Abstract:
Quantum fields responding to "moving mirrors" have been predicted to give rise to thermodynamic paradoxes. I show that the assumption in such work that the mirror can be treated as an external field is invalid: the exotic energy-transfer effects necessary to the paradoxes are well below the scales at which the model is credible. For a first-quantized point-particle mirror, it appears that exotic energy-transfers are lost in the quantum uncertainty in the mirror's state. An accurate accounting of these energies will require a model which recognizes the mirror's finite reflectivity, and almost certainly a model which allows for the excitation of internal mirror modes, that is, a second-quantized model.

Abstract:
We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are discrete, and emission rates for each allowed angular direction are obtained. We discuss the dependence of the generation rates on the cavity length and show that the effect is enhanced for short cavity lengths. We also compute the dissipative force on the moving mirrors and show that it is related to the total radiated energy as predicted by energy conservation.

Abstract:
We study the quantum stress tensor correlation function for a massless scalar field in a flat two-dimensional spacetime containing a moving mirror. We construct the correlation functions for right-moving and left-moving fluxes for an arbitrary trajectory, and then specialize them to the case of a mirror trajectory for which the expectation value of the stress tensor describes a pair of delta-function pulses, one of negative energy and one of positive energy. The flux correlation function describes the fluctuations around this mean stress tensor, and reveals subtle changes in the correlations between regions where the mean flux vanishes.

Abstract:
A simple quantum mechanical model of $N$ free scalar fields interacting with a dynamical moving mirror is formulated and shown to be equivalent to two-dimensional dilaton gravity. We derive the semi-classical dynamics of this system, by including the back reaction due to the quantum radiation. We develop a hamiltonian formalism that describes the time evolution as seen by an asymptotic observer, and write a scattering equation that relates the in-falling and out-going modes at low energies. At higher incoming energy flux, however, the classical matter-mirror dynamics becomes unstable and the mirror runs off to infinity. This instability provides a useful paradigm for black hole formation and introduces an analogous information paradox. Finally, we propose a new possible mechanism for restoring the stability in the super-critical situation, while preserving quantum coherence. This mechanism is based on the notion of an effective time evolution, that takes into account the quantum mechanical effect of the measurement of the Hawking radiation on the state of the infalling matter.

Abstract:
This is a progress report on our current work on moving charges, detectors, and moving mirrors in a quantum field treated in a fully relativistic way via the Feynman-Vernon influence functional method, which preserves maximal quantum coherence of the system with self-consistent back-reaction from the field.

Abstract:
We review the recent work on the mechanics of fast moving strings in anti-de Sitter space times a sphere and discuss the role of conserved charges. An interesting relation between the local conserved charges of rigid solutions was found in the earlier work. We propose a generalization of this relation for arbitrary solutions, not necessarily rigid. We conjecture that an infinite combination of local conserved charges is an action variable generating periodic trajectories in the classical string phase space. It corresponds to the length of the operator on the field theory side.

Abstract:
We present an exact time-dependent solution to the effective D-brane world-volume theory which describes an inhomogeneous decay of a brane-antibrane system. We compute the quantum energy flux induced by the particle creation in this inhomogeneous and time-dependent background. We find that this calculation is essentially equivalent to that of the moving mirror system. In the initial stage, the energy flux turns out to be thermal with the temperature given by the inverse of the distance between the brane and the antibrane. Later it changes its sign and becomes a negative energy flux. Our result may be relevant for the (p)reheating process or/and the evolution of cosmic string network after stringy brane inflation.

Abstract:
We study the creation of photons in a one dimensional oscillating cavity with two perfectly conducting moving walls. By means of a conformal transformation we derive a set of generalized Moore's equations whose solution contains the whole information of the radiation field within the cavity. For the case of resonant oscillations we solve these equations using a renormalization group procedure that appropriately deals with the secular behaviour present in a naive perturbative approach. We study the time evolution of the energy density profile and of the number of created photons inside the cavity.

Abstract:
We employ the Schwinger-Keldysh formalism to study the nonequilibrium dynamics of the mirror with perfect reflection moving in a quantum field. Within the regime of linear response in terms of a first order expansion of the mirror's displacement, the coarse-grained effective action is obtained by integrating out quantum fields with the method of influence functional. The semiclassical Langevin equation is derived, and is found to involve two levels of backreaction effects on the dynamics of mirrors: radiation reaction induced by the motion of the mirror and backreaction dissipation arising from fluctuations in quantum fields via a fluctuation-dissipation relation. Although the theorem of fluctuation and dissipation in linear response theory is of model independence, the study from the first principles derivation shows that the obtained theorem is also {\it independent} of the regulators introduced to deal with short-distance divergences from quantum fields. Thus, when the method of regularization is introduced to compute the dissipation and fluctuation effects, this theorem must be fulfilled as the results are obtained by taking the short-distance limit in the end of calculations. The backreaction effects from vacuum fluctuations on moving mirrors are found to be hardly detected while those effects from thermal fluctuations may be detectable.

Abstract:
We use a functional approach to study various aspects of the quantum effective dynamics of moving, planar, dispersive mirrors, coupled to scalar or Dirac fields, in different numbers of dimensions. We first compute the Euclidean effective action, and use it to derive the imaginary part of the `in-out' effective action. We also obtain, for the case of the real scalar field in 1+1 dimensions, the Schwinger-Keldysh effective action and a semiclassical Langevin equation that describes the motion of the mirror including noise and dissipative effects due to its coupling to the quantum fields.