TY - JOUR

T1 - NonMarkovianity in cosmology

T2 - Memories kept in a quantum field

AU - Hsiang, Jen Tsung

AU - Hu, Bei Lok

N1 - Publisher Copyright:
© 2021 Elsevier Inc.

PY - 2021/11

Y1 - 2021/11

N2 - In this work we ask how an Unruh–DeWitt (UD) detector with harmonic oscillator internal degrees of freedom Q measuring an evolving quantum matter field Φ(x,t) in an expanding universe with scale factor a(t) responds. We investigate the detector's response which contains non-Markovian information about the quantum field squeezed by the dynamical spacetime. The challenge is in the memory effects accumulated over the evolutionary history. We first consider a detector W, the ‘Witness’, which co-existed and evolved with the quantum field from the beginning. We derive a nonMarkovian quantum Langevin equation for the detector's Q by integrating over the squeezed quantum field. The solution of this integro-differential equation would answer our question, in principle, but very challenging, in practice. Striking a compromise, we then ask, to what extent can a detector D introduced at late times, called the ‘Detective’, decipher past memories. This situation corresponds to many cosmological experiments today probing specific stages in the past, such as COBE targeting activities at the surface of last scattering. Somewhat surprisingly we show that it is possible to retrieve to some degree certain global physical quantities, such as the resultant squeezing, particles created, quantum coherence and correlations. The reason is because the quantum field has all the fine-grained information from the beginning in how it was driven by the cosmic dynamics a(t). How long the details of past history can persist in the quantum field depends on the memory time. The fact that a squeezed field cannot come to complete equilibrium under continuous driving, as in an evolving spacetime, actually helps to retain the memory. We discuss interesting features and potentials of this ‘archeological’ perspective toward cosmological issues.

AB - In this work we ask how an Unruh–DeWitt (UD) detector with harmonic oscillator internal degrees of freedom Q measuring an evolving quantum matter field Φ(x,t) in an expanding universe with scale factor a(t) responds. We investigate the detector's response which contains non-Markovian information about the quantum field squeezed by the dynamical spacetime. The challenge is in the memory effects accumulated over the evolutionary history. We first consider a detector W, the ‘Witness’, which co-existed and evolved with the quantum field from the beginning. We derive a nonMarkovian quantum Langevin equation for the detector's Q by integrating over the squeezed quantum field. The solution of this integro-differential equation would answer our question, in principle, but very challenging, in practice. Striking a compromise, we then ask, to what extent can a detector D introduced at late times, called the ‘Detective’, decipher past memories. This situation corresponds to many cosmological experiments today probing specific stages in the past, such as COBE targeting activities at the surface of last scattering. Somewhat surprisingly we show that it is possible to retrieve to some degree certain global physical quantities, such as the resultant squeezing, particles created, quantum coherence and correlations. The reason is because the quantum field has all the fine-grained information from the beginning in how it was driven by the cosmic dynamics a(t). How long the details of past history can persist in the quantum field depends on the memory time. The fact that a squeezed field cannot come to complete equilibrium under continuous driving, as in an evolving spacetime, actually helps to retain the memory. We discuss interesting features and potentials of this ‘archeological’ perspective toward cosmological issues.

KW - NonMarkovianity

KW - Nonequilibrium quantum dynamics

KW - Parametric process

KW - Quantum field in a time-dependent background

KW - Quantum memory in cosmological evolution

UR - http://www.scopus.com/inward/record.url?scp=85120916731&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2021.168656

DO - 10.1016/j.aop.2021.168656

M3 - 期刊論文

AN - SCOPUS:85120916731

VL - 434

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

M1 - 168656

ER -