Coherent State Path Integrals in the Weyl Representation

We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in \cite{Klau85}, which involve the normal or the antinormal ordering of the Hamiltonian. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. We show that the semiclassical limit of the coherent state propagator in Weyl representation is involves classical trajectories that are independent on the coherent states width. This propagator is also free from the phase corrections found in \cite{Bar01} for the two Klauder forms and provides an explicit connection between the Wigner and the Husimi representations of the evolution operator.Comment: 23 page

Conformal quantum mechanics as the CFT1_1 dual to AdS2_2

A 0+1-dimensional candidate theory for the CFT$_1$ dual to AdS$_2$ is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose "non-primary character" conspires with the "non-invariance of the vacuum" to give precisely the correlation functions in a conformally invariant theory.Comment: 6 page

Loading of a Bose-Einstein condensate in the boson-accumulation regime

We study the optical loading of a trapped Bose-Einstein condensate by spontaneous emission of atoms in excited electronic state in the Boson-Accumulation Regime. We generalize the previous simplified analysis of ref. [Phys. Rev. A 53, 2466 (1996)], to a 3D case in which more than one trap level of the excited state trap is considered. By solving the corresponding quantum many-body master equation, we demonstrate that also for this general situation the photon reabsorption can help to increase the condensate fraction. Such effect could be employed to realize a continuous atom laser, and to overcome condensate losses.Comment: 7 pages, 5 eps figures, uses epl.st

Quantum open systems and turbulence

We show that the problem of non conservation of energy found in the spontaneous localization model developed by Ghirardi, Rimini and Weber is very similar to the inconsistency between the stochastic models for turbulence and the Navier-Stokes equation. This sort of analogy may be useful in the development of both areas.Comment: to appear in Physical Review

Bose-Einstein Condensates in Optical Quasicrystal Lattices

We analyze the physics of Bose-Einstein condensates confined in 2D quasi-periodic optical lattices, which offer an intermediate situation between ordered and disordered systems. First, we analyze the time-of-flight interference pattern that reveals quasi-periodic long-range order. Second, we demonstrate localization effects associated with quasi-disorder as well as quasiperiodic Bloch oscillations associated with the extended nature of the wavefunction of a Bose-Einstein condensate in an optical quasicrystal. In addition, we discuss in detail the crossover between diffusive and localized regimes when the quasi-periodic potential is switched on, as well as the effects of interactions

Building analytical three-field cosmological models

A difficult task to deal with is the analytical treatment of models composed by three real scalar fields, once their equations of motion are in general coupled and hard to be integrated. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called "extension method". The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is within inflationary models, where the Einstein-Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.Comment: 11 pages, and 3 figures, updated version published in EPJ