arXiv subjects

Romain Bachelard

Publications and source records attributed to Romain Bachelard.

72 records · Page 4Linked to original sources

arXiv2013

Universal threshold for the dynamical behavior of lattice systems with long-range interactions

Dynamical properties of lattice systems with long-range pair interactions, decaying like 1/r^α with the distance r, are investigated, in particular the time scales governing the relaxation to equilibrium. Upon varying the interaction range α, we find evidence for the existence of a threshold at α=d/2, dependent on the spatial dimension d, at which the relaxation behavior changes qualitatively and the corresponding scaling exponents switch to a different regime. Based on analytical as well as numerical observations in systems of vastly differing nature, ranging from quantum to classical, from ferromagnetic to antiferromagnetic, and including a variety of lattice structures, we conjecture this threshold and some of its characteristic properties to be universal.

cond-mat.stat-mech↗

arXiv2012

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.

cond-mat.stat-mech↗

arXiv2012

The role of Mie scattering in the seeding of matter-wave superradiance

Matter-wave superradiance is based on the interplay between ultracold atoms coherently organized in momentum space and a backscattered wave. Here, we show that this mechanism may be triggered by Mie scattering from the atomic cloud. We show how the laser light populates the modes of the cloud, and thus imprints a phase gradient on the excited atomic dipoles. The interference with the atoms in the ground state results in a grating, that in turn generates coherent emission, contributing to the backward light wave onset. The atomic recoil 'halos' created by the scattered light exhibit a strong anisotropy, in contrast to single-atom scattering.

physics.atom-ph↗

arXiv2012

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.

physics.atom-ph↗

arXiv2011

Resonances in Mie scattering by an inhomogeneous atomic cloud

Despite the quantum nature of the process, collective scattering by dense cold samples of two-level atoms can be interpreted classically describing the sample as a macroscopic object with a complex refractive index. We demonstrate that resonances in Mie theory can be easily observable in the cooperative scattering by tuning the frequency of the incident laser field or the atomic number. The solution of the scattering problem is obtained for spherical atomic clouds who have the parabolic density characteristic of BECs, and the cooperative radiation pressure force calculated exhibits resonances in the cloud displacement for dense clouds. At odds from uniform clouds which show a complex structure including narrow peaks, these densities show resonances, yet only under the form of quite regular and contrasted oscillations.

physics.optics↗

arXiv2011

Cooperative scattering and radiation pressure force in dense atomic clouds

We consider the collective scattering by a cloud of $N$ two-level atoms driven by an uniform radiation field. Dense atomic clouds can be described by a continuous density and the problem reduces to deriving the spectrum of the atom-atom coupling operator. For clouds much larger than the optical wavelength, the spectrum is treated as a continuum, and analytical expressions for several macroscopic quantities, such as scattered radiation intensity and radiation pressure force, are derived. The analytical results are then compared to the exact $N$-body solution and with those obtained assuming a symmetric timed Dicke state. In contrast with the symmetric timed Dicke state, our calculations takes account of the back action of the atoms on the driving field leading to phase shifts due to the finite refraction of the cloud.

physics.optics↗

arXiv2011

Vlasov equation for long-range interactions on a lattice

We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state and a dispersion relation, that depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turn out to depend on the mode number. When this state is unstable, the growth rates are also function of the mode number. Explicit calculations are performed for the $α$-HMF model with $0 \leq α<1$, for which the zero mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.

nlin.CD↗

arXiv2011

Stability of inhomogeneous states in mean-field models with a local potential

The Vlasov equation is well known to provide a good description of the dynamics of mean-field systems in the $N \to \infty$ limit. This equation has an infinity of stationary states and the case of {\it homogeneous} states, for which the single-particle distribution function is independent of the spatial variable, is well characterized analytically. On the other hand, the inhomogeneous case often requires some approximations for an analytical treatment: the dynamics is then best treated in action-angle variables, and the potential generating inhomogeneity is generally very complex in these new variables. We here treat analytically the linear stability of toy-models where the inhomogeneity is created by an external field. Transforming the Vlasov equation into action-angle variables, we derive a dispersion relation that we accomplish to solve for both the growth rate of the instability and the stability threshold for two specific models: the Hamiltonian Mean-Field model with additional asymmetry and the mean-field $ϕ^4$ model. The results are compared with numerical simulations of the $N$-body dynamics. When the {\it inhomogeneous} state is stationary, we expect to observe in the $N$-body dynamics Quasi-Stationary-States (QSS), whose lifetime diverge algebraically with $N$.

cond-mat.stat-mech↗

arXiv2010

Experimental perspectives for systems based on long-range interactions

The possibility of observing phenomena peculiar to long-range interactions, and more specifically in the so-called Quasi-Stationary State (QSS) regime is investigated within the framework of two devices, namely the Free-Electron Laser (FEL) and the Collective Atomic Recoil Laser (CARL). The QSS dynamics has been mostly studied using the Hamiltonian Mean-Field (HMF) toy model, demonstrating in particular the presence of first versus second order phase transitions from magnetized to unmagnetized regimes in the case of HMF. Here, we give evidence of the strong connections between the HMF model and the dynamics of the two mentioned devices, and we discuss the perspectives to observe some specific QSS features experimentally. In particular, a dynamical analog of the phase transition is present in the FEL and in the CARL in its conservative regime. Regarding the dissipative CARL, a formal link is established with the HMF model. For both FEL and CARL, calculations are performed with reference to existing experimental devices, namely the FERMI@Elettra FEL under construction at Sincrotrone Trieste (Italy) and the CARL system at LENS in Florence (Italy).

nlin.CD↗

arXiv2010

Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction

The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g., electrostatic instabilities in plasma physics, particle acceleration and free-electron lasers (FELs). The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent relaxation theory. In the context of free-electron lasers, such a theory is showed to be effective in predicting the saturated regime for energies below the transition. The transition is explained as a dynamical switch between two metastable regimes, and is related to the properties of a stationary point of an entropic functional.

physics.plasm-ph↗

arXiv2009

Analytical results on the magnetization of the Hamiltonian Mean Field model

The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high and low energy limits are investigated and the analytical predictions are compared with direct $N$-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.

nlin.CD↗

arXiv2009

Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems

We investigate the dynamics of many-body long-range interacting systems, taking the Hamiltonian Mean Field model as a case study. We show that an abundance of regular trajectories, associated with invariant tori of the single-particle dynamics, exists. The presence of such tori provides a dynamical interpretation of the emergence of long-lasting out-of-equilibrium regimes observed generically in long-range systems. This is alternative to a previous statistical mechanics approach to such phenomena which was based on a maximum entropy principle. Previously detected out-of-equilibrium phase transitions are also reinterpreted within this framework.

cond-mat.stat-mech↗

arXiv2008

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.

physics.plasm-ph↗

arXiv2007

Targeted mixing in an array of alternating vortices

Transport and mixing properties of passive particles advected by an array of vortices are investigated. Starting from the integrable case, it is shown that a special class of perturbations allows one to preserve separatrices which act as effective transport barriers, while triggering chaotic advection. In this setting, mixing within the two dynamical barriers is enhanced while long range transport is prevented. A numerical analysis of mixing properties depending on parameter values is performed; regions for which optimal mixing is achieved are proposed. Robustness of the targeted mixing properties regarding errors in the applied perturbation are considered, as well as slip/no-slip boundary conditions for the flow.

nlin.CD↗

arXiv2007

Short-time dynamics in presence of wave-particles interactions: a perturbative approach

The self-consistent interaction between a beam of charged particles and a wave is considered, within a Vlasov picture. The model is discussed with reference to the case of a Free Electron Laser. Starting with a spatially bunched waterbag distribution, we derive, via perturbative methods, closed analytical expressions for the time evolution of the main macroscopic observables. Predictions of the theory are shown to agree with direct numerical simulations.

math-ph↗

arXiv2007

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.

nlin.CD↗

arXiv2006

Stabilizing the intensity of a wave amplified by a beam of particles

The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles as in a free electron laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article, we propose a strategy to stabilize the intensity by re-shaping the macro-particle. This strategy involves the study of the linear stability (using the residue method) of selected periodic orbits of a mean-field model. As parameters of an additional perturbation are varied, bifurcations occur in the system which have drastic effect on the modification of the self-consistent dynamics, and in particular, of the macro-particle. We show how to obtain an appropriate tuning of the parameters which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.

nlin.CD↗

arXiv2006

Reducing or enhancing chaos using periodic orbits

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.

nlin.CD↗