35 research outputs found
Area law violation for the mutual information in a nonequilibrium steady state
We study the nonequilibrium steady state of an infinite chain of free
fermions, resulting from an initial state where the two sides of the system are
prepared at different temperatures. The mutual information is calculated
between two adjacent segments of the chain and is found to scale
logarithmically in the subsystem size. This provides the first example of the
violation of the area law in a quantum many-body system outside a zero
temperature regime. The prefactor of the logarithm is obtained analytically
and, furthermore, the same prefactor is shown to govern the logarithmic
increase of mutual information in time, before the system relaxes locally to
the steady state.Comment: 7 pages, 5 figures, final version, references adde
Random walks on complex networks with inhomogeneous impact
In many complex systems, for the activity f(i) of the constituents or nodes
i, a power-law relationship was discovered between the standard deviation
sigma(i) and the average strength of the activity: sigma(i) ~ ^alpha;
universal values alpha = 1/2 or 1 were found, however, with exceptions. With
the help of an impact variable we introduce a random walk model where the
activity is the product of the number of visitors at a node and their impact.
If the impact depends strongly on the node connectivity and the properties of
the carrying network are broadly distributed (like in a scale free network) we
find both analytically and numerically non-universal alpha values. The exponent
always crosses over to the universal value of 1 if the external drive
dominates.Comment: 4 pages, 3 figures, revised tex
Entanglement negativity in the harmonic chain out of equilibrium
We study the entanglement in a chain of harmonic oscillators driven out of
equilibrium by preparing the two sides of the system at different temperatures,
and subsequently joining them together. The steady state is constructed
explicitly and the logarithmic negativity is calculated between two adjacent
segments of the chain. We find that, for low temperatures, the steady-state
entanglement is a sum of contributions pertaining to left- and right-moving
excitations emitted from the two reservoirs. In turn, the steady-state
entanglement is a simple average of the Gibbs-state values and thus its scaling
can be obtained from conformal field theory. A similar averaging behaviour is
observed during the entire time evolution. As a particular case, we also
discuss a local quench where both sides of the chain are initialized in their
respective ground states.Comment: 19 pages, 7 figures, small changes, references added, published
versio
On the partial transpose of fermionic Gaussian states
We consider Gaussian states of fermionic systems and study the action of the
partial transposition on the density matrix. It is shown that, with a suitable
choice of basis, these states are transformed into a linear combination of two
Gaussian operators that are uniquely defined in terms of the covariance matrix
of the original state. In case of a reflection symmetric geometry, this result
can be used to efficiently calculate a lower bound for a well-known
entanglement measure, the logarithmic negativity. Furthermore, exact
expressions can be derived for traces involving integer powers of the partial
transpose. The method can also be applied to the quantum Ising chain and the
results show perfect agreement with the predictions of conformal field theory.Comment: 22 pages, 4 figures, published version, typos corrected, references
adde
Size matters: some stylized facts of the stock market revisited
We reanalyze high resolution data from the New York Stock Exchange and find a
monotonic (but not power law) variation of the mean value per trade, the mean
number of trades per minute and the mean trading activity with company
capitalization. We show that the second moment of the traded value distribution
is finite. Consequently, the Hurst exponents for the corresponding time series
can be calculated. These are, however, non-universal: The persistence grows
with larger capitalization and this results in a logarithmically increasing
Hurst exponent. A similar trend is displayed by intertrade time intervals.
Finally, we demonstrate that the distribution of the intertrade times is better
described by a multiscaling ansatz than by simple gap scaling.Comment: 10 pages, 13 figures, 2 tables, accepted to Eur. Phys. J. B, updated
references, fixed some minor error
The limit order book on different time scales
Financial markets can be described on several time scales. We use data from
the limit order book of the London Stock Exchange (LSE) to compare how the
fluctuation dominated microstructure crosses over to a more systematic global
behavior.Comment: 11 pages, 7 figures, 2 tables, to appear in Proc. SPIE, Fluctuations
and Noise 2007, Florenc