Pair production due to an electric field in 1+1 dimensions and the validity of the semiclassical approximation

Abstract

Solutions to the backreaction equation in 1 þ 1-dimensional semiclassical electrodynamics are obtained and analyzed when considering a time-varying homogeneous electric field initially generated by a classical electric current, coupled to either a quantized scalar field or a quantized spin-1 2 field. Particle production by way of the Schwinger effect leads to backreaction effects that modulate the electric field strength. Details of the particle production process are investigated along with the transfer of energy between the electric field and the particles. The validity of the semiclassical approximation is also investigated using a criterion previously implemented for chaotic inflation and, in an earlier form, semiclassical gravity. The criterion states that the semiclassical approximation will break down if any linearized gauge-invariant quantity constructed from solutions to the linear response equation, with finite nonsingular data, grows rapidly for some period of time. Approximations to homogeneous solutions of the linear response equation are computed and it is found that the criterion is violated when the maximum value, E max , obtained by the electric field is of the order of the critical scale for the Schwinger effect, E max ∼ E crit ≡ m 2 =q, where m is the mass of the quantized field and q is its electric charge. For these approximate solutions the criterion appears to be satisfied in the extreme limits qE max m 2 ≪ 1 and qE max m 2 ≫ 1.

Analog simulations of early universe pre-heating and the back-reaction effect

“…We highlighted non-trivial dynamical effects beyond the semiclassical level: In particular, we observed a quick fluctuations induced decoherence of the initially in-phase breathing excitation, as well as signature of miltimode entanglement. The generality of the microscopic processes underlying our numerically observed results suggests the importance of going beyond semiclassical approaches [48,49] and including quantum fluctuation features in the description of back-reaction phenomena in gravitation and cosmology.…”

Wilson loops in the Hamiltonian formalism

“…This can be studied numerically at nonzero temperature in real time, using either tensor networks on a classical computer [104][105][106][107], or even with the noisy intermediate-scale quantum computers which are available at present. This is similar to studying the screening of background electric fields at nonzero θ [108][109][110][111][112][113][114][115][116][117].…”

Practical derivations of fermion and gauge boson reduction formulae in curved spacetimes

“…scalar decay calculations [4,[8][9][10], scalar decay in to fermions in Robertson-Walker spacetimes [11], and solutions for free fermions in assorted spacetimes [12,13]. There are also recent results for backreaction [14][15][16][17][18][19]. The calculations so far have relied on conformally coupled, massless particles.…”