10,765 research outputs found
Dicke-type phase transition in a multimode optomechanical system
We consider the "membrane in the middle" optomechanical model consisting of a
laser pumped cavity which is divided in two by a flexible membrane that is
partially transmissive to light and subject to radiation pressure. Steady state
solutions at the mean-field level reveal that there is a critical strength of
the light-membrane coupling above which there is a symmetry breaking
bifurcation where the membrane spontaneously acquires a displacement either to
the left or the right. This bifurcation bears many of the signatures of a
second order phase transition and we compare and contrast it with that found in
the Dicke model. In particular, by studying limiting cases and deriving
dynamical critical exponents using the fidelity susceptibility method, we argue
that the two models share very similar critical behaviour. For example, the
obtained critical exponents indicate that they fall within the same
universality class. Away from the critical regime we identify, however, some
discrepancies between the two models. Our results are discussed in terms of
experimentally relevant parameters and we evaluate the prospects for realizing
Dicke-type physics in these systems.Comment: 14 pages, 6 figure
Impurity in a bosonic Josephson junction: swallowtail loops, chaos, self-trapping and the poor man's Dicke model
We study a model describing identical bosonic atoms trapped in a
double-well potential together with a single impurity atom, comparing and
contrasting it throughout with the Dicke model. As the boson-impurity coupling
strength is varied, there is a symmetry-breaking pitchfork bifurcation which is
analogous to the quantum phase transition occurring in the Dicke model. Through
stability analysis around the bifurcation point, we show that the critical
value of the coupling strength has the same dependence on the parameters as the
critical coupling value in the Dicke model. We also show that, like the Dicke
model, the mean-field dynamics go from being regular to chaotic above the
bifurcation and macroscopic excitations of the bosons are observed. Overall,
the boson-impurity system behaves like a poor man's version of the Dicke model.Comment: 17 pages, 16 figure
Scattering theory for Klein-Gordon equations with non-positive energy
We study the scattering theory for charged Klein-Gordon equations:
\{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x,
D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)=
f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq
n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x),
describing a Klein-Gordon field minimally coupled to an external
electromagnetic field described by the electric potential and magnetic
potential . The flow of the Klein-Gordon equation preserves the
energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+
\bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x)
\d x. We consider the situation when the energy is not positive. In this
case the flow cannot be written as a unitary group on a Hilbert space, and the
Klein-Gordon equation may have complex eigenfrequencies. Using the theory of
definitizable operators on Krein spaces and time-dependent methods, we prove
the existence and completeness of wave operators, both in the short- and
long-range cases. The range of the wave operators are characterized in terms of
the spectral theory of the generator, as in the usual Hilbert space case
Experimental realization of catalytic CH_4 hydroxylation predicted for an iridium NNC pincer complex, demonstrating thermal, protic, and oxidant stability
A discrete, air, protic, and thermally stable (NNC)Ir(III) pincer complex was synthesized that catalytically activates the CH bond of methane in trifluoroacetic acid; functionalization using NaIO_4 and KIO_3 gives the oxy-ester
Extended Wertheim theory predicts the anomalous chain length distributions of divalent patchy particles under extreme confinement
Colloidal patchy particles with divalent attractive interaction can
self-assemble into linear polymer chains. Their equilibrium properties in 2D
and 3D are well described by Wertheim's thermodynamic perturbation theory which
predicts a well-defined exponentially decaying equilibrium chain length
distribution. In experimental realizations, due to gravity, particles sediment
to the bottom of the suspension forming a monolayer of particles with a
gravitational height smaller than the particle diameter. In accordance with
experiments, an anomalously high monomer concentration is observed in
simulations which is not well understood. To account for this observation, we
interpret the polymerization as taking place in a highly confined quasi-2D
plane and extend the Wertheim thermodynamic perturbation theory by defining
addition reactions constants as functions of the chain length. We derive the
theory, test it on simple square well potentials, and apply it to the
experimental case of synthetic colloidal patchy particles immersed in a binary
liquid mixture that are described by an accurate effective critical Casimir
patchy particle potential. The important interaction parameters entering the
theory are explicitly computed using the integral method in combination with
Monte Carlo sampling. Without any adjustable parameter, the predictions of the
chain length distribution are in excellent agreement with explicit simulations
of self-assembling particles. We discuss generality of the approach, and its
application range.Comment: The following article has been submitted to The Journal of Chemical
Physic
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