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Search Results: 1 - 10 of 8862 matches for " Nuno;Dias "
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Classicality Criteria
Nuno Costa Dias
Mathematics , 1999,
Abstract: We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and the classical data providing the two alternative descriptions of its initial time configuration. It is proved that a general quantum system satisfying the criteria up to some extend displays a time evolution consistent with the classical predictions up to some degree and thus it is argued that the criteria provide a suitable measure of classicality. The features of the formalism are illustrated through two simple examples.
Half Quantization
Nuno Costa Dias
Mathematics , 1999, DOI: 10.1088/0305-4470/34/4/306
Abstract: A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical systems will be named half quantum. The aim of this paper is to derive the dynamical evolution of a general half quantum system from its full quantum formulation. The standard approach would be to use quantum mechanics to make predictions for the time evolution of the half quantum initial data. The main problem is how can quantum mechanics be applied to a dynamical system whose initial time configuration is not described by a set of fully quantum data. A solution to this problem is presented and used, as a guideline to obtain a general formulation of coupled classical-quantum dynamics. Finally, a quantization prescription mapping a given classical theory to the correspondent half quantum one is presented.
Deformation Quantization of Confined Systems
Nuno Costa Dias,Joao Nuno Prata
Physics , 2006,
Abstract: The Weyl-Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation, as well as the dynamical equation does not display the expected solutions. In this paper we review some previous results in the subject and add some new contributions. We reformulate the confined energy eigenvalue equation by adding to the Hamiltonian a new (distributional) boundary potential. The new Hamiltonian is proved to be globally defined and self-adjoint. Moreover, it yields the correct Weyl-Wigner formulation of the confined system.
The Narcowich-Wigner spectrum of a pure state
Nuno Costa Dias,Joao Nuno Prata
Physics , 2008,
Abstract: We completely characterize the Narcowich-Wigner spectrum of Wigner functions associated with pure states.
Symmetric Classical Mechanics
Nuno Costa Dias,Joao Nuno Prata
Physics , 2000,
Abstract: We investigate the possibility that the semiclassical limit of quantum mechanics might be correctly described by a classical dynamical theory, other than standard classical mechanics. Using a set of classicality criteria proposed in a related paper, we show that the time evolution of a set of quantum initial data satisfying these criteria is fully consistent with the predictions of a new theory of classical dynamics. The dynamical structure of the new theory is given by the Moyal bracket. This is a Lie bracket that was first derived as the dynamical structure of the Moyal-Weyl-Wigner formulation of quantum mechanics. We present a new derivation of the Moyal bracket, this time in the context of the semiclassical limit of quantum mechanics and thus prove that both classical and quantum dynamics can be formulated in terms of the same canonical structure.
Bohmian trajectories and quantum phase space distributions
Nuno Costa Dias,Joao Nuno Prata
Physics , 2002, DOI: 10.1016/S0375-9601(02)01175-1
Abstract: We prove that most quasi-distributions can be written in a form similar to that of the de Broglie-Bohm distribution, except that ordinary products are replaced by some suitable non-commutative star product. In doing so, we show that the Hamilton-Jacobi trajectories and the concept of "classical pure state" are common features to all phase space formulations of quantum mechanics. Furthermore, these results provide an explicit quantization prescription for classical distributions.
Comment on "On infinite walls in deformation quantization"
Nuno Costa Dias,Joao Nuno Prata
Physics , 2005, DOI: 10.1016/j.aop.2005.10.003
Abstract: We discuss a recent method proposed by Kryukov and Walton to address boundary-value problems in the context of deformation quantization. We compare their method with our own approach and establish a connection between the two formalisms.
Symmetric Hybrid Dynamics: A canonical formulation of coupled classical-quantum dynamics
Nuno Costa Dias,Joao Nuno Prata
Physics , 2000,
Abstract: A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover symmetric hybrid dynamics displays a fully consistent canonical structure. Namely, it is formulated over a Lie algebra of observables, time evolution is unitary and the solution of a hybrid type Schr\"odinger equation. A quantization prescription from classical mechanics to hybrid dynamics is presented. The quantization map is a Lie algebra isomorphism. Finally some possible applications of the theory are succinctly suggested.
Causal Interpretation and Quantum Phase Space
Nuno Costa Dias,Joao Nuno Prata
Physics , 2001, DOI: 10.1016/S0375-9601(01)00747-2
Abstract: We show that the de Broglie-Bohm interpretation can be easily implemented in quantum phase space through the method of quasi-distributions. This method establishes a connection with the formalism of the Wigner function. As a by-product, we obtain the rules for evaluating the expectation values and probabilities associated with a general observable in the de Broglie-Bohm formulation. Finally, we discuss some aspects of the dynamics.
Formal solutions of stargenvalue equations
Nuno Costa Dias,Joao Nuno Prata
Physics , 2001, DOI: 10.1016/j.aop.2003.11.004
Abstract: The formal solution of a general stargenvalue equation is presented, its properties studied and a geometrical interpretation given in terms of star-hypersurfaces in quantum phase space. Our approach deals with discrete and continuous spectra in a unified fashion and includes a systematic treatment of non-diagonal stargenfunctions. The formalism is used to obtain a complete formal solution of Wigner quantum mechanics in the Heisenberg picture and to write a general formula for the stargenfunctions of Hamiltonians quadratic in the phase space variables in arbitrary dimension. A variety of systems is then used to illustrate the former results.
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