2018/01/31 by Daniel Boyanovsky, D. Boyanovsky · 27 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Degrees of freedom (physics and chemistry) #Density matrix #Entropy (arrow of time) #Joint quantum entropy #Mathematical physics #Physics #Quantum #Quantum discord #Quantum electrodynamics #Quantum entanglement #Quantum gravity #Quantum many-body systems #Quantum mechanics #Quantum relative entropy #Resummation #Scalar field #Scalar field theory #Thermalisation #Von Neumann entropy #cond-mat.stat-mech #hep-ph #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.97.065008
published in Physical review. D/Physical review. D. 97(6) (American Physical Society) · published version
openalex created_date 2018/02/02 · openalex publication_date 2018/03/12 · arxiv created 2018/03/13 · arxiv updated 2018/03/21 · openalex updated_date 2026/08/06
Integrating out high energy degrees of freedom to yield a low energy effective field theory leads to a loss of information with a concomitant increase in entropy. We obtain the effective field theory of a light scalar field interacting with heavy fields after tracing out the heavy degrees of freedom from the time evolved density matrix. The initial density matrix describes the light field in its ground state and the heavy fields in equilibrium at a common temperature T. For T=0, we obtain the reduced density matrix in a perturbative expansion; it reveals an emergent mixed state as a consequence of the entanglement between light and heavy fields. We obtain the effective action that determines the time evolution of the reduced density matrix for the light field in a nonperturbative Dyson resummation of one-loop correlations of the heavy fields. The Von-Neumann entanglement entropy associated with the reduced density matrix is obtained for the nonresonant and resonant cases in the asymptotic long time limit. In the nonresonant case the reduced density matrix displays an incipient thermalization albeit with a wave-vector, time and coupling dependent effective temperature as a consequence of memory of initial conditions. The entanglement entropy is time independent and is the thermal entropy for this effective, nonequilibrium temperature. In the resonant case the light field fully thermalizes with the heavy fields, the reduced density matrix loses memory of the initial conditions and the entanglement entropy becomes the thermal entropy of the light field. We discuss the relation between the entanglement entropy ultraviolet divergences and renormalization.