726 research outputs found
Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes
The phase transition of Reissner-Nordstr\"om black holes in
-dimensional anti-de Sitter spacetime is studied in details using the
thermodynamic analogy between a RN-AdS black hole and a van der Waals liquid
gas system. We first investigate critical phenomena of the RN-AdS black hole.
The critical exponents of relevant thermodynamical quantities are evaluated. We
find identical exponents for a RN-AdS black hole and a Van der Waals liquid gas
system. This suggests a possible universality in the phase transitions of these
systems. We finally study the thermodynamic behavior using the equilibrium
thermodynamic state space geometry and find that the scalar curvature diverges
exactly at the van der Waals-like critical point where the heat capacity at
constant charge of the black hole diverges.Comment: 18 pages, 5 figure
Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method
We derive a coarse-grained equation of motion of a number density by applying
the projection operator method to a non-relativistic model. The derived
equation is an integrodifferential equation and contains the memory effect. The
equation is consistent with causality and the sum rule associated with the
number conservation in the low momentum limit, in contrast to usual acausal
diffusion equations given by using the Fick's law. After employing the Markov
approximation, we find that the equation has the similar form to the causal
diffusion equation. Our result suggests that current-current correlations are
not necessarily adequate as the definition of diffusion constants.Comment: 10 pages, 1 figure, Final version published in Phys. Rev.
Thermalization of quark-gluon matter by 2-to-2 and 3-to-3 elastic scatterings
Thermalization of quark-gluon matter is studied with a transport equation
that includes contributions of 2-to-2 and 3-to-3 elastic scatterings.
Thermalization time is related to the squared amplitudes for the elastic
scatterings that are calculated in perturbative QCD.Comment: LaTex, 6 pages, 3 figures, talk presented at the 19th international
conference on ultra-relativistic nucleus-nucleus collisions, Shanghai, China,
Nov. 200
Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes
In this paper, we study the phase structure and equilibrium state space
geometry of charged topological Gauss-Bonnet black holes in -dimensional
anti-de Sitter spacetime. Several critical points are obtained in the canonical
ensemble, and the critical phenomena and critical exponents near them are
examined. We find that the phase structures and critical phenomena drastically
depend on the cosmological constant and dimensionality . The
result also shows that there exists an analogy between the black hole and the
van der Waals liquid gas system. Moreover, we explore the phase transition and
possible property of the microstructure using the state space geometry. It is
found that the Ruppeiner curvature diverges exactly at the points where the
heat capacity at constant charge of the black hole diverges. This black hole is
also found to be a multiple system, i.e., it is similar to the ideal gas of
fermions in some range of the parameters, while to the ideal gas of bosons in
another range.Comment: 17 pages, 8 figures, 3 table
Occurrence of normal and anomalous diffusion in polygonal billiard channels
From extensive numerical simulations, we find that periodic polygonal
billiard channels with angles which are irrational multiples of pi generically
exhibit normal diffusion (linear growth of the mean squared displacement) when
they have a finite horizon, i.e. when no particle can travel arbitrarily far
without colliding. For the infinite horizon case we present numerical tests
showing that the mean squared displacement instead grows asymptotically as t
log t. When the unit cell contains accessible parallel scatterers, however, we
always find anomalous super-diffusion, i.e. power-law growth with an exponent
larger than 1. This behavior cannot be accounted for quantitatively by a simple
continuous-time random walk model. Instead, we argue that anomalous diffusion
correlates with the existence of families of propagating periodic orbits.
Finally we show that when a configuration with parallel scatterers is
approached there is a crossover from normal to anomalous diffusion, with the
diffusion coefficient exhibiting a power-law divergence.Comment: 9 pages, 15 figures. Revised after referee reports: redrawn figures,
additional comments. Some higher quality figures available at
http://www.fis.unam.mx/~dsander
Microcanonical Origin of the Maximum Entropy Principle for Open Systems
The canonical ensemble describes an open system in equilibrium with a heat
bath of fixed temperature. The probability distribution of such a system, the
Boltzmann distribution, is derived from the uniform probability distribution of
the closed universe consisting of the open system and the heat bath, by taking
the limit where the heat bath is much larger than the system of interest.
Alternatively, the Boltzmann distribution can be derived from the Maximum
Entropy Principle, where the Gibbs-Shannon entropy is maximized under the
constraint that the mean energy of the open system is fixed. To make the
connection between these two apparently distinct methods for deriving the
Boltzmann distribution, it is first shown that the uniform distribution for a
microcanonical distribution is obtained from the Maximum Entropy Principle
applied to a closed system. Then I show that the target function in the Maximum
Entropy Principle for the open system, is obtained by partial maximization of
Gibbs-Shannon entropy of the closed universe over the microstate probability
distributions of the heat bath. Thus, microcanonical origin of the Entropy
Maximization procedure for an open system, is established in a rigorous manner,
showing the equivalence between apparently two distinct approaches for deriving
the Boltzmann distribution. By extending the mathematical formalism to
dynamical paths, the result may also provide an alternative justification for
the principle of path entropy maximization as well.Comment: 12 pages, no figur
Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics
A new formula to calculate the transport coefficients of the causal
dissipative hydrodynamics is derived by using the projection operator method
(Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This
is an extension of the Green-Kubo-Nakano (GKN) formula to the case of
non-Newtonian fluids, which is the essential factor to preserve the
relativistic causality in relativistic dissipative hydrodynamics. This formula
is the generalization of the GKN formula in the sense that it can reproduce the
GKN formula in a certain limit. In this work, we extend the previous work so as
to apply to more general situations.Comment: 15 pages, no figure. Discussions are added in the concluding remarks.
Accepted for publication in Phys. Rev.
Theory of Orbital Magnetization in Solids
In this review article, we survey the relatively new theory of orbital
magnetization in solids-often referred to as the "modern theory of orbital
magnetization"-and its applications. Surprisingly, while the calculation of the
orbital magnetization in finite systems such as atoms and molecules is straight
forward, in extended systems or solids it has long eluded calculations owing to
the fact that the position operator is ill-defined in such a context.
Approaches that overcome this problem were first developed in 2005 and in the
first part of this review we present the main ideas reaching from a Wannier
function approach to semi-classical and finite-temperature formalisms. In the
second part, we describe practical aspects of calculating the orbital
magnetization, such as taking k-space derivatives, a formalism for
pseudopotentials, a single k-point derivation, a Wannier interpolation scheme,
and DFT specific aspects. We then show results of recent calculations on Fe,
Co, and Ni. In the last part of this review, we focus on direct applications of
the orbital magnetization. In particular, we will review how properties such as
the nuclear magnetic resonance shielding tensor and the electron paramagnetic
resonance g-tensor can elegantly be calculated in terms of a derivative of the
orbital magnetization
Spin-Electromagnetic Hydrodynamics and Magnetization Induced by Spin-Magnetic Interaction
The hydrodynamic model including the spin degree of freedom and the
electromagnetic field was discussed. In this derivation, we applied
electromagnetism for macroscopic medium proposed by Minkowski. For the equation
of motion of spin, we assumed that the hydrodynamic representation of the Pauli
equation is reproduced when the many-body effect is neglected. Then the
spin-magnetic interaction in the Pauli equation was converted to a part of the
magnetization. The fluid and spin stress tensors induced by the many-body
effect were obtained by employing the algebraic positivity of the entropy
production in the framework of the linear irreversible thermodynamics,
including the mixing effect of the irreversible currents. We further
constructed the constitutive equation of the polarization and the
magnetization. Our polarization equation is more reasonable compared to another
result obtained using electromagnetism for macroscopic medium proposed by de
Groot-Mazur.Comment: 24 pages, no figure, the discussion for the modifed thermodynamic
relation is added, several errors are corrected, accepted for publication in
PR
Homoclinic Signatures of Dynamical Localization
It is demonstrated that the oscillations in the width of the momentum
distribution of atoms moving in a phase-modulated standing light field, as a
function of the modulation amplitude, are correlated with the variation of the
chaotic layer width in energy of an underlying effective pendulum. The maximum
effect of dynamical localization and the nearly perfect delocalization are
associated with the maxima and minima, respectively, of the chaotic layer
width. It is also demonstrated that kinetic energy is conserved as an almost
adiabatic invariant at the minima of the chaotic layer width, and that the
system is accurately described by delta-kicked rotors at the zeros of the
Bessel functions J_0 and J_1. Numerical calculations of kinetic energy and
Lyapunov exponents confirm all the theoretical predictions.Comment: 7 pages, 4 figures, enlarged versio
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