(no subject)
In a highly, unstable chaotic system, it is not generally possible to construct a minimum uncertainty wave packet that produces large early recurrences. This is true even if one places the wave packet on the shortest periodic orbit of the system. By extending the wave packet to cover the full length of the orbit, early recurrences are naturally larger from a reduced energy uncertainty argument. Even taking this into account, there can be surprisingly large recurrences for some mean momentum values of the wave packet when applied to the stadium billiard. We have adapted the semiclassical theory based on homoclinic orbits (S. Tomsovic and E. J. Heller, Phys Rev E 47, 282 (1993).) for these new states to quantitatively predict their observed behavior. We investigate the role of phase space structures, such as broken separatrices and flux-crossing turnstiles, on the interference patterns generated by the homoclinic orbits
We study the quantum spectral properties of two-parameter family of classical billiards introduced by Dullin, Richter, and Wittek (H. R. Dullin, P. H. Richter, A. Wittek, Chaos 6), 43 (1996). The parameters can be varied such that paths in the shape space take the billiard smoothly from an integrable system through a mixed phase space system to a completely ergodic system. We explore the behavior of the energy difference spectra in several different regions of energy and show how the semiclassical results, expected to hold at sufficiently high energy, are altered as one moves down to the lower-lying energy levels.
The illusion of transparency -- 'space appears as luminous, as intelligible, as giving action free rein'.( people think that they are 'free to do' - unaffected by their environment.
The realist illusion --' the belief that 'things' have more of an existence than the 'subject,' (people think that 'things' mean something- when really it is only society that gives meaning to things)
We study the quantum spectral properties of two-parameter family of classical billiards introduced by Dullin, Richter, and Wittek (H. R. Dullin, P. H. Richter, A. Wittek, Chaos 6), 43 (1996). The parameters can be varied such that paths in the shape space take the billiard smoothly from an integrable system through a mixed phase space system to a completely ergodic system. We explore the behavior of the energy difference spectra in several different regions of energy and show how the semiclassical results, expected to hold at sufficiently high energy, are altered as one moves down to the lower-lying energy levels.
The illusion of transparency -- 'space appears as luminous, as intelligible, as giving action free rein'.( people think that they are 'free to do' - unaffected by their environment.
The realist illusion --' the belief that 'things' have more of an existence than the 'subject,' (people think that 'things' mean something- when really it is only society that gives meaning to things)