48 research outputs found
Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension
A dispersive medium becomes entangled with zero-point fluctuations in the
vacuum. We consider an arbitrary array of material bodies weakly interacting
with a quantum field and compute the quantum mutual information between them.
It is shown that the mutual information in D dimensions can be mapped to
classical thermodynamic entropy in D+1 dimensions. As a specific example, we
compute the mutual information both analytically and numerically for a range of
separation distances between two bodies in D=2 dimensions and find a
logarithmic correction to the area law at short separations. A key advantage of
our method is that it allows the strong subadditivity property---notoriously
difficult to prove for quantum systems---to be easily verified.Comment: Corrected typos. Added reference
Flight of a heavy particle nonlinearly coupled to a quantum bath
Fluctuation and dissipation are by-products of coupling to the `environment.'
The Caldeira-Leggett model, a successful paradigm of quantum Brownian motion,
views the environment as a collection of harmonic oscillators linearly coupled
to the system. However, symmetry considerations may forbid a linear coupling,
e.g. for a neutral particle in quantum electrodynamics. We argue that nonlinear
couplings can lead to a fundamentally different behavior. Specifically, we
consider a heavy particle quadratically coupled to quantum fluctuations of the
bath. In one dimension the particle undergoes anomalous diffusion, unfolding as
a power-law distribution in space, reminiscent of L\'evy flights. We suggest
condensed matter analogs where similar effects may arise.Comment: Introduction expanded. Appendices adde
Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion
We study the implications of quantum fluctuations of a dispersive medium,
under steady rotation, either in or out of thermal equilibrium with its
environment. A rotating object exhibits a quantum instability by dissipating
its mechanical motion via spontaneous emission of photons, as well as internal
heat generation. Universal relations are derived for the radiated energy and
angular momentum as trace formulas involving the object's scattering matrix. We
also compute the quantum noise by deriving the full statistics of the radiated
photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy
generation is quantified, and the total entropy is shown to be always
increasing. Furthermore, we derive a Fokker-Planck equation governing the
stochastic angular motion resulting from the fluctuating back-reaction
frictional torque. As a result, we find a quantum limit on the uncertainty of
the object's angular velocity in steady rotation. Finally, we show in some
detail that a rotating object drags nearby objects, making them spin parallel
to its axis of rotation. A scalar toy model is introduced in the first part to
simplify the technicalities and ease the conceptual complexities; a detailed
discussion of quantum electrodynamics is presented in the second part
Multicritical behavior in dissipative Ising models
We analyze theoretically the many-body dynamics of a dissipative Ising model
in a transverse field using a variational approach. We find that the steady
state phase diagram is substantially modified compared to its equilibrium
counterpart, including the appearance of a multicritical point belonging to a
different universality class. Building on our variational analysis, we
establish a field-theoretical treatment corresponding to a dissipative variant
of a Ginzburg-Landau theory, which allows us to compute the upper critical
dimension of the system. Finally, we present a possible experimental
realization of the dissipative Ising model using ultracold Rydberg gases.Comment: 8 pages, 4 figure