322 research outputs found
Recurrence and Polya number of general one-dimensional random walks
The recurrence properties of random walks can be characterized by P\'{o}lya
number, i.e., the probability that the walker has returned to the origin at
least once. In this paper, we consider recurrence properties for a general 1D
random walk on a line, in which at each time step the walker can move to the
left or right with probabilities and , or remain at the same position
with probability (). We calculate P\'{o}lya number of this
model and find a simple expression for as, , where is
the absolute difference of and (). We prove this rigorous
expression by the method of creative telescoping, and our result suggests that
the walk is recurrent if and only if the left-moving probability equals to
the right-moving probability .Comment: 3 page short pape
Characterizing flows with an instrumented particle measuring Lagrangian accelerations
We present in this article a novel Lagrangian measurement technique: an
instrumented particle which continuously transmits the force/acceleration
acting on it as it is advected in a flow. We develop signal processing methods
to extract information on the flow from the acceleration signal transmitted by
the particle. Notably, we are able to characterize the force acting on the
particle and to identify the presence of a permanent large-scale vortex
structure. Our technique provides a fast, robust and efficient tool to
characterize flows, and it is particularly suited to obtain Lagrangian
statistics along long trajectories or in cases where optical measurement
techniques are not or hardly applicable.Comment: submitted to New Journal of Physic
Renyi Entropy of the XY Spin Chain
We consider the one-dimensional XY quantum spin chain in a transverse
magnetic field. We are interested in the Renyi entropy of a block of L
neighboring spins at zero temperature on an infinite lattice. The Renyi entropy
is essentially the trace of some power of the density matrix of the
block. We calculate the asymptotic for analytically in terms of
Klein's elliptic - function. We study the limiting entropy as a
function of its parameter . We show that up to the trivial addition
terms and multiplicative factors, and after a proper re-scaling, the Renyi
entropy is an automorphic function with respect to a certain subgroup of the
modular group; moreover, the subgroup depends on whether the magnetic field is
above or below its critical value. Using this fact, we derive the
transformation properties of the Renyi entropy under the map and show that the entropy becomes an elementary function of the
magnetic field and the anisotropy when is a integer power of 2, this
includes the purity . We also analyze the behavior of the entropy as
and and at the critical magnetic field and in the
isotropic limit [XX model].Comment: 28 Pages, 1 Figur
Entropy as a function of Geometric Phase
We give a closed-form solution of von Neumann entropy as a function of
geometric phase modulated by visibility and average distinguishability in
Hilbert spaces of two and three dimensions. We show that the same type of
dependence also exists in higher dimensions. We also outline a method for
measuring both the entropy and the phase experimentally using a simple
Mach-Zehnder type interferometer which explains physically why the two concepts
are related.Comment: 19 pages, 7 figure
Quantum Adiabatic Markovian Master Equations
We develop from first principles Markovian master equations suited for
studying the time evolution of a system evolving adiabatically while coupled
weakly to a thermal bath. We derive two sets of equations in the adiabatic
limit, one using the rotating wave (secular) approximation that results in a
master equation in Lindblad form, the other without the rotating wave
approximation but not in Lindblad form. The two equations make markedly
different predictions depending on whether or not the Lamb shift is included.
Our analysis keeps track of the various time- and energy-scales associated with
the various approximations we make, and thus allows for a systematic inclusion
of higher order corrections, in particular beyond the adiabatic limit. We use
our formalism to study the evolution of an Ising spin chain in a transverse
field and coupled to a thermal bosonic bath, for which we identify four
distinct evolution phases. While we do not expect this to be a generic feature,
in one of these phases dissipation acts to increase the fidelity of the system
state relative to the adiabatic ground state.Comment: 31 pages, 9 figures. v2: Generalized Markov approximation bound.
Included a section on thermal equilibration. v3: Added text that appears in
NJP version. Generalized Lindblad ME to include degenerate subspaces. v3.
Corrections made to Appendix E and F. We thank Kabuki Takada and Hidetoshi
Nishimori for pointing out the errors. v4: Corrected a typo in Eqt. B
Computing welfare losses from data under imperfect competition with heterogeneous goods
We study the percentage of welfare losses (PWL) yielded by imperfect competition under
product differentiation. When demand is linear, if prices, outputs, costs and the number of firms
can be observed, PWL is arbitrary in both Cournot and Bertrand equilibria. If in addition, the
elasticity of demand (resp. cross elasticity of demand) is known, we can calculate PWL in
Cournot (resp. Bertrand) equilibrium. When demand is isoelastic and there are many firms, PWL
can be computed from prices, outputs, costs and the number of .rms. In all these cases we find
that price-marginal cost margins and demand elasticities may influence PWL in a
counterintuitive way. We also provide conditions under which PWL increases or decreases with
concentration
Abundance of unknots in various models of polymer loops
A veritable zoo of different knots is seen in the ensemble of looped polymer
chains, whether created computationally or observed in vitro. At short loop
lengths, the spectrum of knots is dominated by the trivial knot (unknot). The
fractional abundance of this topological state in the ensemble of all
conformations of the loop of segments follows a decaying exponential form,
, where marks the crossover from a mostly unknotted
(ie topologically simple) to a mostly knotted (ie topologically complex)
ensemble. In the present work we use computational simulation to look closer
into the variation of for a variety of polymer models. Among models
examined, is smallest (about 240) for the model with all segments of the
same length, it is somewhat larger (305) for Gaussian distributed segments, and
can be very large (up to many thousands) when the segment length distribution
has a fat power law tail.Comment: 13 pages, 6 color figure
TESELA: a new Virtual Observatory tool to determine blank fields for astronomical observations
The observation of blank fields, regions of the sky devoid of stars down to a
given threshold magnitude, constitutes one of the typical important calibration
procedures required for the proper reduction of astronomical data obtained in
imaging mode. This work describes a method, based on the use of the Delaunay
triangulation on the surface of a sphere, that allows the easy generation of
blank fields catalogues. In addition to that, a new tool named TESELA,
accessible through the WEB, has been created to facilitate the user to
retrieve, and visualise using the VO-tool Aladin, the blank fields available
near a given position in the sky.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical
Society. 11 pages, 10 figures. Related Web tool accessible at
http://sdc.cab.inta-csic.es/tesel
A photonic basis for deriving nonlinear optical response
Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as coefficients in a power series - nonlinear optical susceptibilities signifying a propensity to generate optical harmonics, for example. Taking the subject to a deeper level requires a more detailed knowledge of the structure and properties of each nonlinear susceptibility tensor, the latter differing in form according to the process under investigation. Typically, the derivations involve intricate development based on time-dependent perturbation theory, assisted by recourse to a set of Feynman diagrams. This paper presents a more direct route to the required results, based on photonic rather than semiclassical principles, and offers a significantly clearer perspective on the photophysics underlying nonlinear optical response. The method, here illustrated by specific application to harmonic generation and down-conversion processes, is simple, intuitive and readily amenable for processes of arbitrary photonic order. © 2009 IOP Publishing Ltd
- …