Adiabatic number operators and vacua for coupled bosonic systems are constructed order by order from a linear recursion for complex structures, generalizing WKB and Lewis-Riesenfeld invariant methods beyond a single mode.
Super-Adiabatic Particle Number in Schwinger and de Sitter Particle Production
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abstract
We consider the time evolution of the adiabatic particle number in both time-dependent electric fields and in de Sitter spaces, and define a super-adiabatic particle number in which the (divergent) adiabatic expansion is truncated at optimal order. In this super-adiabatic basis, the particle number evolves smoothly in time, according to Berry's universal adiabatic smoothing of the Stokes phenomenon. This super-adiabatic basis also illustrates clearly the quantum interference effects associated with particle production, in particular for sequences of time-dependent electric field pulses, and in eternal de Sitter space where there is constructive interference in even dimensions, and destructive interference in odd dimensions.
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Adiabatic vacua from linear complex structures
Adiabatic number operators and vacua for coupled bosonic systems are constructed order by order from a linear recursion for complex structures, generalizing WKB and Lewis-Riesenfeld invariant methods beyond a single mode.