24,278 research outputs found
On the apparent horizon in fluid-gravity duality
This article develops a computational framework for determining the location
of boundary-covariant apparent horizons in the geometry of conformal
fluid-gravity duality in arbitrary dimensions. In particular, it is shown up to
second order and conjectured to hold to all orders in the gradient expansion
that there is a unique apparent horizon which is covariantly expressible in
terms of fluid velocity, temperature and boundary metric. This leads to the
first explicit example of an entropy current defined by an apparent horizon and
opens the possibility that in the near-equilibrium regime there is preferred
foliation of apparent horizons for black holes in asymptotically-AdS
spacetimes
An amended MaxEnt formulation for deriving Tsallis factors, and associated issues
An amended MaxEnt formulation for systems displaced from the conventional
MaxEnt equilibrium is proposed. This formulation involves the minimization of
the Kullback-Leibler divergence to a reference (or maximization of Shannon
-entropy), subject to a constraint that implicates a second reference
distribution and tunes the new equilibrium. In this setting, the
equilibrium distribution is the generalized escort distribution associated to
and . The account of an additional constraint, an observable given
by a statistical mean, leads to the maximization of R\'{e}nyi/Tsallis
-entropy subject to that constraint. Two natural scenarii for this
observation constraint are considered, and the classical and generalized
constraint of nonextensive statistics are recovered. The solutions to the
maximization of R\'{e}nyi -entropy subject to the two types of constraints
are derived. These optimum distributions, that are Levy-like distributions, are
self-referential. We then propose two `alternate' (but effectively computable)
dual functions, whose maximizations enable to identify the optimum parameters.
Finally, a duality between solutions and the underlying Legendre structure are
presented.Comment: Presented at MaxEnt2006, Paris, France, july 10-13, 200
Duality for open fermion systems: energy-dependent weak coupling and quantum master equations
Open fermion systems with energy-independent bilinear coupling to a fermionic
environment have been shown to obey a general duality relation [Phys. Rev. B
93, 81411 (2016)] which allows for a drastic simplification of time-evolution
calculations. In the weak-coupling limit, such a system can be associated with
a unique dual physical system in which all energies are inverted, in particular
the internal interaction. This paper generalizes this fermionic duality in two
ways: we allow for weak coupling with arbitrary energy dependence and describe
both occupations and coherences coupled by a quantum master equation for the
density operator. We also show that whenever generalized detailed balance holds
(Kolmogorov criterion), the stationary probabilities for the dual system can be
expressed explicitly in terms of the stationary recurrence times of the
original system, even at large bias.
We illustrate the generalized duality by a detailed analysis of the rate
equation for a quantum dot with strong onsite Coulomb repulsion, going beyond
the commonly assumed wideband limit. We present predictions for (i) the decay
rates for transient charge and heat currents after a gate-voltage quench and
(ii) the thermoelectric linear response coefficients in the stationary limit.
We show that even for pronouncedly energy-dependent coupling, all nontrivial
parameter dependence in these problems is entirely captured by just two
well-understood stationary variables, the average charge of the system and of
the dual system. Remarkably, it is the latter that often dictates the most
striking features of the measurable quantities (e.g., positions of resonances),
underscoring the importance of the dual system for understanding the actual
one.Comment: 25 pages + 2 pages appendix + 2 pages references, 7 figures. To be
submitted to Phys. Rev.
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