Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes

The phase transition of Reissner-Nordstr\"om black holes in $(n+1)$-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 $d$-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 $\Lambda$ and dimensionality $d$. 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