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Springer theses

Transition to a Relaxation-Free Regime

Marine Pigneur

Published Jan 1, 2020• 0 citations
Publisher
DOI
10.1007/978-3-030-52844-7_4

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arXiv:hep-th/0212308•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•May 30, 2003•90 citations
Relaxation cavityless optical bistability is studied when a semiconductor is exposed to light quanta with an energy exceeding the transition energy and the free-electron relaxation time depends on temperature. The numerical analysis of dynamic equations for temperature and free-electron density demonstrates that 11 regimes of light-semiconductor interaction are possible. The regimes are classified in terms of the features of temperature-intensity characteristic curves, namely, by the number and arrangement of instability and quasistability segments and by the presence or absence of bistability. It is found that both the upper and the lower branch of a bistable characteristic curve may be unstable, which results in spontaneous switchings between the respective states. Similarly, if the upper state is unstable and the lower state is stable, a small perturbation of the parameters (free-electron temperature and density) near the former causes the transition to the oscillatory regime. If the upper state is unstable and a small perturbation of the lower (stable) state excites a damped oscillation, spontaneous switchings result if the fluctuating temperature exceeds some critical value for the lower state.
We study the process of relaxation back to thermal equilibrium in (1+1)(1+1)(1+1)-dimensional conformal field theory at finite temperature. When the size of the system is much larger than the inverse temperature, perturbations decay exponentially with time. On the other hand, when the inverse temperature is large, the relaxation is oscillatory with the characteristic period set by the size of the system. We then analyze the intermediate regime in two specific models: namely, free fermions, and a strongly coupled large k conformal field theory which is dual to string theory on (2+1)(2+1)(2+1)-dimensional anti--de Sitter spacetime. In the latter case, there is a sharp transition between the two regimes in the $k=\ensuremath{\infty}$ limit, which is a manifestation of the gravitational Hawking-Page phase transition. In particular, we establish a direct connection between quasinormal and normal modes of the gravity system, and the decaying and oscillating behavior of the conformal field theory.