13 research outputs found
Amplitude and phase representation of quantum invariants for the time dependent harmonic oscillator
The correspondence between classical and quantum invariants is established.
The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator
is translated from the coordinate and momentum operators into amplitude and
phase operators. In doing so, Turski's phase operator as well as
Susskind-Glogower operators are generalized to the time dependent harmonic
oscillator case. A quantum derivation of the Manley-Rowe relations is shown as
an example
Novel approach to the study of quantum effects in the early universe
We develop a theoretical frame for the study of classical and quantum
gravitational waves based on the properties of a nonlinear ordinary
differential equation for a function of the conformal time
, called the auxiliary field equation. At the classical level,
can be expressed by means of two independent solutions of the
''master equation'' to which the perturbed Einstein equations for the
gravitational waves can be reduced. At the quantum level, all the significant
physical quantities can be formulated using Bogolubov transformations and the
operator quadratic Hamiltonian corresponding to the classical version of a
damped parametrically excited oscillator where the varying mass is replaced by
the square cosmological scale factor . A quantum approach to the
generation of gravitational waves is proposed on the grounds of the previous
dependent Hamiltonian. An estimate in terms of and
of the destruction of quantum coherence due to the gravitational
evolution and an exact expression for the phase of a gravitational wave
corresponding to any value of are also obtained. We conclude by
discussing a few applications to quasi-de Sitter and standard de Sitter
scenarios.Comment: 20 pages, to appear on PRD. Already published background material has
been either settled up in a more compact form or eliminate