2,009 research outputs found
"Hot Entanglement"? -- A Nonequilibrium Quantum Field Theory Scrutiny
The possibility of maintaining entanglement in a quantum system at finite,
even high, temperatures -- the so-called `hot entanglement' -- has obvious
practical interest, but also requires closer theoretical scrutiny. Since
quantum entanglement in a system evolves in time and is continuously subjected
to environmental degradation, a nonequilibrium description by way of open
quantum systems is called for. To identify the key issues and the contributing
factors that may permit `hot entanglement' to exist, or the lack thereof, we
carry out a model study of two spatially-separated, coupled oscillators in a
shared bath depicted by a finite-temperature scalar field. From the Langevin
equations we derived for the normal modes and the entanglement measure
constructed from the covariance matrix we examine the interplay between direct
coupling, field-induced interaction and finite separation on the structure of
late-time entanglement. We show that the coupling between oscillators plays a
crucial role in sustaining entanglement at intermediate temperatures and over
finite separations. In contrast, the field-induced interaction between the
oscillators which is a non-Markovian effect, becomes very ineffective at high
temperature. We determine the critical temperature above which entanglement
disappears to be bounded in the leading order by the inverse frequency of the
center-of-mass mode of the reduced oscillator system, a result not unexpected,
which rules out hot entanglement in such settings.Comment: 13 pages, 2 figure
Quantum Entanglement at High Temperatures? II. Bosonic Systems in Nonequilibrium Steady State
This is the second of a series of three papers examining how viable it is for
entanglement to be sustained at high temperatures for quantum systems in
thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium
steady state conditions (Case C). The system we analyze here consists of two
coupled quantum harmonic oscillators each interacting with its own bath
described by a scalar field, set at temperatures . For
\textit{constant bilinear inter-oscillator coupling} studied here (Case C1)
owing to the Gaussian nature, the problem can be solved exactly at arbitrary
temperatures even for strong coupling. We find that the valid entanglement
criterion in general is not a function of the bath temperature difference, in
contrast to thermal transport in the same NESS setting [1]. Thus lowering the
temperature of one of the thermal baths does not necessarily help to safeguard
the entanglement between the oscillators. Indeed, quantum entanglement will
disappear if any one of the thermal baths has a temperature higher than the
critical temperature . With the Langevin equations derived we give a full
display of how entanglement dynamics in this system depends on ,
, the inter-oscillator coupling and the system-bath coupling strengths. For
weak oscillator-bath coupling the critical temperature is about the order
of the inverse oscillator frequency, but for strong oscillator-bath coupling it
will depend on the bath cutoff frequency. We conclude that in most realistic
circumstances, for bosonic systems in NESS with constant bilinear coupling,
`hot entanglement' is largely a fiction. In Paper III we will examine the case
(C2) of \textit{time-dependent driven coupling } which contains the parametric
pumping type described in [2] wherein entanglement was first shown to sustain
at high temperatures.Comment: 47 pages, 9 figure
NonMarkovian Abraham--Lorentz--Dirac Equation: Radiation Reaction without Pathology
Motion of a point charge emitting radiation in an electromagnetic field obeys
the Abraham-Lorenz-Dirac (ALD) equation, with the effects of radiation reaction
or self-force incorporated. This class of equations describing backreaction,
including also the equations for gravitational self-force or Einstein's
equation for cosmology driven by trace anomaly, contain third-order derivative
terms. They are known to have pathologies like the possession of runaway
solutions, causality violation in pre-acceleration and the need for an extra
second-order derivative initial condition. In our current program we reexamine
this old problem from the perspective of non-Markovian dynamics in open
systems, applied earlier to backreaction problems in the early universe. Here
we consider a harmonic atom coupled to a scalar field, which acts effectively
like a supra-Ohmic environment, as in scalar electrodynamics. Our analysis
shows that a) there is no need for specifying a second derivative for the
initial condition; b) there is no pre-acceleration. These undesirable features
in conventional treatments arise from an inconsistent Markovian assumption:
these equations were regarded as Markovian ab initio, not as a limit of the
backreaction-imbued non-Markovian equation of motion. If one starts with the
full non-Markovian dynamical equation and takes the proper Markovian limit
judiciously, no harms are done. Finally, c) There is no causal relation between
the higher-derivative term in the equation of motion and the existence of
runaway solutions. If the charge has an effective size greater than this
critical value, its dynamics is stable. When this reasonable condition is met,
radiation reaction understood and treated correctly in the non-Ohmic
non-Markovian dynamics still obeys a third-order derivative equation, but it
does not require a second derivative initial condition, and there is no
pre-acceleration.Comment: 37 pages, 8 figure
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