arXiv subjects

G. Flores-Hidalgo

Publications and source records attributed to G. Flores-Hidalgo.

27 records · Page 2Linked to original sources

arXiv2005

Sum rules in the oscillator radiation processes

We consider the problem of an harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution.

physics.atom-ph↗

arXiv2005

Dressed-state approach to a simple radiating atom

We consider a system consisting of an atom in the dipole approximation, coupled to the electromagnetic field. Using recently introduced renormalized coordinates and dressed states, we give a non-perturbative solution to the atom radiation process. From this formalism a non-exponential decay law naturally emerges. However, at least for low frequencies and weak coupling, there is only a very small, practically non-detectable, deviation from a purely exponential decay, in agreement with all previous results in the literature.

physics.atom-ph↗

arXiv2004

Anharmonic oscillator radiation process in a large cavity

We consider a particle represented by an anharmonic oscillator, coupled to an environment (a field) modeled by an ensemble of anharmonic oscillators, the whole system being confined in a cavity of diameter $L$. Up to the first perturbative order in the quartic interaction (interaction parameter $λ$), we use the formalism of {\it dressed} states introduced in previous publications, to obtain for a large cavity explicit $λ$-dependent formulas for the particle radiation process. These formulas are obtained in terms of the corresponding exact expressions for the linear case. We conclude for the enhancement of the particle decay induced by the quartic interaction.

physics.class-ph↗

arXiv2003

Nonequilibrium Dynamics of Coupled Quantum Systems

The nonequilibrium dynamics of coupled quantum oscillators subject to different time dependent quenches are analyzed in the context of the Liouville-von Neumann approach. We consider models of quantum oscillators in interaction that are exactly soluble in the cases of both sudden and smooth quenches. The time evolution of number densities and the final equilibration distribution for the problem of a quantum oscillator coupled to an infinity set of other oscillators (a bath) are explicitly worked out.

hep-th↗

arXiv2003

Time evolution of quantum systems in microcavities and in free space -- a non-perturbative approach

We consider a system consisting of a particle in the harmonic approximation, having frequency $\barω$, coupled to a scalar field inside a spherical reflecting cavity of diameter $L$. By introducing {\it dressed} coordinates we define {\it dressed} states which allow a non-perturbative unified description of the radiation process, for weak and strong coupling regimes. We perform a study of the energy distribution in a small cavity, with the initial condition that the particle is in the first excited state. In the {\it weak} coupling regime, we conclude for the quasi-stability of the excited particle. For instance, for a frequency $\barω$ of the order $\barω\sim 4.00\times 10^{14}/s$ (in the visible red), starting from the initial condition that the particle is in the first excited level, we find that for a cavity with diameter $L\sim 1.0\times 10^{-6}m$, the probability that the particle be at any time still in the first excited level, will be of the order of 97%. For appropriate cavity dimensions, which are of the same order of those ensuring stability for weak coupling, we ensure for strong coupling the complete decay of the particle to the ground state in a small ellapsed time. Also we consider briefly the effects of a quartic interaction up to first order in the interaction parameter $λ$. We obtain for a large cavity an explicit $λ$-dependent expression for the particle radiation process. This formula is obtained in terms of the corresponding exact expression for the linear case and we conclude for the enhancement of the particle decay induced by the quartic interaction.

hep-th↗

arXiv2002

Reply to "Comment on One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models" (hep-th/0211149)

I agree with the authors of hep-th/0211149 that the claim made in Phys.Lett. B542, 282 (2002) is incorrect and that the derivation of its main formula, although correct, contains two compensating errors. In this reply the main formula of Phys.Lett. B542, 282 (2002) is rederived. This new derivation shows that not only the energy momentum cut off regularization method still works in the calculation of the soliton quantum mass corrections, but also that the so called mode number regularization emerges naturally from it.

hep-th↗

arXiv2002

One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models

The bare one loop soliton quantum mass corrections can be expressed in two ways: as a sum over the zero-point energies of small oscillations around the classical configuration, or equivalently as the (Euclidean) effective action per unit time. In order to regularize the bare one loop quantum corrections (expressed as the sum over the zero-point energies) we subtract and add from it the tadpole graph that appear in the expansion of the effective action per unit time. The subtraction renders the one loop quantum corrections finite. Next, we use the renormalization prescription that the added tadpole graph cancels with adequate counterterms, obtaining in this way a finite unambiguous expression for the one loop soliton quantum mass corrections. When we apply the method to the solitons of the sine-Gordon and phi^4 kink models we obtain results that agree with known results. Finally we apply the method to compute the soliton quantum mass corrections in the recently introduced phi^2 cos^2 ln(phi^2) model.

hep-th↗

arXiv2002

Stability of excited atoms in small cavities

We consider a system consisting of an atom in the approximation of a harmonic oscillator of frequency $\barω$, coupled to the scalar potential inside a spherical reflecting cavity of radius R. We use {\it dressed} states introduced in a previous publication [Andion, Malbouisson and Matos Neto, J. Phys. A34, 3735 (2001)], which allow a non-perturbative unified description of the atom radiation process, in both cases, of a finite or an arbitrarily large cavity. We perform a study of the energy distribution in a small cavity, with the initial condition that the atom is in the first excited state and we conclude for the quasi-stability of the excited atom. For instance, for a frequency $\barω$ of the order $\barω\sim 4.00\times 10^{14}/s$ (in the visible red), starting from the initial condition that the atom is in the first excited level, we find that for a cavity with diameter $2R\sim 1.0\times 10^{-6}m$, the probability that the atom be at any time still in the first excited level, will be of the order of 97%. For a typical microwave frequency $\barω\sim 2,00\times 10^{10}/s$ we find stability in the first excited state also of the order of 97% for a cavity radius $R\sim 1.4\times 10^{-2}m$.

physics.atom-ph↗

arXiv2002

Dressed States Approach to Quantum Systems

Using the non-perturbative method of {\it dressed} states previously introduced in JPhysA, we study effects of the environment on a quantum mechanical system, in the case the environment is modeled by an ensemble of non interacting harmonic oscillators. This method allows to separate the whole system into the {\it dressed} mechanical system and the {\it dressed} environment, in terms of which an exact, non-perturbative approach is possible. When applied to the Brownian motion, we give explicit non-perturbative formulas for the classical path of the particle in the weak and strong coupling regimes. When applied to study atomic behaviours in cavities, the method accounts very precisely for experimentally observed inhibition of atomic decay in small cavities PhysLA, physics0111042.

quant-ph↗