63 research outputs found
Non-mean-field effects in systems with long-range forces in competition
We investigate the canonical equilibrium of systems with long-range forces in
competition. These forces create a modulation in the interaction potential and
modulated phases appear at the system scale. The structure of these phases
differentiate this system from monotonic potentials, where only the mean-field
and disordered phases exist. With increasing temperature, the system switches
from one ordered phase to another through a first-order phase transition. Both
mean-field and modulated phases may be stable, even at zero temperature, and
the long-range nature of the interaction will lead to metastability
characterized by extremely long time scales
Spreading of Perturbations in Long-Range Interacting Classical Lattice Models
Lieb-Robinson-type bounds are reported for a large class of classical
Hamiltonian lattice models. By a suitable rescaling of energy or time, such
bounds can be constructed for interactions of arbitrarily long range. The bound
quantifies the dependence of the system's dynamics on a perturbation of the
initial state. The effect of the perturbation is found to be effectively
restricted to the interior of a causal region of logarithmic shape, with only
small, algebraically decaying effects in the exterior. A refined bound, sharper
than conventional Lieb-Robinson bounds, is required to correctly capture the
shape of the causal region, as confirmed by numerical results for classical
long-range chains. We discuss the relevance of our findings for the
relaxation to equilibrium of long-range interacting lattice models.Comment: 4+6 pages, 3+2 figure
Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves
The Hamiltonian description of the self-consistent interaction between an
electromagnetic plane-wave and a co-propagating beam of charged particles is
considered. We show how the motion can be reduced to a one-dimensional
Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson
brackets. The reduction to this paradigmatic Hamiltonian model is performed
using a Lie algebraic formalism which allows us to remain Hamiltonian at each
step of the derivation
Cooperativity in light scattering by cold atoms
A cloud of cold N two-level atoms driven by a resonant laser beam shows
cooperative effects both in the scattered radiation field and in the radiation
pressure force acting on the cloud center-of-mass. The induced dipoles
synchronize and the scattered light presents superradiant and/or subradiant
features. We present a quantum description of the process in terms of a master
equation for the atomic density matrix in the scalar, Born-Markov
approximations, reduced to the single-excitation limit. From a perturbative
approach for weak incident field, we derive from the master equation the
effective Hamiltonian, valid in the linear regime. We discuss the validity of
the driven timed Dicke ansatz and of a partial wave expansion for different
optical thicknesses and we give analytical expressions for the scattered
intensity and the radiation pressure force on the center of mass. We also
derive an expression for collective suppression of the atomic excitation and
the scattered light by these correlated dipoles.Comment: 15 pages, 8 figure
Intensity fluctuations signature of 3D Anderson localization of light
Apart from the difficulty of producing highly scattering samples, a major
challenge in the observation of Anderson localization of 3D light is
identifying an unambiguous signature of the phase transition in experimentally
feasible situations. In this letter we establish a clear correspondence between
the collapse of the conductance, the increase in intensity fluctuations at the
localization transition and the scaling analysis results based on the Thouless
number, thus connecting the macroscopic and microscopic approaches of
localization. Furthermore, the transition thus inferred is fully compatible
both with the results based on the eigenvalue analysis of the microscopic
description and with the effective-medium Ioffe-Regel criterion
Enhancement of particle trapping in the wave-particle interaction
The saturated dynamics of a Single-Pass Free Electron Laser is considered
within a simplified mean-field approach. A method is proposed to increase the
size of the macro-particle, which is responsible for the oscillations of the
intensity of the wave. This approach is based on the reconstruction of
invariant tori of the dynamics of test particles. To this aim a dedicated
control term is derived, the latter acting as a small apt perturbation of the
system dynamics. Implications of these findings are discussed in relation to
the optimization of the laser source
Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces
Inspired by one--dimensional light--particle systems, the dynamics of a
non-Hamiltonian system with long--range forces is investigated. While the
molecular dynamics does not reach an equilibrium state, it may be approximated
in the thermodynamic limit by a Vlasov equation that does possess stable
stationary solutions. This implies that on a macroscopic scale, the molecular
dynamics evolves on a slow timescale that diverges with the system size. At the
single-particle level, the evolution is driven by incoherent interaction
between the particles, which may be effectively modeled by a noise, leading to
a Brownian-like dynamics of the momentum. Because this self-generated diffusion
process depends on the particle distribution, the associated Fokker-Planck
equation is nonlinear, and a subdiffusive behavior of the momentum fluctuation
emerges, in agreement with numerics
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