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 $XY$ 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

Localization versus subradiance in three-dimensional scattering of light

We study the scattering modes of light in a three-dimensional disordered medium, in the scalar approximation and above the critical density for Anderson localization. Localized modes represent a minority of the total number of modes, even well above the threshold density, whereas spatially extended subradiant modes predominate. For specific energy ranges however, almost all modes are localized, yet adjusting accordingly the probe frequency does not allow to address these only in the regime accessible numerically. Finally, their lifetime is observed to be dominated by finite-size effects, and more specifically by the ratio of the localization length to their distance to the system boundaries.Comment: Add figure comparing localization percentage via frequency, fixed text, addition of Ioffe-Regel criterion limits, figure axis were normalize

Narrative and epistemology: Georges Canguilhem’s concept of scientific ideology

In the late 1960s, Georges Canguilhem introduced the concept of ‘scientific ideology’. This concept had not played any role in his previous work, so why introduce it at all? This is the central question of my paper. Although it may seem a rather modest question, its answer in fact uncovers hidden tensions in the tradition of historical epistemology, in particular between its normative and descriptive aspects. The term ideology suggests the influence of Althusser’s and Foucault’s philosophies. However, I show the differences between Canguilhem’s concept of scientific ideology and Althusser’s and Foucault’s respective concepts of ideology. I argue that Canguilhem was in fact attempting to solve long-standing problems in the tradition of historical epistemology, rather than following the lead of his younger colleagues. I argue that Canguilhem’s ‘refurbishment without rejection’ of Bachelard’s epistemology, which the concept of scientific ideology was aimed to implement, was necessary to justify the historical narratives that Canguilhem had constructed in his own work as a historian of concepts. A strict acceptance of Bachelard’s epistemology would have made it impossible to justify them. Canguilhem’s concept of scientific ideology therefore served as a theoretical justification of his practice as a historian. I maintain that the concept of scientific ideology was needed to reconcile Bachelard’s normative epistemology with Canguilhem’s view of the history of science and its aims, which differed from Bachelard’s more than it is generally acknowledged

Linear and Non-linear Rabi Oscillations of a Two-Level System Resonantly Coupled to an Anderson-Localized Mode

We use time-domain numerical simulations of a two-dimensional (2D) scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a small electric field intensity, we observe the strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a larger intensity induces non-linear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in non-linear Rabi oscillations. The transition between both regimes is observed and an analytical model is proposed which accurately describes our numerical observations.Comment: 11 pages, 6 figure

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