Statistical Thermodynamics of Polymer Quantum Systems

Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional {\em polymer} quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal gas. We first study the spectra of these polymer systems. It turns out useful for the analysis to consider the length scale required by the quantization and which we shall refer to as polymer length. The dynamics of the polymer oscillator can be given the form of that for the standard quantum pendulum. Depending on the dominance of the polymer length we can distinguish two regimes: vibrational and rotational. The first occur for small polymer length and here the standard oscillator in Schr\"odinger quantization is recovered at leading order. The second one, for large polymer length, features dominant polymer effects. In the case of the polymer particles in the box, a bounded and oscillating spectrum that presents a band structure and a Brillouin zone is found. The thermodynamical quantities calculated with these spectra have corrections with respect to standard ones and they depend on the polymer length. For generic polymer length, thermodynamics of both systems present an anomalous peak in their heat capacity $C_V$

Spectrum of Charged Black Holes - The Big Fix Mechanism Revisited

Following an earlier suggestion of the authors(gr-qc/9607030), we use some basic properties of Euclidean black hole thermodynamics and the quantum mechanics of systems with periodic phase space coordinate to derive the discrete two-parameter area spectrum of generic charged spherically symmetric black holes in any dimension. For the Reissner-Nordstrom black hole we get $A/4G\hbar=\pi(2n+p+1)$, where the integer p=0,1,2,.. gives the charge spectrum, with $Q=\pm\sqrt{\hbar p}$. The quantity $\pi(2n+1)$, n=0,1,... gives a measure of the excess of the mass/energy over the critical minimum (i.e. extremal) value allowed for a given fixed charge Q. The classical critical bound cannot be saturated due to vacuum fluctuations of the horizon, so that generically extremal black holes do not appear in the physical spectrum. Consistency also requires the black hole charge to be an integer multiple of any fundamental elementary particle charge: $Q= \pm me$, m=0,1,2,.... As a by-product this yields a relation between the fine structure constant and integer parameters of the black hole -- a kind of the Coleman big fix mechanism induced by black holes. In four dimensions, this relationship is $e^2/\hbar=p/m^2$ and requires the fine structure constant to be a rational number. Finally, we prove that the horizon area is an adiabatic invariant, as has been conjectured previously.Comment: 21 pages, Latex. 1 Section, 1 Figure added. To appear in Class. and Quant. Gravit

Quantum Mechanics of Charged Black Holes

We quantize the spherically symmetric sector of generic charged black holes. Thermal properties are encorporated by imposing periodicity in Euclidean time, with period equal to the inverse Hawking temperature of the black hole. This leads to an exact quantization of the area (A) and charge (Q) operators. For the Reissner-Nordstr\"om black hole, $A=4\pi G \hbar (2n+p+1)$ and $Q=me$, for integers $n,p,m$. Consistency requires the fine structure constant to be quantized: $e^2/\hbar=p/m^2$. Remarkably, vacuum fluctuations exclude extremal black holes from the spectrum, while near extremal black holes are highly quantum objects. We also prove that horizon area is an adiabatic invariant.Comment: 5 pages, Latex. Minor changes. To appear in Phys. Lett.

Quantum-mechanical study of optical excitations in nanoscale systems: first-principles description of plasmons, tunneling-induced light emission and ultrastrong light-matter interaction

245 p.This theoretical thesis applies quantum methodologies to nanophotonic systems in order to investigate the properties of optical excitations in metals, as well as the interaction of matter excitations with optical modes in cavities. Initially, we adopt a first-principles description of electrons in metals to analyze the properties of plasmonic excitations. Specifically, surface plasmons on the Pd(110) surface and in two-dimensional anisotropic metals are investigated. In the two-dimensional system, we notably find collective excitations with a linear dispersion that are called acoustic plasmons and that differ from the conventional plasmon. In the second part of the thesis, we focus on metal-insulator-metal tunneling junctions. We demonstrate the importance of considering the electronic wavefunctions in the full device to accurately model the excitation of plasmons by tunneling electrons and the resulting light emission. Last, we use the framework of cavity quantum electrodynamics to find the appropriate quantum description of the interaction of matter excitations with optical modes in different nanophotonic systems, and show the equivalences of these descriptions with classical models based on coupled harmonic oscillators. These harmonic oscillator models are also applied to analyze experimental results that demonstrate strong and ultrastrong coupling between phonons and infrared modes of a microcavity

Black Hole Thermodynamics

The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this chapter I will review the discovery of black hole thermodynamics and summarize the many independent ways of obtaining the thermodynamic and (perhaps) statistical mechanical properties of black holes. I will then describe some of the remaining puzzles, including the nature of the quantum microstates, the problem of universality, and the information loss paradox.Comment: Invited review article. A few parts based on an earlier review, arXiv:0807.4520. To appear in Int. J. Mod. Phys. D and in "One Hundred Years of General Relativity: Cosmology and Gravity," edited by Wei-Tou Ni (World Scientific, Singapore, 2015). v2: added references and appendi

Black Holes as Effective Geometries

Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or approximate description of a pure state, in a closed string theory, which semiclassical observers are unable to distinguish from the "naive" geometry. In cases with enough supersymmetry it has been possible to explicitly construct these microstates in spacetime, and understand how coarse-graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise for examples in Type II string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8 supercharges respectively. For such a picture of black holes as effective geometries to extend to cases with finite horizon area the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective theory. By studying examples in M-theory on AdS_3 x S^2 x CY that preserve 4 supersymmetries we show how this can happen.Comment: Review based on lectures of JdB at CERN RTN Winter School and of VB at PIMS Summer School. 68 pages. Added reference

Decoherence: Concepts and Examples

We give a pedagogical introduction to the process of decoherence - the irreversible emergence of classical properties through interaction with the environment. After discussing the general concepts, we present the following examples: Localisation of objects, quantum Zeno effect, classicality of fields and charges in QED, and decoherence in gravity theory. We finally emphasise the important interpretational features of decoherence.Comment: 24 pages, LATEX, 9 figures, needs macro lamuphys.sty, to appear in the Proceedings of the 10th Born Symposiu

The quantum of area ΔA=8πlP2\Delta A = 8\pi l_P^{2} and a statistical interpretation of black hole entropy

In contrast to alternative values, the quantum of area $\Delta A = 8\pi l_P^{2}$ does not follow from the usual statistical interpretation of black hole entropy; on the contrary, a statistical interpretation follows from it. This interpretation is based on the two concepts: nonadditivity of black hole entropy and Landau quantization. Using nonadditivity a microcanonical distribution for a black hole is found and it is shown that the statistical weight of black hole should be proportional to its area. By analogy with conventional Landau quantization, it is shown that quantization of black hole is nothing but the Landau quantization. The Landau levels of black hole and their degeneracy are found. The degree of degeneracy is equal to the number of ways to distribute a patch of area $8\pi l_P^{2}$ over the horizon. Taking into account these results, it is argued that the black hole entropy should be of the form $S_{bh} =2\pi\cdot\Delta\Gamma$, where the number of microstates is $\Delta\Gamma = A/8\pi l_P^{2}$. The nature of the degrees of freedom responsible for black hole entropy is elucidated. The applications of the new interpretation are presented. The effect of noncommuting coordinates is discussed.Comment: 12 pages, revtex, no figures; v.3, revised and enlarged; Sec. III "Quantization of black hole as Landau quantization" added; references added; conclusions changed in some point