7,209 research outputs found

### Convergence of continuous-time quantum walks on the line

The position density of a "particle" performing a continuous-time quantum
walk on the integer lattice, viewed on length scales inversely proportional to
the time t, converges (as t tends to infinity) to a probability distribution
that depends on the initial state of the particle. This convergence behavior
has recently been demonstrated for the simplest continuous-time random walk
[see quant-ph/0408140]. In this brief report, we use a different technique to
establish the same convergence for a very large class of continuous-time
quantum walks, and we identify the limit distribution in the general case.Comment: Version to appear in Phys. Rev.

### Statistical Curse of the Second Half Rank

In competitions involving many participants running many races the final rank
is determined by the score of each participant, obtained by adding its ranks in
each individual race. The "Statistical Curse of the Second Half Rank" is the
observation that if the score of a participant is even modestly worse than the
middle score, then its final rank will be much worse (that is, much further
away from the middle rank) than might have been expected. We give an
explanation of this effect for the case of a large number of races using the
Central Limit Theorem. We present exact quantitative results in this limit and
demonstrate that the score probability distribution will be gaussian with
scores packing near the center. We also derive the final rank probability
distribution for the case of two races and we present some exact formulae
verified by numerical simulations for the case of three races. The variant in
which the worst result of each boat is dropped from its final score is also
analyzed and solved for the case of two races.Comment: 16 pages, 10 figure

### Equations of structural relaxation

In the mode coupling theory of the liquid to glass transition the long time
structural relaxation follows from equations solely determined by equilibrium
structural parameters. The present extension of these structural relaxation
equations to arbitrarily short times on the one hand allows calculations
unaffected by model assumptions about the microscopic dynamics and on the other
hand supplies new starting points for analytical studies. As a first
application, power-law like structural relaxation at a glass-transition
singularity is explicitly proven for a special schematic MCT model.Comment: 11 pages, 3 figures; talk given at the Seventh international Workshop
on disordered Systems, Molveno, Italy, March 199

### Exact results for the Barabasi queuing model

Previous works on the queuing model introduced by Barab\'asi to account for
the heavy tailed distributions of the temporal patterns found in many human
activities mainly concentrate on the extremal dynamics case and on lists of
only two items. Here we obtain exact results for the general case with
arbitrary values of the list length $L$ and of the degree of randomness that
interpolates between the deterministic and purely random limits. The
statistically fundamental quantities are extracted from the solution of master
equations. From this analysis, new scaling features of the model are uncovered

### On-off intermittency over an extended range of control parameter

We propose a simple phenomenological model exhibiting on-off intermittency
over an extended range of control parameter. We find that the distribution of
the 'off' periods has as a power-law tail with an exponent varying continuously
between -1 and -2, at odds with standard on-off intermittency which occurs at a
specific value of the control parameter, and leads to the exponent -3/2. This
non-trivial behavior results from the competition between a strong slowing down
of the dynamics at small values of the observable, and a systematic drift
toward large values.Comment: 4 pages, 3 figure

### Subexponential instability implies infinite invariant measure

We study subexponential instability to characterize a dynamical instability
of weak chaos. We show that a dynamical system with subexponential instability
has an infinite invariant measure, and then we present the generalized Lyapunov
exponent to characterize subexponential instability.Comment: 7 pages, 5 figure

### Global fluctuations and Gumbel statistics

We explain how the statistics of global observables in correlated systems can
be related to extreme value problems and to Gumbel statistics. This
relationship then naturally leads to the emergence of the generalized Gumbel
distribution G_a(x), with a real index a, in the study of global fluctuations.
To illustrate these findings, we introduce an exactly solvable nonequilibrium
model describing an energy flux on a lattice, with local dissipation, in which
the fluctuations of the global energy are precisely described by the
generalized Gumbel distribution.Comment: 4 pages, 3 figures; final version with minor change

### Localization, anomalous diffusion and slow relaxations: a random distance matrix approach

We study the spectral properties of a class of random matrices where the
matrix elements depend exponentially on the distance between uniformly and
randomly distributed points. This model arises naturally in various physical
contexts, such as the diffusion of particles, slow relaxations in glasses, and
scalar phonon localization. Using a combination of a renormalization group
procedure and a direct moment calculation, we find the eigenvalue distribution
density (i.e., the spectrum) and the localization properties of the eigenmodes,
for arbitrary dimension. Finally, we discuss the physical implications of the
results

### Chaotic itinerancy and power-law residence time distribution in stochastic dynamical system

To study a chaotic itinerant motion among varieties of ordered states, we
propose a stochastic model based on the mechanism of chaotic itinerancy. The
model consists of a random walk on a half-line, and a Markov chain with a
transition probability matrix. To investigate the stability of attractor ruins
in the model, we analyze the residence time distribution of orbits at attractor
ruins. We show that the residence time distribution averaged by all attractor
ruins is given by the superposition of (truncated) power-law distributions, if
a basin of attraction for each attractor ruin has zero measure. To make sure of
this result, we carry out a computer simulation for models showing chaotic
itinerancy. We also discuss the fact that chaotic itinerancy does not occur in
coupled Milnor attractor systems if the transition probability among attractor
ruins can be represented as a Markov chain.Comment: 6 pages, 10 figure

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