|
| related topics |
| {classical, space, random} |
| {time, wave, function} |
| {equation, function, exp} |
| {time, decoherence, evolution} |
| {state, phys, rev} |
| {state, algorithm, problem} |
|
Semiclassical evaluation of quantum fidelity
Jiri Vanicek, Eric J. Heller
abstract: We present a numerically feasible semiclassical (SC) method to evaluate
quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It
was thought that such evaluation would be intractable, but instead we show that
a uniform SC expression not only is tractable but it gives remarkably accurate
numerical results for the standard map in both the Fermi-golden-rule and
Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform
expression is accurate at times when there are 10^70 semiclassical
contributions. Remarkably, it also explicitly contains the ``building blocks''
of analytical theories of recent literature, and thus permits a direct test of
the approximations made by other authors in these regimes, rather than an a
posteriori comparison with numerical results. We explain in more detail the
extended validity of the classical perturbation approximation (CPA) and show
that within this approximation, the so-called ``diagonal approximation'' is
automatic and does not require ensemble averaging.
- oai_identifier:
- oai:arXiv.org:quant-ph/0302192
- categories:
- quant-ph nlin.CD
- comments:
- Added references, small textual improvements
- doi:
- 10.1103/PhysRevE.68.056208
- arxiv_id:
- quant-ph/0302192
- journal_ref:
- Phys. Rev. E 68, 056208 (2003).
- created:
- 2003-02-26
- updated:
- 2003-09-17
Full article ▸
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