Schwinger pair production in space and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory - INSPIRE

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Schwinger pair production in space and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory

Florian Hebenstreit
(
- Graz U.
)
,
Reinhard Alkofer
(
- Graz U.
)
,
Holger Gies
(
- Jena U., TPI and
- Helmholtz Inst., Jena
)

Jul, 2010

17 pages

Published in:

Phys.Rev.D 82 (2010) 105026

e-Print:

1007.1099 [hep-ph]

DOI:

10.1103/PhysRevD.82.105026

View in:

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Abstract: (arXiv)

The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields

\vec{E}(\vec{x},t)

. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial differential equations of infinite order for the sixteen irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory (QKT) is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field

E(t)=E_0

and the Sauter-type electric field

E(t)=E_0\operatorname{sech}^2(t/\tau)

. These analytic solutions translate into corresponding expressions within the DHW formalism and allow to discuss the effect of higher derivatives. We observe that spatial field variations typically exert a strong influence on the components of the Wigner function for large momenta or for late times.

11.15.Tk
12.20.Ds
electric field: space-time dependence
expansion: derivative
electron: pair production
differential equations
nonperturbative
Vlasov equation
phase space
higher-order: 0

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