Moments of the Wigner delay times

The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be well described by random matrix theory. Here we present a semiclassical derivation showing the validity of random matrix results. In order to simplify the semiclassical treatment, we express the moments of the delay times in terms of correlation functions of scattering matrices at different energies. In the semiclassical approximation, the elements of the scattering matrix are given in terms of the classical scattering trajectories, requiring one to study correlations between sets of such trajectories. We describe the structure of correlated sets of trajectories and formulate the rules for their evaluation to the leading order in inverse channel number. This allows us to derive a polynomial equation satisfied by the generating function of the moments. Along with showing the agreement of our semiclassical results with the moments predicted by random matrix theory, we infer that the scattering matrix is unitary to all orders in the semiclassical approximation.Comment: Refereed version. 18 pages, 5 figure

Delay Times and Rates for Type Ia Supernovae and Thermonuclear Explosions from Double-detonation Sub-Chandrasekhar Mass Models

We present theoretical delay times and rates of thermonuclear explosions that are thought to produce Type Ia supernovae, including the double-detonation sub-Chandrasekhar mass model, using the population synthesis binary evolution code StarTrack. If detonations of sub-Chandrasekhar mass carbon-oxygen white dwarfs following a detonation in an accumulated layer of helium on the white dwarf's surface ("double-detonation" models) are able to produce thermonuclear explosions which are characteristically similar to those of SNe Ia, then these sub-Chandrasekhar mass explosions may account for at least some substantial fraction of the observed SN Ia rate. Regardless of whether all double-detonations look like 'normal' SNe Ia, in any case the explosions are expected to be bright and thus potentially detectable. Additionally, we find that the delay time distribution of double-detonation sub-Chandrasekhar mass SNe Ia can be divided into two distinct formation channels: the 'prompt' helium-star channel with delay times <500 Myr (~10% of all sub-Chandras), and the 'delayed' double white dwarf channel, with delay times >800 Myr spanning up to a Hubble time (~90%). These findings coincide with recent observationally-derived delay time distributions which have revealed that a large number of SNe Ia are prompt with delay times <500 Myr, while a significant fraction also have delay times spanning ~1 Gyr to a Hubble time.Comment: MNRAS Accepted: 13 pages, shortened text, now 3 figure

Spontaneous ignition characteristics of gaseous hydrocarbon-air mixtures

Experiments are conducted to determine the spontaneous ignition delay times of gaseous propane, kerosine vapor, and n-heptane vapor in mixtures with air, and oxygen-enriched air, at atmospheric pressure. Over a range of equivalence ratios from 0.2 to 0.8 it is found that ignition delay times are sensibly independent of fuel concentration. However, the results indicate a strong dependence of delay times on oxygen concentration. The experimental data for kerosine and propane demonstrate very close agreement with the results obtained previously by Mullins and Lezberg respectively

Synchronization of Chaotic Oscillators due to Common Delay Time Modulation

We have found a synchronization behavior between two identical chaotic systems^M when their delay times are modulated by a common irregular signal. ^M This phenomenon is demonstrated both in two identical chaotic maps whose delay times are driven by a common^M chaotic or random signal and in two identical chaotic oscillators whose delay times are driven by^M a signal of another chaotic oscillator. We analyze the phenomenon by using^M the Lyapunov exponents and discuss it in relation with generalized synchronization.^MComment: 5 pages, 4 figures (to be published in PRE

Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations

We reveal a general explicit relation between the statistics of delay times in one-channel reflection from a mesoscopic sample of any spatial dimension and the statistics of the eigenfunction intensities in its closed counterpart. This opens a possibility to use experimentally measurable delay times as a sensitive probe of eigenfunction fluctuations. For the particular case of quasi-one dimensional geometry of the sample we use an alternative technique to derive the probability density of partial delay times for any number of open channels.Comment: 12 pages; published version with updated reference