Concepts of particles in curved spacetime :through the window of a harmonic oscillator

Abstract

We study the particle concepts through the window of a harmonic oscillator. At first we exactly quantize the forced harmonic oscillator using the Lewis-Liesenfeld invariant method. It was shown that the invariant eigen-state has lower energy than the ground state of the hamiltonian of unforced oscillator and the dispersions of p and q on this states do not depends on the external force. With this in hand, we try the quantum Brownian motion (QBM) in which the system is quantum oscillator and its environment is the scalar field in 1+1 dimension. This system also quantized by the invariant method. The Fock space is constructed from the eigenstates of the invariants. The exact time evolutions of the Hiesenberg operators are obtained and then it is shown that the final state of the oscillator becomes the ground state if the coupling is small irrespective of initial state of the oscillator if the environment is in ground state. QBM can be seen in a different point of view - the particle detector. In this respect the oscillator is some kinds of particle detector which detect the scalar field quantum. It is shown that the interaction of the oscillator and the field can be given using a single scalar function. When the coupling change abruptly, we found the logarithmic UV divergence in the radiation and it is shown that the stress tensor generated by the uniformly accelerating detector has the same form with that of the inertial in the initial transient region and become different at the time scale of observation.