Eigenstate structures around a hyperbolic point

Details Eigenstate structures around a hyperbolic point Eigenstate structures around a hyperbolic point

1996-09-05

arxiv.org/abs/chao-dyn/9609002v1

J. Phys. A: Math. Gen 30, 295-315 (1997)

Nonlinear Sciences

Chaotic Dynamics

27 pages, 6 Encapsulated Postscript figures

Scientific paper

10.1088/0305-4470/30/1/021

Using coherent-state representations of quantum mechanics (Bargmann, Husimi, and stellar representations), we describe analytically the phase-space structure of the general eigenstates corresponding to a 1-dimensional bilinear hyperbolic Hamiltonian, H=pq or equivalently H=1/2(P^2-Q^2). Their semi-classical behaviour is discussed for eigenvalues either near or away from the separatrix energy {H=0}, especially in the phase-space vicinity of the saddle-point (q,p)=(0,0).

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