346 research outputs found
Why do Hurst exponents of traded value increase as the logarithm of company size?
The common assumption of universal behavior in stock market data can
sometimes lead to false conclusions. In statistical physics, the Hurst
exponents characterizing long-range correlations are often closely related to
universal exponents. We show, that in the case of time series of the traded
value, these Hurst exponents increase logarithmically with company size, and
thus are non-universal. Moreover, the average transaction size shows scaling
with the mean transaction frequency for large enough companies. We present a
phenomenological scaling framework that properly accounts for such
dependencies.Comment: 10 pages, 4 figures, to appear in the Proceedings of the
International Workshop on Econophysics of Stock Markets and Minority Games,
Calcutta, 200
Entanglement negativity bounds for fermionic Gaussian states
The entanglement negativity is a versatile measure of entanglement that has
numerous applications in quantum information and in condensed matter theory. It
can not only efficiently be computed in the Hilbert space dimension, but for
non-interacting bosonic systems, one can compute the negativity efficiently in
the number of modes. However, such an efficient computation does not carry over
to the fermionic realm, the ultimate reason for this being that the partial
transpose of a fermionic Gaussian state is no longer Gaussian. To provide a
remedy for this state of affairs, in this work we introduce efficiently
computable and rigorous upper and lower bounds to the negativity, making use of
techniques of semi-definite programming, building upon the Lagrangian
formulation of fermionic linear optics, and exploiting suitable products of
Gaussian operators. We discuss examples in quantum many-body theory and hint at
applications in the study of topological properties at finite temperature.Comment: 13 pages, 7 figure
Endogenous and exogenous dynamics in the fluctuations of capital fluxes: An empirical analysis of the Chinese stock market
A phenomenological investigation of the endogenous and exogenous dynamics in
the fluctuations of capital fluxes is investigated on the Chinese stock market
using mean-variance analysis, fluctuation analysis and their generalizations to
higher orders. Non-universal dynamics have been found not only in
exponents different from the universal value 1/2 and 1 but also in the
distributions of the ratios . Both the scaling exponent of fluctuations and
the Hurst exponent increase in logarithmic form with the time scale
and the mean traded value per minute , respectively. We find
that the scaling exponent of the endogenous fluctuations
is found to be independent of the time scale, while the exponent of exogenous
fluctuations . Multiscaling and multifractal features are
observed in the data as well. However, the inhomogeneous impact model is not
verified.Comment: 9 Latx pages for EPJB including 13 figure
Entanglement in the XX spin chain with an energy current
We consider the ground state of the XX chain that is constrained to carry a
current of energy. The von Neumann entropy of a block of neighboring spins,
describing entanglement of the block with the rest of the chain, is computed.
Recent calculations have revealed that the entropy in the XX model diverges
logarithmically with the size of the subsystem. We show that the presence of
the energy current increases the prefactor of the logarithmic growth. This
result indicates that the emergence of the energy current gives rise to an
increase of entanglement.Comment: 4 pages, 4 figure
Fluctuations in subsystems of the zero temperature XX chain: Emergence of an effective temperature
The zero-temperature XX chain is studied with emphasis on the properties of a
block of spins inside the chain. We investigate the quantum fluctuations
resulting from the entanglement of the block with the rest of the chain using
analytical as well as numerical (density matrix renormalization group) methods.
It is found that the rest of the chain acts as a thermal environment and an
effective temperature can be introduced to describe the fluctuations. We show
that the effective temperature description is robust in the sense that several
independent definitions (through fluctuation dissipation theorem, comparing
with a finite temperature system) yield the same functional form in the limit
of large block size (). The effective temperature can also be shown
to satisfy the basic requirements on how it changes when two bodies of equal or
unequal temperatures are brought into contact.Comment: 19 pages, 7 figure
Liquidity and the multiscaling properties of the volume traded on the stock market
We investigate the correlation properties of transaction data from the New
York Stock Exchange. The trading activity f(t) of each stock displays a
crossover from weaker to stronger correlations at time scales 60-390 minutes.
In both regimes, the Hurst exponent H depends logarithmically on the liquidity
of the stock, measured by the mean traded value per minute. All multiscaling
exponents tau(q) display a similar liquidity dependence, which clearly
indicates the lack of a universal form assumed by other studies. The origin of
this behavior is both the long memory in the frequency and the size of
consecutive transactions.Comment: 7 pages, 3 figures, submitted to Europhysics Letter
The components of empirical multifractality in financial returns
We perform a systematic investigation on the components of the empirical
multifractality of financial returns using the daily data of Dow Jones
Industrial Average from 26 May 1896 to 27 April 2007 as an example. The
temporal structure and fat-tailed distribution of the returns are considered as
possible influence factors. The multifractal spectrum of the original return
series is compared with those of four kinds of surrogate data: (1) shuffled
data that contain no temporal correlation but have the same distribution, (2)
surrogate data in which any nonlinear correlation is removed but the
distribution and linear correlation are preserved, (3) surrogate data in which
large positive and negative returns are replaced with small values, and (4)
surrogate data generated from alternative fat-tailed distributions with the
temporal correlation preserved. We find that all these factors have influence
on the multifractal spectrum. We also find that the temporal structure (linear
or nonlinear) has minor impact on the singularity width of the
multifractal spectrum while the fat tails have major impact on ,
which confirms the earlier results. In addition, the linear correlation is
found to have only a horizontal translation effect on the multifractal spectrum
in which the distance is approximately equal to the difference between its DFA
scaling exponent and 0.5. Our method can also be applied to other financial or
physical variables and other multifractal formalisms.Comment: 6 epl page
Quantum Quench from a Thermal Initial State
We consider a quantum quench in a system of free bosons, starting from a
thermal initial state. As in the case where the system is initially in the
ground state, any finite subsystem eventually reaches a stationary thermal
state with a momentum-dependent effective temperature. We find that this can,
in some cases, even be lower than the initial temperature. We also study
lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor
change
- …