arXiv subjects

Octavio Castaños

Publications and source records attributed to Octavio Castaños.

25 records · Page 2Linked to original sources

arXiv2014

Entropy-energy inequalities for qudit states

We establish a procedure to find the extremal density matrices for any finite Hamiltonian of a qudit system. These extremal density matrices provide an approximate description of the energy spectra of the Hamiltonian. In the case of restricting the extremal density matrices by pure states, we show that the energy spectra of the Hamiltonian is recovered for $d=2$ and $3$. We conjecture that by means of this approach the energy spectra can be recovered for the Hamiltonian of an arbitrary finite qudit system. For a given qudit system Hamiltonian, we find new inequalities connecting the mean value of the Hamiltonian and the entropy of an arbitrary state. We demonstrate that these inequalities take place for both the considered extremal density matrices and generic ones.

quant-ph↗

arXiv2013

Quantum phase transitions of three-level atoms interacting with a one-mode electromagnetic field

We apply the energy surface method to study a system of Na three-level atoms interacting with a one-mode radiation field in the Ξ, Λand V configurations. We obtain an estimation of the ground-state energy, the expectation value of the total number of excitations, and the separatrix of the model in the interaction parameter space, and compare the results with the exact solutions. We have first and second-order phase transitions, except for the V configuration which only presents second-order phase-transitions.

quant-ph↗

arXiv2012

Mathematical Methods in Quantum Optics: the Dicke Model

We show how various mathematical formalisms, specifically the catastrophe formalism and group theory, aid in the study of relevant systems in quantum optics. We describe the phase transition of the Dicke model for a finite number N of atoms, via 3 different methods, which lead to universal parametric curves for the expectation value of the first quadrature of the electromagnetic field and the expectation value of the number operator, as functions of the atomic relative population. These are valid for all values of the matter-field coupling parameter, and valid for both the ground and first-excited states. Using these mathematical tools, the critical value of the atom-field coupling parameter is found as a function of the number of atoms, from which its critical exponent is derived.

quant-ph↗

arXiv2012

Generalized coherent states for time-dependent and nonlinear Hamiltonians via complex Riccati equations

Based on the Gaussian wave packet solution for the harmonic oscillator and the corresponding creation and annihilation operators, a generalization is presented that also applies for wave packets with time-dependent width as they occur for systems with different initial conditions, time-dependent frequency or in contact with a dissipative environment. In all these cases the corresponding coherent states, position and momentum uncertainties and quantum mechanical energy contributions can be obtained in the same form if the creation and annihilation operators are expressed in terms of a complex variable that fulfills a nonlinear Riccati equation which determines the time-evolution of the wave packet width. The solutions of this Riccati equation depend on the physical system under consideration and on the (complex) initial conditions and have close formal similarities with general superpotentials leading to isospectral potentials in supersymmetric quantum mechanics. The definition of the generalized creation and annihilation operator is also in agreement with a factorization of the operator corresponding to the Ermakov invariant that exists in all cases considered.

math-ph↗

arXiv2012

Universal Critical Behavior in the Dicke Model

The critical value of the atom-field coupling strength for a finite number of atoms is deter- mined by means of both, semiclassical and exact solutions. In the semiclassical approach we use a variational procedure with coherent and symmetry-adapted states, while for the exact quantum solution the concept of fidelity is employed. These procedures allow for the determination of the phase transitions in the model, and coincide in the thermodynamic limit. For the three cases men- tioned above, universal parametric curves are obtained for the expectation values of both the first quadrature of the electromagnetic field, and the atomic relative population, as implicit functions of the atom-field coupling parameter, valid for the ground- and first-excited states.

quant-ph↗

arXiv1995

Double beta decay to excited states in Nd150

The pseudo SU(3) model is used to study the double beta decay of Nd150 to the ground and excited states of Sm150 . Low lying collective excitations of Sm150 and its BE(2) intensities are well reproduced. Expressions for the two neutrino double beta decay to excited states are developed and used to describe the decay of Nd150 . The existence of selection rules which strongly restrict the decay is discussed.

nucl-th↗

arXiv1994

Pseudo SU(3) Model and Abnormal Parity States

The most important features of the pseudo SU(3) model are reviewed. This description of heavy deformed nuclei is based on pseudo spin symmetry, and is able to correctly predict the collective spectra and their transition amplitudes, using appropriate effective charges. It also gives a very good description of the exotic double beta decay, a hard test of any nuclear model. The simplest pseudo SU(3) assumptions describe nucleons in the abnormal parity states as having seniority zero. This idea is very useful as a mathematical simplification, and is also able to give a nice description of the backbending phenomena, but has been challenged in a recent study about effective charges and $BE2(0^+_1 \rightarrow 2^+_1)$ systematics. We carefully checked this statement and conclude that the seniority zero approach is a formal way of assign abnormal parity nucleons a passive role. The contribution of the abnormal parity nucleons to the nuclear quadrupole moments is finite but only a fraction of their asymptotic Nilsson values.

nucl-th↗