Fenômeno de interferência na densidade de energia em cavidades com duas fronteiras oscilantes

Abstract

We consider a real massless scalar field inside a cavity with two moving mirrors in a two-dimensional spacetime, satisfying Dirichlet boundary condition at the instantaneous position of the boundaries, for arbitrary and relativistic laws of motion. Considering vacuum as the initial field state, we show that the exact value of the the energy density in the cavity can be obtained by tracing back a sequence of null lines, connecting the value of the energy density at the given spacetime point to a certain known value of the energy density at a point in the region where the initial field modes are not affected by the boundaries motion. We obtain formulas for the energy density of the field and the quantum force acting on the boundaries. We also show that for a large class of movements, including resonant cases found in the literature, the exact method proposed here enable us to find analytical solutions written as series in the parameter that controls the amplitudes of the movements. Using these analytical solutions, we investigate the interference phenomena in the energy density and total energy stored in the cavity.