4 research outputs found
Studies on the SJ Vacuum in de Sitter Spacetime
In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime
for free scalar field theory. For the massless theory we find that the SJ
vacuum can neither be obtained from the Fock vacuum of Allen and Folacci
nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using
a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find
the causal set SJ vacuum for a range of masses of the free scalar
field. While our simulations are limited to a finite volume slab of global de
Sitter spacetime, they show good convergence as the volume is increased. We
find that the 4d causal set SJ vacuum shows a significant departure from the
continuum Motolla-Allen -vacua. Moreover, the causal set SJ vacuum is
well-defined for both the minimally coupled massless and the conformally
coupled massless cases. This is at odds with earlier work on the
continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum
is ill-defined for these masses. Our results hint at an important tension
between the discrete and continuum behaviour of the SJ vacuum in de Sitter and
suggest that the former cannot in general be identified with the Mottola-Allen
-vacua even for .Comment: 43 pages, 25 figure
Entanglement Entropy of Causal Set de Sitter Horizons
de Sitter cosmological horizons are known to exhibit thermodynamic properties
similar to black hole horizons. In this work we study causal set de Sitter
horizons, using Sorkin's spacetime entanglement entropy (SSEE) formula, for a
conformally coupled quantum scalar field. We calculate the causal set SSEE for
the Rindler-like wedge of a symmetric slab of de Sitter spacetime in
spacetime dimensions using the Sorkin-Johnston vacuum state. We find that the
SSEE obeys an area law when the spectrum of the Pauli-Jordan operator is
appropriately truncated in both the de Sitter slab as well as its restriction
to the Rindler-like wedge. Without this truncation, the SSEE satisfies a volume
law. This is in agreement with Sorkin and Yazdi's calculations for the causal
set SSEE for nested causal diamonds in , where they showed that
an area law is obtained only after truncating the Pauli-Jordan spectrum. In
this work we explore different truncation schemes with the criterion that the
SSEE so obtained obeys an area law.Comment: 30 pages, 16 figure
Motivating semiclassical gravity: a classical-quantum approximation for bipartite quantum systems
We derive a "classical-quantum" approximation scheme for a broad class of
bipartite quantum systems from fully quantum dynamics. In this approximation,
one subsystem evolves via classical equations of motion with quantum
corrections, and the other subsystem evolves quantum mechanically with
equations of motion informed by the evolving classical degrees of freedom.
Using perturbation theory, we derive an estimate for the growth rate of
entanglement of the subsystems and deduce a "scrambling time" - the time
required for the subsystems to become significantly entangled from an initial
product state. We argue that a necessary condition for the validity of the
classical-quantum approximation is consistency of initial data with the
generalized Bohr correspondence principle. We illustrate the general formalism
by numerically studying the fully quantum, fully classical, and
classical-quantum dynamics of a system of two oscillators with nonlinear
coupling. This system exhibits parametric resonance, and we show that quantum
effects quench parametric resonance at late times. Lastly, we present a curious
late-time scaling relation between the average value of the von Neumann
entanglement of the interacting oscillator system and its total energy: .Comment: 32 pages, 11 figures, 4 supplementary videos online at
http://www.youtube.com/playlist?list=PLDRdFkFA2uqfp-CGfbhrfZDmfoC-Ng1x