Black hole entropy, log corrections and quantum ergosphere

Quantum-gravity corrections to the probability of emission of a particle from a black hole in the Parikh-Wilczek tunneling framework are studied. We consider the effects of zero-point quantum fluctuations of the metric on the emission probability for a tunneling shell. Quantum properties of the geometry are responsible for the formation of a "quantum egosphere" whose effects on the emission probability can be related to the emergence of a logarithmic correction to the Bekenstein-Hawking entropy-area formula.Comment: RevTex4, 10 pages, no figure

Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.Comment: 9 pages, 2 figure

Quantum phase transition of the sub-Ohmic rotor model

We investigate the behavior of an $N$-component quantum rotor coupled to a bosonic dissipative bath having a sub-Ohmic spectral density $J(\omega) \propto \omega^s$ with $s<1$. With increasing dissipation strength, this system undergoes a quantum phase transition from a delocalized phase to a localized phase. We determine the exact critical behavior of this transition in the large-$N$ limit. For $1>s>1/2$, we find nontrivial critical behavior corresponding to an interacting renormalization group fixed point while we find mean-field behavior for $s<1/2$. The results agree with those of the corresponding long-range interacting classical model. The quantum-to-classical mapping is therefore valid for the sub-Ohmic rotor model.Comment: 7 pages, final version as publishe

Quantum phase transitions in impurity models and percolating lattices

This thesis investigates the influence of random disorder and dissipation on zero-temperature quantum phase transitions. Both phenomena can fundamentally change the character of the phases of a quantum many-particle system and of the transitions between them. If dissipation and disorder occur simultaneously in a system undergoing a quantum phase transition, particularly strong effects can be expected. In the first paper reproduced in this thesis, we study a single quantum rotor coupled to a sub-Ohmic dissipative bath. We find that this system undergoes a quantum phase transition from a delocalized phase to a localized phase as the dissipation strength is increased. We determine the exact critical behavior of this transition; it agrees with that of the corresponding long-range interacting classical model. Therefore, the quantum-to-classical mapping is valid for the sub-Ohmic rotor model. In the second paper, we investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. We find that the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases, and we relate our results to the smeared transition scenario for disordered quantum phase transitions. In the last paper, the influence of Ohmic dissipation on the random transverse-field Ising chain is studied by means of large-scale Monte-Carlo simulations. Our simulations show that Ohmic dissipation destroys the infinite-randomness quantum critical point of the dissipationless system. Instead, the quantum phase transition between the paramagnetic and ferromagnetic phases is smeared, as predicted by a recent strong-disorder renormalization group approach --Abstract, page iv

Investigation in the Theory of Stochastic Processes.

In Chapter I of this dissertation, we present a pedagogical introduction to the basic concepts of stochastic theory and review the progress made as well as the outstanding unsolved problems in the field. For the rest of this dissertation, we use a generalized quantum Langevin equation (GLE) approach to investigate various properties of quantum dissipative systems. In Chapter II, calculations for the displacement and random force correlation functions for Brownian motion are generalized to the case of an arbitrary heat bath for a damped harmonic quantum oscillator. The mean square displacement of such an oscillator is then evaluated for both Ohmic and blackbody radiation heat baths, to determine the effects of many parameters on the localization of the oscillator. In Chapter III, the formalism is extended to the Brownian motion of a charged particle in an external magnetic field as well as in a potential. The influence of the magnetic field on the memory function and random force is determined, with the blackbody radiation heat bath analyzed as a special case. For a charged harmonic oscillator, the generalized susceptibility is obtained, which enables us to derive the symmetrized position correlation functions using the fluctuation-dissipation theorem. In addition, we obtain the free energy of the system by generalizing the remarkable formula of Ford, Lewis, and O\u27Connell. Explicit calculations are performed for Ohmic and blackbody radiation heat baths. Furthermore, the effect of dissipation on the localization of the oscillator in an Ohmic heat bath at zero temperature is shown to differ qualitatively from that without the magnetic field. Finally, we formulate retarded Green\u27s functions and symmetrized position correlation functions for the oscillator, reach some general conclusions, and make explicit calculations for the Ohmic heat bath. For the special case of Brownian motion at both zero and nonzero temperatures, we prove two general asymptotic relations between the retarded Green\u27s functions and the displacement correlation functions, which we use to evaluate the long-time behaviors of the latter from those of the former, for both the Ohmic heat bath and a rather general class of heat baths discussed extensively in the literature

Aspects of Quantum Gravity: Quantum Space-Time and Black Hole Thermodynamics

This work is devoted to the study of certain quantum properties of space-time at the Planck scale and of black holes. We discuss the possibility that in quantum gravity scenarios the symmetry structure of flat space-time might deviate from the classical relativistic picture and lead to broken or deformed Poincar´e invariance. The striking feature of these "quantum" space-time models is the possibility that they might have experimentally observable effects. We discuss how a purely kinematical model within these frameworks, besides providing the threshold anomalies needed to explain the existence of above-GZK cosmic rays, can modify the Bachall-Waxman bound on the flux of neutrinos that are expected to be produced together with such cosmic rays. A relevant characteristic of "quantum" space-time scenarios with modifications of relativistic kinematics is the emergence of a Planck-scale particle localization limit that reflects the presence of the Planck length as an intrinsic spatial resolution limit for regimes in which quantum and gravitational effects are of the same magnitude. We propose a remarkable argument which relates the type of quantum gravity corrections to the Bekenstein-Hawking entropy-area relation for black holes and the form of the Planck-scale particle localization limit. Using this argument we are able to constraint the form of the deformed energy-momentum dispersion relation expected to emerge in the low-energy limit of loop quantum gravity. The same argument is then generalized to quantum gravity frameworks which predict a modifications of Heisenberg's uncertainty relation. We carried on a systematic study of the effects of modified energy-momentum dispersion relation and generalized uncertainty principle for an evaporating black hole obii taining also results for Planck-scale modifications of the spectrum of a radiating black-body. Finally, we extend our study of quantum gravity corrections to the Hawking radiation spectrum by adapting the tunneling picture proposed by Parikh and Wilczek including, in such a way, non-thermal corrections due to back-reaction of the emitted particle. It is also showed that a quantum fluctuating black hole horizon, characterized by a "quantum ergosphere" produces the same type of modification to the emission spectrum expected when higher order quantum gravity corrections to the entropy-area relation are present

Quantum oscillator in a heat bath

In the present article, We use the density matrix evolution method to study the effect of a model solvent on the vibrational spectrum of a diatomic solute particle. The effect of the solvent is considered as a perturbation oil the Hamiltonian of the quantum subsystem consisting of a harmonic oscillator. The bath particles are treated classically. The perturbation potential representing the interaction between the solute and the solvent is represented in a bi-exponential form. This provides ail effective way to evaluate the required matrix elements needed to compute the evolution of the density matrix. The model calculations indicate that the repulsive parts of the potential dominate causing blue shifts in the vibrational frequencies