1,316 research outputs found
Characterizing and Quantifying Frustration in Quantum Many-Body Systems
We present a general scheme for the study of frustration in quantum systems.
We introduce a universal measure of frustration for arbitrary quantum systems
and we relate it to a class of entanglement monotones via an exact inequality.
If all the (pure) ground states of a given Hamiltonian saturate the inequality,
then the system is said to be inequality saturating. We introduce sufficient
conditions for a quantum spin system to be inequality saturating and confirm
them with extensive numerical tests. These conditions provide a generalization
to the quantum domain of the Toulouse criteria for classical frustration-free
systems. The models satisfying these conditions can be reasonably identified as
geometrically unfrustrated and subject to frustration of purely quantum origin.
Our results therefore establish a unified framework for studying the
intertwining of geometric and quantum contributions to frustration.Comment: 8 pages, 1 figur
Fractional calculus and continuous-time finance II: the waiting-time distribution
We complement the theory of tick-by-tick dynamics of financial markets based
on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et
al., and we point out its consistency with the behaviour observed in the
waiting-time distribution for BUND future prices traded at LIFFE, London.Comment: Revised version, 17 pages, 4 figures. Physica A, Vol. 287, No 3-4,
468--481 (2000). Proceedings of the International Workshop on "Economic
Dynamics from the Physics Point of View", Bad-Honnef (Germany), 27-30 March
200
Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: Low-temperature behavior
We propose a model of a heterogeneous glass forming liquid and compute the
low-temperature behavior of a tagged molecule moving within it. This model
exhibits stretched-exponential decay of the wavenumber-dependent, self
intermediate scattering function in the limit of long times. At temperatures
close to the glass transition, where the heterogeneities are much larger in
extent than the molecular spacing, the time dependence of the scattering
function crosses over from stretched-exponential decay with an index at
large wave numbers to normal, diffusive behavior with at small
wavenumbers. There is a clear separation between early-stage, cage-breaking
relaxation and late-stage relaxation. The spatial
representation of the scattering function exhibits an anomalously broad
exponential (non-Gaussian) tail for sufficiently large values of the molecular
displacement at all finite times.Comment: 9 pages, 6 figure
Modeling of waiting times and price changes in currency exchange data
A theory which describes the share price evolution at financial markets as a
continuous-time random walk has been generalized in order to take into account
the dependence of waiting times t on price returns x. A joint probability
density function (pdf) which uses the concept of a L\'{e}vy stable distribution
is worked out. The theory is fitted to high-frequency US$/Japanese Yen exchange
rate and low-frequency 19th century Irish stock data. The theory has been
fitted both to price return and to waiting time data and the adherence to data,
in terms of the chi-squared test statistic, has been improved when compared to
the old theory.Comment: 22 pages, 5 postscript figures, LaTeX2e using elsart.cl
k-Generalized Statistics in Personal Income Distribution
Starting from the generalized exponential function
, with
, proposed in Ref. [G. Kaniadakis, Physica A \textbf{296},
405 (2001)], the survival function ,
where , , and , is
considered in order to analyze the data on personal income distribution for
Germany, Italy, and the United Kingdom. The above defined distribution is a
continuous one-parameter deformation of the stretched exponential function
\textemdash to which reduces as
approaches zero\textemdash behaving in very different way in the and
regions. Its bulk is very close to the stretched exponential one,
whereas its tail decays following the power-law
. This makes the
-generalized function particularly suitable to describe simultaneously
the income distribution among both the richest part and the vast majority of
the population, generally fitting different curves. An excellent agreement is
found between our theoretical model and the observational data on personal
income over their entire range.Comment: Latex2e v1.6; 14 pages with 12 figures; for inclusion in the APFA5
Proceeding
Superdiffusion in Decoupled Continuous Time Random Walks
Continuous time random walk models with decoupled waiting time density are
studied. When the spatial one jump probability density belongs to the Levy
distribution type and the total time transition is exponential a generalized
superdiffusive regime is established. This is verified by showing that the
square width of the probability distribution (appropriately defined)grows as
with when . An important connection
of our results and those of Tsallis' nonextensive statistics is shown. The
normalized q-expectation value of calculated with the corresponding
probability distribution behaves exactly as in the asymptotic
limit.Comment: 9 pages (.tex file), 1 Postscript figures, uses revtex.st
Forcing anomalous scaling on demographic fluctuations
We discuss the conditions under which a population of anomalously diffusing
individuals can be characterized by demographic fluctuations that are
anomalously scaling themselves. Two examples are provided in the case of
individuals migrating by Gaussian diffusion, and by a sequence of L\'evy
flights.Comment: 5 pages 2 figure
A Solvable Nonlinear Reaction-Diffusion Model
We construct a coupled set of nonlinear reaction-diffusion equations which
are exactly solvable. The model generalizes both the Burger equation and a
Boltzman reaction equation recently introduced by Th. W. Ruijgrok and T. T. Wu.Comment: 6 pages, LATe
Theory of Single File Diffusion in a Force Field
The dynamics of hard-core interacting Brownian particles in an external
potential field is studied in one dimension. Using the Jepsen line we find a
very general and simple formula relating the motion of the tagged center
particle, with the classical, time dependent single particle reflection and transmission coefficients. Our formula describes rich
physical behaviors both in equilibrium and the approach to equilibrium of this
many body problem.Comment: 4 Phys. Rev. page
Relativistic Weierstrass random walks
The Weierstrass random walk is a paradigmatic Markov chain giving rise to a
L\'evy-type superdiffusive behavior. It is well known that Special Relativity
prevents the arbitrarily high velocities necessary to establish a
superdiffusive behavior in any process occurring in Minkowski spacetime,
implying, in particular, that any relativistic Markov chain describing
spacetime phenomena must be essentially Gaussian. Here, we introduce a simple
relativistic extension of the Weierstrass random walk and show that there must
exist a transition time delimiting two qualitative distinct dynamical
regimes: the (non-relativistic) superdiffusive L\'evy flights, for ,
and the usual (relativistic) Gaussian diffusion, for . Implications of
this crossover between different diffusion regimes are discussed for some
explicit examples. The study of such an explicit and simple Markov chain can
shed some light on several results obtained in much more involved contexts.Comment: 5 pages, final version to appear in PR
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