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arXiv:physics/9803041

Semiclassical spin damping: Superradiance revisited

Petr A. Braun, Daniel Braun, Fritz Haake, Jan David Weber

Published Mar 27, 1998• 0 citations
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Abstract

A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a semiclassical evaluation. The clue is a saddle-point approximation for an inverse Laplace transform. All previous approximate treatments, disparate as they may appear, are encompassed in our systematic formulation. A byproduct is a hitherto unknown rigorous relation between coherences and probabilities. Our results allow for generalizations to spin dynamics with chaos in the classical limit.

DOI
10.48550/arxiv.physics/9803041

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A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a semiclassical evaluation. The clue is a saddle-point approximation for an inverse Laplace transform. All previous approximate treatments, disparate as they may appear, are encompassed in our systematic formulation. A byproduct is a hitherto unknown rigorous relation between coherences and probabilities. Our results allow for generalizations to spin dynamics with chaos in the classical limit.
\n \nA well known description of superradiance from pointlike collections of many\natoms involves the dissipative motion of a large spin. The pertinent\n"superradiance master equation" allows for a formally exact solution which\nwe subject to a semiclassical evaluation. The clue is a saddle-point\napproximation for an inverse Laplace transform. All previous approximate\ntreatments, disparate as they may appear, are encompassed in our systematic\nformulation. A byproduct is a hitherto unknown rigorous relation between\ncoherences and probabilities. Our results allow for generalizations to spin\ndynamics with chaos in the classical limit. \n\n\n\n
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A semiclassical approximation to the time evolution of coherent states may be derived from a saddle point approximation to the exact quantum propagator, and in general it involves complex classical dynamics. We generalize previous one-dimensional results to ddd dimensions, and for the case d=2d=2d=2 we present several applications. We also consider other simple approximations that depend only on real classical trajectories, but are not initial value representations. These approximations are able to reproduce interference and tunneling effects and involve propagating a few classical initial conditions compatible with the quantum uncertainties.