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An encyclopedia article on mathematical aspects of quantum field theory in curved spacetime. Section titles are: Introduction and preliminaries; Construction of *-algebra for a real linear scalar field on globally hyperbolic spacetimes and…
We study the emergence of universal scaling in the time-evolving momentum distribution of a harmonically trapped three-dimensional Bose-Einstein condensate, parametrically driven to a turbulent state. We demonstrate that the…
Based on the Unruh effect, we calculate the critical acceleration for the Bose-Einstein condensation in a free complex scalar field at finite density in the Rindler space. Our model corresponds to an ideal gas performing constantly…
Ultracold atomic quantum gases belong to the most exciting challenges of modern physics. Their theoretical description has drawn much from classical field equations. These mean-field approximations are in general reliable for dilute gases…
The current accelerating phase of the evolution of the universe is considered by constructing most economical cosmic models that use just general relativity and some dominating quantum effects associated with the probabilistic description…
The lateral Casimir-Polder force between an atom and a corrugated surface should allow one to study experimentally non trivial geometrical effects in quantum vacuum. Here, we derive the theoretical expression of this force in a scattering…
Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and…
In this thesis, we investigate quantum vacuum effects in the presence of gravitational fields. After discussing the general theory of vacuum effects in strong fields we apply it to the relevant issue of the interaction of the quantum vacuum…
A new type of global embedding of curved space-times in higher dimensional flat ones is introduced to present a unified description of Hawking and Unruh effects. Our analysis simplifies as well as generalises the conventional embedding…
Fully covariant wave equations predict the existence of a class of inertial-gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical fields, but, by conforming to general…
We aim to build a simple model of a gas with temperature ($T$) in thermal equilibrium with a black-body that plays the role of the adiabatically expanding universe, so that each particle of such a gas mimics a kind of "particle" (quantum)…
In the context of Quantum Cosmology and the Wheeler-DeWitt equation we investigate the possible effects of a non semiclassical wave-function of the universe on the evolution of the inflationary perturbations. These are associated with the…
The $q$-theory approach to the cosmological constant problem is reconsidered. The new observation is that the effective classical $q$-theory gets modified due to the backreaction of quantum-mechanical particle production by spacetime…
To date, both quantum theory, and Einstein's theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be…
A Gauss-Bonnet dark energy model is considered, which is inspired in string/M-theory and takes also into account quantum contributions. Those are introduced from a conformal quantum anomaly. The corresponding solutions for the Hubble rate,…
For general quantum systems the power expansion of the Gibbs potential and consequently the power expansion of the self energy is derived in terms of the interaction strength. Employing a generalization of the projector technique a compact…
Although the Unruh and Hawking phenomena are commonly linked to field quantization in "accelerated" coordinates or in curved spacetimes, we argue that they are deeply rooted at the classical level. We maintain in particular that these…
We present a kinetic theory for Bose-Einstein condensation of a weakly interacting atomic gas in a trap. Starting from first principles, we establish a Markovian kinetic description for the evolution towards equilibrium. In particular, we…
The two main predictions of quantum field theory in curved space-time, namely Hawking radiation and cosmological pair production, have not been directly tested and involve ultra high energy configurations. As a consequence, they should be…
Quantum effects in the era of reheating of the universe after inflation are considered. A semiclassical approach to gravity theory is applied within Starobinsky's inflationary model with backreaction. Some subtleties associated with…