142,670 research outputs found
State-dependent Fractional Point Processes
The aim of this paper is the analysis of the fractional Poisson process where
the state probabilities , , are governed by
time-fractional equations of order depending on the number
of events occurred up to time . We are able to obtain explicitely the
Laplace transform of and various representations of state
probabilities. We show that the Poisson process with intermediate waiting times
depending on differs from that constructed from the fractional state
equations (in the case , for all , they coincide with the
time-fractional Poisson process). We also introduce a different form of
fractional state-dependent Poisson process as a weighted sum of homogeneous
Poisson processes. Finally we consider the fractional birth process governed by
equations with state-dependent fractionality
Semi-Markov models and motion in heterogeneous media
In this paper we study continuous time random walks (CTRWs) such that the
holding time in each state has a distribution depending on the state itself.
For such processes, we provide integro-differential (backward and forward)
equations of Volterra type, exhibiting a position dependent convolution kernel.
Particular attention is devoted to the case where the holding times have a
power-law decaying density, whose exponent depends on the state itself, which
leads to variable order fractional equations. A suitable limit yields a
variable order fractional heat equation, which models anomalous diffusions in
heterogeneous media
Exactly solvable nonlinear model with two multiplicative Gaussian colored noises
An overdamped system with a linear restoring force and two multiplicative
colored noises is considered. Noise amplitudes depend on the system state
as and . An exactly soluble model of a system is constructed
due to consideration of a specific relation between noises. Exact expressions
for the time-dependent univariate probability distribution function and the
fractional moments are derived. Their long-time asymptotic behavior is
investigated analytically. It is shown that anomalous diffusion and stochastic
localization of particles, not subjected to a restoring force, can occur.Comment: 15 page
On the origin of space
Within the framework of fractional calculus with variable order the evolution
of space in the adiabatic limit is investigated. Based on the Caputo definition
of a fractional derivative using the fractional quantum harmonic oscillator a
model is presented, which describes space generation as a dynamic process,
where the dimension of space evolves smoothly with time in the range 0 <=
d(t) <=3, where the lower and upper boundaries of dimension are derived from
first principles. It is demonstrated, that a minimum threshold for the space
dimension is necessary to establish an interaction with external probe
particles. A possible application in cosmology is suggested.Comment: 14 pages 3 figures, some clarifications adde
Detecting Majorana fermions by use of superconductor-quantum Hall liquid junctions
The point contact tunnel junctions between a one-dimensional topological
superconductor and single-channel quantum Hall (QH) liquids are investigated
theoretically with bosonization technology and renormalization group methods.
For the integer QH liquid, the universal low-energy tunneling transport
is governed by the perfect Andreev reflection fixed point with quantized
zero-bias conductance , which can serve as a definitive
fingerprint of the existence of a Majorana fermion. For the Laughlin
fractional QH liquids, its transport is governed by the perfect normal
reflection fixed point with vanishing zero-bias conductance and bias-dependent
conductance . Our setup is within reach of present
experimental techniques.Comment: 6 pages, 1 figure, Added references,Corrected typo
Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic fractional Chern insulator state
We propose a simple scheme for the realization of a topological quasienergy
band structure with ultracold atoms in a periodically driven optical square
lattice. It is based on a circular lattice shaking in the presence of a
superlattice that lowers the energy on every other site. The topological band
gap, which separates the two bands with Chern numbers , is opened in a
way characteristic to Floquet topological insulators, namely, by terms of the
effective Hamiltonian that appear in subleading order of a high-frequency
expansion. These terms correspond to processes where a particle tunnels several
times during one driving period. The interplay of such processes with particle
interactions also gives rise to new interaction terms of several distinct
types. For bosonic atoms with on-site interactions, they include nearest
neighbor density-density interactions introduced at the cost of weakened
on-site repulsion as well as density-assisted tunneling. Using exact
diagonalization, we investigate the impact of the individual induced
interaction terms on the stability of a bosonic fractional Chern insulator
state at half filling of the lowest band.Comment: 10 pages, 4 figures, submitted to Physical Review
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