Semiclassical energy transition of driven chaotic systems: phase
coherence on scar disks
- URL: http://arxiv.org/abs/2203.10668v2
- Date: Sat, 13 Aug 2022 17:54:51 GMT
- Title: Semiclassical energy transition of driven chaotic systems: phase
coherence on scar disks
- Authors: Alfredo M. Ozorio de Almeida
- Abstract summary: A trajectory segment in an energy shell combines to form a closed curve with a segment in another canonically driven energy shell.
The exact representation of the transition density as an integral over spectral Wigner functions is here generalized to arbitrary unitary transformations.
The actions of the compound orbits depend on the driving time, or on any other parameter of the transformation of the original eigenstates.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A trajectory segment in an energy shell, which combines to form a closed
curve with a segment in another canonically driven energy shell, adds an
oscillatory semiclassical contribution to the smooth classical background of
the quantum probability density for a transition between their energies. If
either segment is part of a Bohr-quantized periodic orbit of either shell, the
centre of its endpoints lies on a scar disk of the spectral Wigner function for
single static energy shell and the contribution to the transition is reinforced
by phase coherence. The exact representation of the transition density as an
integral over spectral Wigner functions, which was previously derived for the
special case where the system undergoes a reflection in phase space, is here
generalized to arbitrary unitary transformations. If these are generated
continuously by a driving Hamiltonian, there will be a finite lapse in the
driving time for the transition to start, until the initially nested shells
touch each other and then start to overlap.
The stationary phase evaluation of the multidimensional integral for the
transition density selects the pair of matching trajectory segments on each
shell, which close to form a piecewise smooth compound orbit. Each compound
orbit shows up as a fixed point of a product of mappings that generalize
Poincar\'e maps on the intersection of the shells. Thus, the closed compound
orbits are isolated if the original Hamiltonian is chaotic. The actions of the
compound orbits depend on the driving time, or on any other parameter of the
transformation of the original eigenstates.
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