Quantum dissipative effects for a real scalar field coupled to a dynamical Neumann surface in d+1 dimensions

TL;DR

This work analyzes dissipative effects for a massless real scalar field with Neumann boundary conditions on a time-dependent surface in $d+1$ dimensions, comparing to the Dirichlet case. Building on the in-out effective action framework, it perturbatively expands the action in the surface deformation $oldsymbol{ psi}$ up to fourth order and computes the imaginary part of the effective action, which governs dynamical Casimir radiation. A key result is that for $d=1$ the Neumann and Dirichlet results agree up to second order for arbitrary surfaces and up to fourth order for wavelike surfaces, while for $d>1$ explicit expressions for the difference arise from two- and three-propagator loop integrals, with Neumann boundary conditions generally enhancing pair production. The findings provide dimensional benchmarks and indicate strongest dissipative effects in low-dimensional systems, with potential implications for quasi-one- and two-dimensional experimental setups and extensions to other boundary conditions.

Abstract

We study dissipative effects for a system consisting of a massless real scalar field satisfying Neumann boundary conditions on a space and time-dependent surface, in d+1 dimensions. We focus on the comparison of the results for this system with the ones corresponding to Dirichlet conditions, and the same surface space-time geometry. We show that, in d=1, the effects are equal up to second order for rather arbitrary surfaces, and up to fourth order for wavelike surfaces. For d>1, we find general expressions for their difference.

Figures (4)

• Figure 1: Successions $\eta_D$ and $\eta_N$ in logarithmic scale.
• Figure 2: Successions $\zeta_D$ and $\zeta_N$ in logarithmic scale.
• Figure 3: Successions $\sigma_D$ and $\sigma_N$ in logarithmic scale.
• Figure 4: Successions $\kappa_D$ and $\kappa_N$ in logarithmic scale.