The Higher Orders of the Theory of Strong Perturbations in Quantum Mechanics and the Secularity Problem

We solve the higher order equations of the theory of the strong perturbations in quantum mechanics given in M. Frasca, Phys. Rev. A 45, 43 (1992), by assuming that, at the leading order, the wave function goes adiabatically. This is accomplished by deriving the unitary operator of adiabatic evolution for the leading order. In this way it is possible to show that at least one of the causes of the problem of phase-mixing, whose effect is the polynomial increase in time of the perturbation terms normally called secularities, arises from the shifts of the perturbation energy levels due to the unperturbed part of the hamiltonian. An example is given for a two-level system that, anyway, shows a secularity at second order also in the standard theory of small perturbations. The theory is applied to the quantum analog of a classical problem that can become chaotic, a particle under the effect of two waves of different amplitudes, frequencies and wave numbers.Comment: 13 pages, Late

Duality in Perturbation Theory and the Quantum Adiabatic Approximation

Duality is considered for the perturbation theory by deriving, given a series solution in a small parameter, its dual series with the development parameter being the inverse of the other. A dual symmetry in perturbation theory is identified. It is then shown that the dual to the Dyson series in quantum mechanics is given by a recent devised series having the adiabatic approximation as leading order. A simple application of this result is given by rederiving a theorem for strongly perturbed quantum systems.Comment: 9 pages, revtex. Improved english and presentation. Final version accepted for publication by Physical Review

Theory of dressed states in quantum optics

The dual Dyson series [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both Dyson series and its dual, through renormalization group methods to remove secular terms from the perturbation series, give the opportunity of a full study of the solution of the Schr\"{o}dinger equation in different ranges of the parameters of the given hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to exploit the method at the best, a study is accomplished of the well-known Jaynes-Cummings model in the rotating wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is needed to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.Comment: Revtex, 17 page

Accretion, disks, and magnetic activity in the TW Hya association

We present new photometric and spectroscopic data for the M-type members of the TW Hya association with the aim of a comprehensive study of accretion, disks and magnetic activity at the critical age of ~10 Myr where circumstellar matter disappears.Comment: 4 pages, to appear in Proceedings IAU Symposium No. 314, Young Stars & Planets Near the Sun, 201

Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.Comment: 7 pages, no figures. Added proof of existence of a zero mode and two more references. Accepted for publication in Journal of Nonlinear Mathematical Physic

Contemporaneous broad-band photometry and Hα\alpha observations of T Tauri stars

The study of contemporaneous variations of the continuum flux and emission lines is of great importance to understand the different astrophysical processes at work in T Tauri stars. In this paper we present the results of a simultaneous $BVRI$ and H$\alpha$ photometric monitoring, contemporaneous to medium-resolution spectroscopy of six T Tauri stars in the Taurus-Auriga star forming region. We have characterized the H$\alpha$ photometric system using synthetic templates and the contemporaneous spectra of the targets. We show that we can achieve a precision corresponding to 2$-$3 \AA\ in the H$\alpha$ equivalent width, in typical observing conditions. The spectral analysis has allowed us to determine the basic stellar parameters and the values of quantities related to the accretion. In particular, we have measured a significant veiling only for the three targets with the strongest H$\alpha$ emission (T Tau, FM Tau, and DG Tau). The broad-band photometric variations are found to be in the range 0.05$-$0.70 mag and are often paired to variations in the H$\alpha$ intensity, which becomes stronger when the stellar continuum is weaker. In addition, we have mostly observed a redder $V-I$ and a bluer $B-V$ color as the stars become fainter. For most of the targets, the timescales of these variations seem to be longer than the rotation period. One exception is T Tau, for which the broad-band photometry varies with the rotation period. The most plausible interpretation of these photometric and H$\alpha$ variations is that they are due to non-stationary mass accretion onto the stars, but rotational modulation can play a major role in some cases.Comment: 21 pages, 11 figures, accepted for publication in Acta Astronomic

Dynamical decoherence in a cavity with a large number of two-level atoms

We consider a large number of two-level atoms interacting with the mode of a cavity in the rotating-wave approximation (Tavis-Cummings model). We apply the Holstein-Primakoff transformation to study the model in the limit of the number of two-level atoms, all in their ground state, becoming very large. The unitary evolution that we obtain in this approximation is applied to a macroscopic superposition state showing that, when the coherent states forming the superposition are enough distant, then the state collapses on a single coherent state describing a classical radiation mode. This appear as a true dynamical effect that could be observed in experiments with cavities.Comment: 9 pages, no figures. This submission substitutes paper quant-ph/0212148 that was withdrawn. Version accepted for publication in Journal of Physics B: Atomic, Molecular & Optical Physic