No abstract

2D Jackiw-Teitelboim gravity is represented as a completely integrable nonlinear reaction-diffusion system, whose Euclidean version leads to the nonlinear Schrödinger equation. The solitonlike solutions, called dissipatons, to such systems characterize completely the black holes of the considered gravity model ͑the black hole horizon, the Hawking temperature, and the causal structure͒. The collision of black holes is described in terms of elastic scattering of dissipatons, which shows a novel transmissionless character, creating a metastable state with a specific lifetime. Finally, alternative descriptions of the model in terms of other completely integrable systems are overlooked. ͓S0556-2821͑98͒02716-7͔

We study the information transmission through a quantum channel, defined over a continuous alphabet and losing its energy en route, in presence of correlated noise among different channel uses. We then show that entangled inputs improve the rate of transmission of such a channel.

The Jackiw-Teitelboim gauge formulation of the 1+1 dimensional gravity allows us to relate different gauge fixing conditions with integrable hierarchies of evolution equations. We show that the equations for the Zweibein fields can be written as a pair of time reversed evolution equations of the reaction-diffusion type, admitting dissipative solutions. The spectral parameter for the related Lax pair appears as the constant valued spin connection associated with the SO(1, 1) gauge symmetry. Spontaneous breaking of the non-compact symmetry and the irreversible evolution are discussed.

We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function σ(η) of the conformal time η, called the auxiliary field equation. At the classical level, σ(η) can be expressed by means of two independent solutions of the "master equation" to which the perturbed Einstein equations for the gravitational waves can be reduced.At the quantum level, all the significant physical quantities can be formulated using Bogolubov transformations and the operator quadratic Hamiltonian corresponding to the classical version of a damped parametrically excited oscillator where the varying mass is replaced by the square cosmological scale factor a 2 (η). A quantum approach to the generation of gravitational waves is proposed on the grounds of the previous η−dependent Hamiltonian. An estimate in terms of σ(η) and a(η) of the destruction of quantum coherence due to the gravitational evolution and an exact expression for the phase of a gravitational wave corresponding to any value of η are also obtained. We conclude by discussing a few applications to quasi-de Sitter and standard de Sitter scenarios.