Delay time and tunneling transient phenomena

Analytic solutions to the time-dependent Schr\"odinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential barrier opacity $\alpha$, we find that the probability density exhibits two evolving structures. One refers to the propagation of a {\it forerunner} related to a {\it time domain resonance} [Phys. Rev. A {\bf 64}, 0121907 (2001)], while the other consists of a semiclassical propagating wavefront. We find a regime where the {\it forerunners} are absent, corresponding to positive {\it time delays}, and show that this regime is characterized by opacities $\alpha < \alpha_c$. The critical opacity $\alpha_c$ is derived from the analytical expression for the {\it delay time}, that reflects a link between transient effects in tunneling and the {\it delay time}Comment: To be published in Physical Review

A Comparison of Sensitivity Metrics for Two-Stage Ignition Behavior in Rapid Compression Machines

A rapid compression machine (RCM) multi-zone model is used to simulate the ignition of primary reference fuel (PRF) mixtures that exhibit two-stage ignition behavior. Sensitivity coefficients for each reaction in the PRF mechanism are calculated from four different metrics: (1) first-stage energy release, (2) first-stage pressure rise, (3) first-stage ignition delay time, and (4) total ignition delay time. The sensitivity coefficients are used to provide four unique rankings, and the rankings are compared using Spearman’s rank correlation coefficient. Special emphasis is given to comparing the rankings based on first-stage energy release and total ignition delay time. The level of agreement between these two rankings is shown to depend on the reaction conditions. Simulation cases with high peak heat release rates during the first stage of ignition tend to exhibit disagreement in the rankings, indicating that new kinetic information can be obtained by studying first stage energy release in addition to total ignition delay time. Simulations show that the high peak heat release rates are associated with energy release across a broad range of temperatures (range can be in excess of 100 K even for lean conditions). This distribution leads to a discrepancy between sensitivity coefficients calculated for the total ignition delay time and the first-stage energy release. Sensitivity coefficients for the total ignition delay time are characterized by reactivity at the highest temperatures in the RCM, while sensitivity coefficients for the first-stage energy release are characterized by reactivity across the full range of temperatures in the RCM

Phase delay time and superluminal propagation in barrier tunneling

In this work we study the behaviour of Wigner phase delay time for tunneling in the reflection mode. Our system consists of a circular loop connected to a single wire of semi-infinite length in the presence of Aharonov-Bohm flux. We calculate the analytical expression for the saturated delay time. This saturated delay time is independent of Aharonov- Bohm flux and the width of the opaque barrier thereby generalizing the Hartman effect. This effect implies superluminal group velocities as a consequence. We also briefly discuss the concept called "space collapse or space destroyer".Comment: 5 pages, 5 figure

Characteristics of a Delayed System with Time-dependent Delay Time

The characteristics of a time-delayed system with time-dependent delay time is investigated. We demonstrate the nonlinearity characteristics of the time-delayed system are significantly changed depending on the properties of time-dependent delay time and especially that the reconstructed phase trajectory of the system is not collapsed into simple manifold, differently from the delayed system with fixed delay time. We discuss the possibility of a phase space reconstruction and its applications.Comment: 4 pages, 6 figures (to be published in Phys. Rev. E

Distribution of Wigner delay time from single channel disordered systems

We consider the scattering of an electron from a semi-infinite one-dimensional random medium. The random medium is characterized by force, -\d V/\d L being the basic random variable. We obtain an analytical expression for the stationary delay time ($\tau$) distribution $P_s(\tau)$ within a random phase approximation. Our result agrees with earlier analytical expressions, where the random potential is taken to be of different kind, indicating universality of the delay time distribution, i.e., delay time distribution is independent of the nature of disorder.Comment: 8 pages RevTeX, no figure

Direct tunneling delay time measurement in an optical lattice

We report on the measurement of the time required for a wave packet to tunnel through the potential barriers of an optical lattice. The experiment is carried out by loading adiabatically a Bose-Einstein condensate into a 1D optical lattice. A sudden displacement of the lattice by a few tens of nm excites the micromotion of the dipole mode. We then directly observe in momentum space the splitting of the wave packet at the turning points and measure the delay between the reflected and the tunneled packets for various initial displacements. Using this atomic beam splitter twice, we realize a chain of coherent micron-size Mach-Zehnder interferometers at the exit of which we get essentially a wave packet with a negative momentum, a result opposite to the prediction of classical physics

Statistics of Dynamics of Localized Waves

The measured distribution of the single-channel delay time of localized microwave radiation and its correlation with intensity differ sharply from the behavior of diffusive waves. The delay time is found to increase with intensity, while its variance is inversely proportional to the fourth root of the intensity. The distribution of the delay time weighted by the intensity is found to be a double-sided stretched exponential to the 1/3 power centered at zero. The correlation between dwell time and intensity provides a dynamical test of photon localization.Comment: submitted to PRL; 4 pages including 6 figure

The Delay Time of Gravitational Wave — Gamma-Ray Burst Associations

The first gravitational wave (GW) — gamma-ray burst (GRB) association, GW170817/GRB 170817A, had an offset in time, with the GRB trigger time delayed by ∼1.7 s with respect to the merger time of the GW signal. We generally discuss the astrophysical origin of the delay time, Δt, of GW-GRB associations within the context of compact binary coalescence (CBC) — short GRB (sGRB) associations and GW burst — long GRB (lGRB) associations. In general, the delay time should include three terms, the time to launch a clean (relativistic) jet, Δtjet; the time for the jet to break out from the surrounding medium, Δtbo; and the time for the jet to reach the energy dissipation and GRB emission site, ΔtGRB. For CBC-sGRB associations, Δtjet and Δtbo are correlated, and the final delay can be from 10 ms to a few seconds. For GWB-lGRB associations, Δtjet and Δtbo are independent. The latter is at least ∼10 s, so that Δt of these associations is at least this long. For certain jet launching mechanisms of lGRBs, Δt can be minutes or even hours long due to the extended engine waiting time to launch a jet. We discuss the cases of GW170817/GRB 170817A and GW150914/GW150914-GBM within this theoretical framework and suggest that the delay times of future GW/GRB associations will shed light into the jet launching mechanisms of GRBs