Trace formula for systems with spin from the coherent state propagator

We present a detailed derivation of the trace formula for a general Hamiltonian with two degrees of freedom where one of them is canonical and the other a spin. Our derivation starts from the semiclassical formula for the propagator in a basis formed by the product of a canonical and a spin coherent...

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Bibliographic Details
Published in:Journal of mathematical physics 2007-11, Vol.48 (11), p.112103-112103-17
Main Authors: Ribeiro, A. D., de Aguiar, M. A. M., de Toledo Piza, A. F. R.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
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Summary:We present a detailed derivation of the trace formula for a general Hamiltonian with two degrees of freedom where one of them is canonical and the other a spin. Our derivation starts from the semiclassical formula for the propagator in a basis formed by the product of a canonical and a spin coherent states and is valid in the limit ℏ → 0 , j → ∞ with j ℏ constant. The trace formula, obtained by taking the trace and the Fourier transform of the coherent state propagator, is compared to others found in the literature.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2806487