Multidimensional quantum tunneling in the Schwinger effect

We study the Schwinger effect, in which the external field having a spatiotemporal profile creates electron-positron pairs via multidimensional quantum tunneling. Our treatment is based on the trace formula for the QED effective action, whose imaginary part is represented by a sum over complex worldline solutions. The worldlines are multiperiodic, and the periods of motion collectively depend on the strength of spatial and temporal inhomogeneity. We argue that the classical action that leads to the correct tunneling amplitude must take into account both the full period, $\tilde{T}$ and the first fundamental period, $T_1$. In view of this argument we investigate pair production in an exponentially damped sinusoidal field and find that the initial momenta for multiperiodic trajectories lie on parabolic curves, such that on each curve the ratio $\tilde{T}/T_1$ stays uniform. Evaluation of the tunneling amplitude using these trajectories shows that vacuum decay rate is reduced by an order of magnitude, with respect to the purely time-dependent case, due to the presence of magnetic field.Comment: 6 pages, 4 figures. Revised and extende

Hawking Radiation via Complex Geodesics

We describe in detail the quantum tunneling of massive particles from Kerr black hole by using complex trajectories, which are solutions to the Hamilton's equations of motion with imaginary proper time. The trajectories are smooth and cover the inner and outer horizon regions. Following the worldline approach, we compute the energy flux at the event horizon as a summation over these complex trajectories. Density of states is given with the aid of Carter's constant and it is shown to be linear in momenta in the leading order, as long as the phase portrait of the system stays uniform. Under this assumption, we obtain the thermal spectrum $\sim (T^{+}_H)^4$.Comment: 18 pages, 5 figures. Revised and extended. To appear PR

Vacuum decay and the transmission resonances in space-dependent electric fields

We investigate the decay of quantum electrodynamical (QED) vacuum in arbitrary space-dependent electric fields. In particular, we analyze the resonance peaks of the positron emission spectrum for the external fields with subcycle structure. For this, we study the transmission probability in the framework of scattering approach to vacuum pair production. In under-the-barrier scattering regime, we show that the width of a transmission resonance can be enhanced when the effective scattering potential contains multiple wells. Such a broadening in the resonance width corresponds to a decrease in the tunneling time. This may be relevant for observing the vacuum decay at shorter timescales before the external field is adiabatically turned off. In above-the-barrier scattering regime, we give a set of coupled differential equations for the numerical computation of the Bogoliubov coefficients.Comment: 11 pages, 5 figures. v2: Revised and extended, to appear in PR

The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses

Particle production due to external fields (electric, chromo-electric or gravitational) requires evolving an initial state through an interaction with a time-dependent background, with the rate being computed from a Bogoliubov transformation between the in and out vacua. When the background fields have temporal profiles with sub-structure, a semiclassical analysis of this problem confronts the full subtlety of the Stokes phenomenon: WKB solutions are only local, while the production rate requires global information. Incorporating the Stokes phenomenon, we give a simple quantitative explanation of the recently computed [Phys. Rev. Lett. 102, 150404 (2009)] oscillatory momentum spectrum of e+e- pairs produced from vacuum subjected to a time-dependent electric field with sub-cycle laser pulse structure. This approach also explains naturally why for spinor and scalar QED these oscillations are out of phase.Comment: 5 pages, 4 figs.; v2 sign typo corrected, version to appear in PR

Interference Effects in Schwinger Vacuum Pair Production for Time-Dependent Laser Pulses

We present simple new approximate formulas, for both scalar and spinor QED, for the number of particles produced from vacuum by a time dependent electric field, incorporating the interference effects that arise from an arbitrary number of distinct semiclassical turning points. Such interference effects are important when the temporal profile of the laser pulse has subcycle structure. We show how the resulting semiclassical intuition may be used to guide the design of temporal profiles that enhance the momentum spectrum due to interference effects. The result is easy to implement and generally applicable to time-dependent tunneling problems, such as appear in many other contexts in particle and nuclear physics, condensed matter physics, atomic physics, chemical physics, and gravitational physics.Comment: 19 pages; 21 figures; v2 refs update

The Schwinger Effect in Time Dependent Electric Fields

We study the Schwinger effect which is the non-perturbative production of e− e+ pairs from the vacuum by an external electric field. Basic quantitative analysis consists of extracting pair production probabilities which could be done exactly for only few cases. Thus, as far as realistic electric fields are concerned, application of numerical methods becomes essential for the analysis. We present two well known numerical methods which are developed for the electric fields varying only in one dimension and we give the treatment for the electric fields varying in time. The first methods employs a Riccati type equation and relates the reflection probability of the associated scattering problem to the produced particle density. The second approach makes use of a time-dependent number operator whose evolution given by the quantum Vlasov equation, and its asymptotic value gives the density of the produced pairs. We show that these two methods are equivalent and the evolution equations can be reduced to a second order nonlinear differential equation which is free of phase integrals. Pair production probabilities are expressed for fixed values of longitudinal momentum which is conserved during the evolution, and in this way momentum spectrum for the created e− e + pairs are computed. In the following, we present a detailed semiclassical analysis both within the framework of Jeffreys-Wentzel-Kramers-Brillouin (JWKB) approximation and worldline instanton formalism. In the former method analytical continuation rules for the approximate JWKB solutions are introduced and the reflection amplitude is obtained for a generic time dependent potential with an arbitrary number of critical points located in the complex plane. The latter method deals with classical tunneling trajectories such that evaluation of path integral on the semiclassical trajectories gives the same results with JWKB solutions. The semiclassical treatment shows how the qualitative features of the momentum spectrum such as interference effects and shift along the momentum axis can effectively be linked to the critical point distribution of the effective potential. In conjunction with the experimental studies, we compute the momentum spectra for realistic laser pulses with sub-cycle structure which might be relevant for the planned laser facilities.