Abstract
We study the dynamics of a classical scalar field that rolls down a linear potential as it interacts bi-quadratically with a quantum field. We explicitly solve the dynamical problem by using the classical-quantum correspondence (CQC). Rolling solutions on the effective potential are shown to compare very poorly with the full solution. Spatially homogeneous initial conditions maintain their homogeneity and small inhomogeneities in the initial conditions do not grow.
Highlights
Often we are interested in the dynamics of quantum fields in classical backgrounds
IV we study dynamics with inhomogeneous initial conditions to see if ROLLING CLASSICAL SCALAR FIELD IN A
We have solved for the dynamics of a classical rolling field that is coupled to a quantum field using the classicalquantum correspondence (CQC)
Summary
Often we are interested in the dynamics of quantum fields in classical backgrounds. A prime example is that of phase transitions in which an order parameter evolves to develop a vacuum expectation value while interacting with other quantum degrees of freedom. The background dynamics is assumed to be well described by the semiclassical approximation in which the classical background dynamics couples to the expectation value of the quantum operators in the equation of motion. The expectation value is evaluated in the dynamical background in terms of the classical variables The validity of this approach has been explicitly tested in a quantum mechanical setting where the full quantum solution can be compared to the CQC result [2]. The underlying reason is that the effective potential assumes the quantum state of the fields, for example the vacuum state or a thermal state, and expectation values of operators are taken in this state. This leads to a very different picture from that obtained by considering static solutions of the effective potential.
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