1,176 research outputs found

    The sound of violets: the ethnographic potency of poetry?

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    This paper takes the form of a dialogue between the two authors, and is in two halves, the first half discursive and propositional, and the second half exemplifying the rhetorical, epistemological and metaphysical affordances of poetry in critically scrutinising the rhetoric, epistemology and metaphysics of educational management discourse. Phipps and Saunders explore, through ideas and poems, how poetry can interrupt and/or illuminate dominant values in education and in educational research methods, such as: ‱ alternatives to the military metaphors – targets, strategies and the like – that dominate the soundscape of education; ‱ the kinds and qualities of the cognitive and feeling spaces that might be opened up by the shifting of methodological boundaries; ‱ the considerable work done in ethnography on the use of the poetic: anthropologists have long used poetry as a medium for expressing their sense of empathic connection to their field and their subjects, particularly in considering the creativity and meaning-making that characterise all human societies in different ways; ‱ the particular rhetorical affordances of poetry, as a discipline, as a practice, as an art, as patterned breath; its capacity to shift phonemic, and therewith methodological, authority; its offering of redress to linear and reductive attempts at scripting social life, as always already given and without alternative

    Coalescence of Anderson-localized modes at an exceptional point in 2D random media

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    In non-hermitian systems, the particular position at which two eigenstates coalesce under a variation of a parameter in the complex plane is called an exceptional point. A non-perturbative theory is proposed which describes the evolution of modes in 2D open dielectric systems when permittivity distribution is modified. We successfully test this theory in a 2D disordered system to predict the position in the parameter space of the exceptional point between two Anderson-localized states. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such an exceptional point is experimentally accessible in practically relevant disordered photonic systems. Losses are inherent to most physical systems, either because of dissipation or as a result of openness. These systems are described mathematically by a non-hermitian Hamiltonian, where eigenvalues are complex and eigen-states form a nonorthogonal set. In such systems, interaction between pairs of eigenstates when a set of external parameters is varied is essentially driven by the existence of exceptional points (EP). At an EP, eigenstates coa-lesce: Complex eigenvalues degenerate and spatial distributions become collinear. In its vicinity, eigenvalues display a singular topology [1] and encircling the EP in the parameter space leads to a residual geometrical phase [2, 3]. Since their introduction by Kato in 1966 [4], EPs have turned to be involved in a rich variety of physical effects: Level repulsion [5], mode hybridization [6], quantum phase transition [7], lasing mode switching [8], PT symmetry breaking [9, 10] or even strong coupling [11]. They have been observed experimentally in different systems such as microwave billiards [12], chaotic optical mi-crocavities [13] or two level atoms in high-Q cavities [11]. Open random media are a particular class of non-hermitian systems. Here, modal confinement may be solely driven by the degree of scattering. For sufficiently strong scattering, the spatial extension of the modes becomes smaller than the system size, resulting in transport inhibition and Anderson localization [14]. Disordered-induced localized states have raised increasing interest. They provide with natural optical cavities in random lasers [15, 16]. They recently appeared to be good candidate for cavity QED [17, 18], with the main advantage of being inherently disorder-robust. These modes can be manipulated by a local change of the disorder and can be coupled to form necklace states [19-21], which open channels in a nominally localized system [22, 23]. These necklace states are foreseen as a key mechanism in the transition from localization to diffusive regime [24]. PT symmetry has been studied in the context of disordered media and Anderson localization [25-27] but so far EPs between localized modes have not been investigated. In this letter, coalescence at an EP between two Anderson-localized optical modes is demonstrated in a two dimensional (2D) dielectric random system. To bring the system in the vicinity of an EP, the dielectric permit-tivity is varied at two different locations in the random system. We first propose a general theory to follow the spectral and spatial evolution of modes in 2D dielectric open media. This theory is applied to the specific case of Anderson-localized modes to identify the position of an EP in the parameter space. This prediction is confirmed by Finite Element Method (FEM) simulations. We show that this is a highly complex problem of multiple mode interaction where a large number of modes are involved. We believe that our theory opens the way to a controlled local manipulation of the permittivity and the possibility to engineer the modes. Furthermore, we think this approach can be easily extended to others kinds of networks e.g. coupled arrays of cavities [28, 29]. We first consider the general case of a finite-size dielec-tric medium in 2D space, with inhomogeneous dielectric constant distribution, Ç«(r). In the frequency domain, the electromagnetic field follows the Helmholtz equation: ∆E(r, ω) + Ç«(r)ω 2 E(r, ω) = 0 (1) where E(r, ω) stands for the electrical field and the speed of light, c = 1. Eigensolutions of eq. (1), define the modes or eigenstates of the problem: (℩ i , |Κ i) i∈N | ∆|Κ i + Ç«(r)℩ 2 i |Κ i = 0 (2) Because of its openness, the system has inherent losses, thus is described by a non-hermitian Hamiltonian. For non-hermitian systems, modes are a priori non-orthogonal, complex and their completeness is not ensured. Here, we consider open systems with finite range permittivity Ç«(r) and where a discontinuity in the permit-tivity provides a natural demarcation of the problem. Fo

    Targeted mixing in an array of alternating vortices

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    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

    Resonances in Mie scattering by an inhomogeneous atomic cloud

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    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

    Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems

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    Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called "exactness of the mean-field theory". It is found out that this expectation is not necessarily true if the microcanonical ensemble is not equivalent to the canonical ensemble in the mean-field model. Moreover, necessary and sufficient conditions for exactness of the mean-field theory are obtained. These conditions are investigated for two concrete models, the \alpha-Potts model with annealed vacancies and the \alpha-Potts model with invisible states.Comment: 23 pages, to appear in J. Stat. Phy

    Phase transitions of quasistationary states in the Hamiltonian Mean Field model

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    The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell's theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.Comment: 6 pages, 7 figure
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