2,648 research outputs found
Cooperative quantum electrodynamical processes in an ellipsoidal cavity
We investigate spontaneous photon emission and absorption processes of two
two-level atoms trapped close to the focal points of an ellipsoidal cavity,
thereby taking into account the full multimode scenario. In particular, we
calculate the excitation probabilities of the atoms by describing the field
modes semiclassically. Based on this approach, we express the excitation
probabilities by a semiclassical photon path representation. Due to the special
property of an ellipsoidal cavity of having two focal points, we are able to
study interesting intermediate instances between well-known quantum-optical
scenarios. Furthermore, the semiclassical photon path representation enables us
to address the corresponding retardation effects and causality questions in a
straightforward manner.Comment: 14 pages, 3 figures, Optics and its Application
Uniform Approximation from Symbol Calculus on a Spherical Phase Space
We use symbol correspondence and quantum normal form theory to develop a more
general method for finding uniform asymptotic approximations. We then apply
this method to derive a result we announced in an earlier paper, namely, the
uniform approximation of the -symbol in terms of the rotation matrices. The
derivation is based on the Stratonovich-Weyl symbol correspondence between
matrix operators and functions on a spherical phase space. The resulting
approximation depends on a canonical, or area preserving, map between two pairs
of intersecting level sets on the spherical phase space.Comment: 18 pages, 5 figure
Quantum Theory of Reactive Scattering in Phase Space
We review recent results on quantum reactive scattering from a phase space
perspective. The approach uses classical and quantum versions of normal form
theory and the perspective of dynamical systems theory. Over the past ten years
the classical normal form theory has provided a method for realizing the phase
space structures that are responsible for determining reactions in high
dimensional Hamiltonian systems. This has led to the understanding that a new
(to reaction dynamics) type of phase space structure, a {\em normally
hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the phase
space structures governing reaction dynamics are built. The quantum normal form
theory provides a method for quantizing these phase space structures through
the use of the Weyl quantization procedure. We show that this approach provides
a solution of the time-independent Schr\"odinger equation leading to a (local)
S-matrix in a neighborhood of the saddle point governing the reaction. It
follows easily that the quantization of the directional flux through the
dividing surface with the properties noted above is a flux operator that can be
expressed in a "closed form". Moreover, from the local S-matrix we easily
obtain an expression for the cumulative reactio probability (CRP).
Significantly, the expression for the CRP can be evaluated without the need to
compute classical trajectories. The quantization of the NHIM is shown to lead
to the activated complex, and the lifetimes of quantum states initialized on
the NHIM correspond to the Gamov-Siegert resonances. We apply these results to
the collinear nitrogen exchange reaction and a three degree-of-freedom system
corresponding to an Eckart barrier coupled to two Morse oscillators.Comment: 59 pages, 13 figure
Felix Alexandrovich Berezin and his work
This is a survey of Berezin's work focused on three topics: representation
theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page
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