Rethinking Dynamical Condensates: Effective Potentials, Equations of Motion, and Particle Production

Misaligned scalar condensates are a popular model building tool for solving open questions in particle physics and cosmology. At tree level, these homogeneous expectation values of quantum fields satisfy the equations of motion for classical fields. One typically turns to the effective potential to encode the effects of quantum mechanical fluctuations, including with regards to condensate dynamics. Is this accurate or even sufficient? We consider a condensate of a scalar field with Yukawa couplings to N_f identical, massless fermions in Minkowski spacetime as an illustrative model. We review the usual effective potential derivation using a Hamiltonian-based approach, highlighting the necessary static and equilibrium assumptions. The use of the effective potential in dynamical equations of motion is shown to produce significant violations of energy conservation. Thus, an adiabatic approximation is introduced to obtain equations of motion for the dynamical condensate. By turning off the Yukawa couplings, we study the purely scalar degrees of freedom in the theory and investigate two prominent, potential breakdowns of adiabaticity: 1. spinodal instabilities for potentials with spontaneous symmetry breaking, 2. parametric amplification for condensates oscillating around their potential minimum. Both effects are shown to induce profuse particle and (entanglement) entropy production. Next, we turn on the Yukawa couplings but consider the large N_f limit, which naturally suppresses the scalar fluctuations. We find that beyond leading order, the adiabatic equations of motion induce a dynamical field renormalization and concomitant production of fermions as the condensate evolves over time. Finally, we relax the large N_f limit and introduce a complete set of consistent, energy conserving, fully renormalized equations of motion for the scalar condensate and fermion modes which are amenable to numerical study. Guided by manifest energy conservation, we conjecture the emergence of asymptotic, highly excited (and entangled) stationary states in this system. Possible cosmological and symmetry breaking implications are discussed.