3,342 research outputs found
Rabi oscillations and macroscopic quantum superposition states
A two-level atom interacting with a single radiation mode is considered,
without the rotating-wave approximation, in the strong coupling regime. It is
shown that, in agreement with the recent results on Rabi oscillations in a
Josephson junction (Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, Phys. Rev.
Lett. {\bf 87}, 246601 (2001)), the Rabi frequency is indeed proportional to
first kind integer order Bessel functions in the limit of a large number of
photons and the dressed states are macroscopic quantum superposition states. To
approach this problem analytically use is made of the dual Dyson series and the
rotating-wave approximation.Comment: 7 pages, revtex, no figures. I have to thank Kazuyuki Fujii for
pointing me out some corrections to introduce into the paper. Besides, the
title and the nomenclature has been changed in agreement to editorial
requirements. Finally, the correct citation for the paper by Nakamura et al.
has been introduce
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
On the mean square error of randomized averaging algorithms
This paper regards randomized discrete-time consensus systems that preserve
the average "on average". As a main result, we provide an upper bound on the
mean square deviation of the consensus value from the initial average. Then, we
apply our result to systems where few or weakly correlated interactions take
place: these assumptions cover several algorithms proposed in the literature.
For such systems we show that, when the network size grows, the deviation tends
to zero, and the speed of this decay is not slower than the inverse of the
size. Our results are based on a new approach, which is unrelated to the
convergence properties of the system.Comment: 11 pages. to appear as a journal publicatio
Localization in a strongly disordered system: A perturbation approach
We prove that a strongly disordered two-dimensional system localizes with a
localization length given analytically. We get a scaling law with a critical
exponent is in agreement with the Chayes criterion . The case
we are considering is for off-diagonal disorder. The method we use is a
perturbation approach holding in the limit of an infinitely large perturbation
as recently devised and the Anderson model is considered with a Gaussian
distribution of disorder. The localization length diverges when energy goes to
zero with a scaling law in agreement to numerical and theoretical expectations.Comment: 5 pages, no figures. Version accepted for publication on
International Journal of Modern Physics
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
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
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