39,809 research outputs found
Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator
Recent experiments on quantum behavior in microfabricated solid-state systems
suggest tantalizing connections to quantum optics. Several of these experiments
address the prototypical problem of cavity quantum electrodynamics: a two-level
system coupled to a quantum harmonic oscillator. Such devices may allow the
exploration of parameter regimes outside the near-resonance and weak-coupling
assumptions of the ubiquitous rotating-wave approximation (RWA), necessitating
other theoretical approaches. One such approach is an adiabatic approximation
in the limit that the oscillator frequency is much larger than the
characteristic frequency of the two-level system. A derivation of the
approximation is presented and the time evolution of the two-level-system
occupation probability is calculated using both thermal- and coherent-state
initial conditions for the oscillator. Closed-form evaluation of the time
evolution in the weak-coupling limit provides insight into the differences
between the thermal- and coherent-state models. Finally, potential experimental
observations in solid-state systems, particularly the Cooper-pair
box--nanomechanical resonator system, are discussed and found to be promising.Comment: 16 pages, 11 figures; revised abstract; some text revisions; added
two figures and combined others; added references. Submitted to Phys. Rev.
A Morse index theorem for elliptic operators on bounded domains
Given a selfadjoint, elliptic operator , one would like to know how the
spectrum changes as the spatial domain is
deformed. For a family of domains we prove that the
Morse index of on differs from the Morse index of on
by the Maslov index of a path of Lagrangian subspaces on the
boundary of . This is particularly useful when is a domain
for which the Morse index is known, e.g. a region with very small volume. Then
the Maslov index computes the difference of Morse indices for the "original"
problem (on ) and the "simplified" problem (on ). This
generalizes previous multi-dimensional Morse index theorems that were only
available on star-shaped domains or for Dirichlet boundary conditions. We also
discuss how one can compute the Maslov index using crossing forms, and present
some applications to the spectral theory of Dirichlet and Neumann boundary
value problems.Comment: 21 pages; weaker regularity assumptions than in the first versio
Disorder-Induced Shift of Condensation Temperature for Dilute Trapped Bose Gases
We determine the leading shift of the Bose-Einstein condensation temperature
for an ultracold dilute atomic gas in a harmonic trap due to weak disorder by
treating both a Gaussian and a Lorentzian spatial correlation for the quenched
disorder potential. Increasing the correlation length from values much smaller
than the geometric mean of the trap scale and the mean particle distance to
much larger values leads first to an increase of the positive shift to a
maximum at this critical length scale and then to a decrease.Comment: Author information under
http://www.theo-phys.uni-essen.de/tp/ags/pelster_di
Genuine phase diffusion of a Bose-Einstein condensate in the microcanonical ensemble: A classical field study
Within the classical field model, we find that the phase of a Bose-Einstein
condensate undergoes a true diffusive motion in the microcanonical ensemble,
the variance of the condensate phase change between time zero and time
growing linearly in . The phase diffusion coefficient obeys a simple scaling
law in the double thermodynamic and Bogoliubov limit. We construct an
approximate calculation of the diffusion coefficient, in fair agreement with
the numerical results over the considered temperature range, and we extend this
approximate calculation to the quantum field.Comment: 9 pages, 6 figure
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