55 research outputs found
Fokker-Planck equation approach to optical bistability in the bad-cavity limit
In the general framework of the system size expansion of Van Kampen and Kubo, we consider the Fokker-Planck equation for a model of absorptive bistability in the bad-cavity limit. The physical system is described by the reduced atomic density operators after adiabatic elimination of the cavity field variables. Mapping of the master equation into c-number form according to the normal-ordering mapping scheme yields known results for the atomic fluctuations and correlation functions; however, it also leads to a Fokker-Planck equation with a non-positive-definite diffusion matrix. The symmetrical-order-mapping scheme eliminates this difficulty. The leading contribution to the system size expansion yields a Fokker-Planck equation for the symmetrical-ordered density function having a positive-definite diffusion matrix. The atomic expectation values and fluctuations previously derived from the quantum Langevin equations emerge naturally from this Fokker-Planck equation
Quantum analysis of optical bistability and spectrum of fluctuations
We discuss the approach to equilibrium and the fluctuations of a bistable system under dynamical conditions such that the field variables can be eliminated adiabatically. The atomic system evolves under the action of the coherent pumping of an external field and of collective and incoherent relaxation processes. The competition between pumping and relaxation effects causes the atomic steady-state configurations to depend discontinuously on the strength of the driving field. We derive an explicit expression for the spectrum of the forward-scattered light, which exhibits hysteresis and a discontinuous dependence on the driving-field amplitude
Optical bistability: a self-consistent analysis of fluctuations and the spectrum of scattered light
The main purpose of this paper is to study the behavior of the atomic fluctuations and the spectrum of the light transmitted by an absorptive bistable device. To this end we develop an approximation scheme based on the so-called system-size expansion and apply it to the quantum-mechanical Langevin equations for the atomic fluctuation operators. The Bonifacio-Lugiato mean-field equations for bistability are derived from the lowest-order approximation to the system-size expansion, while the atomic correlation functions result from the next-higher-order expansion. The calculated spectrum of the transmitted light exhibits line narrowing near the bistable thresholds, discontinuous formation of sidebands along the high-transmission branch of the device, and hysteresis effects
A Revisit of SO(6) Dynamical Symmetry in Nuclear Structure
According to the analysis based on the fermion dynamical symmetry model,
nuclei previously regarded as SO(6)-like (e.g. Xe and Pt) are
shown to be more akin to the transitional nuclei between SO(7) and SO(6)
symmetries
Varied Signature Splitting Phenomena in Odd Proton Nuclei
Varied signature splitting phenomena in odd proton rare earth nuclei are
investigated. Signature splitting as functions of and in the angular
momentum projection theory is explicitly shown and compared with those of the
particle rotor model. The observed deviations from these rules are due to the
band mixings. The recently measured Ta high spin data are taken as a
typical example where fruitful information about signature effects can be
extracted. Six bands, two of which have not yet been observed, were calculated
and discussed in detail in this paper. The experimentally unknown band head
energies are given
Is Schr\"{o}dinger's Conjecture for the Hydrogen Atom Coherent States Attainable
We construct the most general SO(4,2) hydrogen atom coherent states which are
the counterpart of Schr\"{o}dinger's harmonic oscillator coherent states. We
show that these states cannot be localized and cannot follow the classical
orbits. Thus, Schr\"{o}dinger's conjecture for the hydrogen atom coherent
states is unattainable.Comment: 10 pages, report
Lifetime Measurements in 120Xe
Lifetimes for the lowest three transitions in the nucleus Xe have
been measured using the Recoil Distance Technique. Our data indicate that the
lifetime for the transition is more than a factor of
two lower than the previously adopted value and is in keeping with more recent
measurements performed on this nucleus. The theoretical implications of this
discrepancy and the possible reason for the erroneous earlier results are
discussed. All measured lifetimes in Xe, as well as the systematics of
the lifetimes of the 2 states in Xe isotopes, are compared with
predictions of various models. The available data are best described by the
Fermion Dynamic Symmetry Model (FDSM).Comment: 9 pages, RevTeX, 3 figures with Postscript file available on request
at [email protected], [email protected]. Submitted to Phys.
Rev.
Anomalous Crossing Frequency in Odd Proton Nuclei
A generic explanation for the recently observed anomalous crossing
frequencies in odd proton rare earth nuclei is given. As an example, the proton
band in Ta is discussed in detail by using the
angular momentum projection theory. It is shown that the quadrupole pairing
interaction is decisive in delaying the crossing point and the changes in
crossing frequency along the isotope chain are due to the different neutron
shell fillings
- …