a scheme to explore two-photon high-dimensional entanglement
associated with a transverse pattern by means of two-photon interference in a
beamsplitter. We find that the topological symmetry of the angular spectrum of
the two-photon state governs the nature of the two-photon interference. We
prove that the anti-coalescence interference is the signature of two-photon
entanglement. On the basis of this feature, we propose a special Mach-Zehnder
interferometer incorporated with two spiral phase plates which can change the
interference from a coalescence to an anti-coalescence type only for a
two-photon entangled state. The scheme is simple and straightforward compared
with the test for a Bell inequality.Comment: 3 pages, 3 figure
Phase Randomization and Doppler Peaks in the CMB Angular Power Spectrum
Using the Boltzmann equation with a Langevin-like term describing the
stochastic force in a baryon-photon plasma, we investigate the influence of the
incoherent electron-photon scattering on the subhorizon evolution of the cosmic
microwave radiation. The stochastic fluctuation caused by each collision on
average is found to be small. Nevertheless, it leads to a significant Brownian
drifting of the phase in the acoustic oscillation, and the coherent
oscillations cannot be maintained during their dynamical evolution. As a
consequence, the proposed Doppler peaks probably do not exist.Comment: 11 Pages in RevTe
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