1,082 research outputs found
Quantum Dynamics of the Driven and Dissipative Rabi Model
The Rabi model considers a two-level system (or spin-1/2) coupled to a
quantized harmonic oscillator and describes the simplest interaction between
matter and light. The recent experimental progress in solid-state circuit
quantum electrodynamics has engendered theoretical efforts to quantitatively
describe the mathematical and physical aspects of the light-matter interaction
beyond the rotating wave approximation. We develop a stochastic Schr\"{o}dinger
equation approach which enables us to access the strong-coupling limit of the
Rabi model and study the effects of dissipation, and AC drive in an exact
manner. We include the effect of ohmic noise on the non-Markovian spin dynamics
resulting in Kondo-type correlations, as well as cavity losses. We compute the
time evolution of spin variables in various conditions. As a consideration for
future work, we discuss the possibility to reach a steady state with one
polariton in realistic experimental conditions.Comment: 13 pages, final versio
Optimal projection of observations in a Bayesian setting
Optimal dimensionality reduction methods are proposed for the Bayesian
inference of a Gaussian linear model with additive noise in presence of
overabundant data. Three different optimal projections of the observations are
proposed based on information theory: the projection that minimizes the
Kullback-Leibler divergence between the posterior distributions of the original
and the projected models, the one that minimizes the expected Kullback-Leibler
divergence between the same distributions, and the one that maximizes the
mutual information between the parameter of interest and the projected
observations. The first two optimization problems are formulated as the
determination of an optimal subspace and therefore the solution is computed
using Riemannian optimization algorithms on the Grassmann manifold. Regarding
the maximization of the mutual information, it is shown that there exists an
optimal subspace that minimizes the entropy of the posterior distribution of
the reduced model; a basis of the subspace can be computed as the solution to a
generalized eigenvalue problem; an a priori error estimate on the mutual
information is available for this particular solution; and that the
dimensionality of the subspace to exactly conserve the mutual information
between the input and the output of the models is less than the number of
parameters to be inferred. Numerical applications to linear and nonlinear
models are used to assess the efficiency of the proposed approaches, and to
highlight their advantages compared to standard approaches based on the
principal component analysis of the observations
Existence of nodal solutions for Dirac equations with singular nonlinearities
We prove, by a shooting method, the existence of infinitely many solutions of
the form of the nonlinear Dirac
equation {equation*} i\underset{\mu=0}{\overset{3}{\sum}} \gamma^\mu
\partial_\mu \psi- m\psi - F(\bar{\psi}\psi)\psi = 0 {equation*} where
is compactly supported and \[F(x) = \{{array}{ll}
p|x|^{p-1} & \text{if} |x|>0 0 & \text{if} x=0 {array}.] with
under some restrictions on the parameters and We study also the
behavior of the solutions as tends to zero to establish the link between
these equations and the M.I.T. bag model ones
Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model
We introduce an extension of a variationally optimized perturbation method,
by combining it with renormalization group properties in a straightforward
(perturbative) form. This leads to a very transparent and efficient procedure,
with a clear improvement of the non-perturbative results with respect to
previous similar variational approaches. This is illustrated here by deriving
optimized results for the mass gap of the O(2N) Gross-Neveu model, compared
with the exactly know results for arbitrary N. At large N, the exact result is
reproduced already at the very first order of the modified perturbation using
this procedure. For arbitrary values of N, using the original perturbative
information only known at two-loop order, we obtain a controllable percent
accuracy or less, for any N value, as compared with the exactly known result
for the mass gap from the thermodynamical Bethe Ansatz. The procedure is very
general and can be extended straightforwardly to any renormalizable Lagrangian
model, being systematically improvable provided that a knowledge of enough
perturbative orders of the relevant quantities is available.Comment: 18 pages, 1 figure, v2: Eq. (4.5) corrected, comments adde
Discovery of the Widest Very Low Mass Binary
We report the discovery of a very low mass binary system (primary mass <0.1
Msol) with a projected separation of ~5100 AU, more than twice that of the
widest previously known system. A spectrum covering the 1-2.5 microns
wavelength interval at R ~1700 is presented for each component. Analysis of the
spectra indicates spectral types of M6.5V and M8V, and the photometric distance
of the system is ~62 pc. Given that previous studies have established that no
more than 1% of very low mass binary systems have orbits larger than 20 AU, the
existence of such a wide system has a bearing on very low mass star formation
and evolution models.Comment: accepted ApJL, 4 page
Quadproj: a Python package for projecting onto quadratic hypersurfaces
Quadratic hypersurfaces are a natural generalization of affine subspaces, and
projections are elementary blocks of algorithms in optimization and machine
learning. It is therefore intriguing that no proper studies and tools have been
developed to tackle this nonconvex optimization problem. The quadproj package
is a user-friendly and documented software that is dedicated to project a point
onto a non-cylindrical central quadratic hypersurface
Geant4 simulations of bêta + emitters and prompt gamma yields for in beam TOF PET hadrontherapy application
Nonequilibrium phase transition in a driven Potts model with friction
We consider magnetic friction between two systems of -state Potts spins
which are moving along their boundaries with a relative constant velocity .
Due to the interaction between the surface spins there is a permanent energy
flow and the system is in a steady state which is far from equilibrium. The
problem is treated analytically in the limit (in one dimension, as
well as in two dimensions for large- values) and for and finite by
Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase
transitions take place, the properties of which depend on the type of phase
transition in equilibrium. When this latter transition is of first order, a
sequence of second- and first-order nonequilibrium transitions can be observed
when the interaction is varied.Comment: 13 pages, 9 figures, one journal reference adde
Attractive and repulsive cracks in a heterogeneous material
We study experimentally the paths of an assembly of cracks growing in
interaction in a heterogeneous two-dimensional elastic brittle material
submitted to uniaxial stress. For a given initial crack assembly geometry, we
observe two types of crack path. The first one corresponds to a repulsion
followed by an attraction on one end of the crack and a tip to tip attraction
on the other end. The second one corresponds to a pure attraction. Only one of
the crack path type is observed in a given sample. Thus, selection between the
two types appears as a statistical collective process.Comment: soumis \`a JSTA
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