Rolling classical scalar field in a linear potential coupled to a quantum field

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 classicalquantum 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.

Inflationary quantum dynamics and backreaction using a classical-quantum correspondence

“…To proceed in this way demands an extension of the CQC to a system with interacting QHOs each of which is also coupled to the same spacetime background. Alternatively, the construction of a spatial lattice could be established as in the field theoryextension of the CQC [40][41][42]. Either way is more computationally exhausting but is irrefutably a relevant future work.…”

“…Physical insights on backreaction have already been drawn by using the CQC in its early applications to a rolling ball-QHO system [35] and Hawking radiation [39] but it is the elegance by which these important results have been obtained that speaks loudly about the potential of the method. Moreover, the CQC has been extended to cover field theory applications [40] and applied for instance to a coupled scalar field system [41], one of which is the rolling inflaton familiar in the inflationary context, and the evaporation of breathers [42]. It is important to stress out that the CQC is an exact solution to the field equations and that perhaps its only limitation is whenever the coupled classicalquantum d.o.f.s picture no longer holds.…”

Emergence of classical structures from the quantum vacuum

“…Setting λ ¼ 0, the problem now is that of a quantum field interacting with a classical background. As discussed in [21][22][23], the solution to the quantum problem can be written in terms of the solution of a classical problem but in higher dimensions. More specifically, let us discretize a compactified space of size L by N lattice points i ¼ 1; …; N, with lattice spacing a ¼ L=N.…”

“…The matrix A − BD −1 C is called the Schur complement of D. This formula is used in the main text in the lead up to Eq. (23). Assuming invertibility of the Schur complement, we can also write…”

Quantum Formation of Topological Defects

“…However, it turns out that not all components of the matrix Z are relevant and we can reduce the number of differential equations that need to be solved. It can be shown that the matrix Z is circulant [36] i.e., its matrix elements Z jl only depend on j − l (mod N ). We can therefore diagonalize it via the discrete Fourier transform:…”