99 research outputs found

    Lagrangian formulation of neoclassical transport theory

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    Breakdown of Onsager symmetry in neoclassical transport theory

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    Bernstein modes in a weakly relativistic electron-positron plasma

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    The kinetic theory of weakly relativistic electron-positron plasmas, producing dispersion relations for the electrostatic Bernstein modes was addressed. The treatment presented preserves the full momentum dependence of the cyclotron frequency, albeit with a relaxation on the true relativistic form of the distribution function. The implications of this new treatment were confined largely to astrophysical plasmas, where relativistic electronpositron plasmas occur naturally

    Non-stationary Rayleigh-Taylor instability in supernovae ejecta

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    The Rayleigh-Taylor instability plays an important role in the dynamics of several astronomical objects, in particular, in supernovae (SN) evolution. In this paper we develop an analytical approach to study the stability analysis of spherical expansion of the SN ejecta by using a special transformation in the co-moving coordinate frame. We first study a non-stationary spherical expansion of a gas shell under the pressure of a central source. Then we analyze its stability with respect to a no radial, non spherically symmetric perturbation of the of the shell. We consider the case where the polytropic constant of the SN shell is =5/3\gamma=5/3 and we examine the evolution of a arbitrary shell perturbation. The dispersion relation is derived. The growth rate of the perturbation is found and its temporal and spatial evolution is discussed. The stability domain depends on the ejecta shell thickness, its acceleration, and the perturbation wavelength.Comment: 16 page

    A sharp stability criterion for the Vlasov-Maxwell system

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    We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria

    Hard-Loop Effective Action for Anisotropic Plasmas

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    We generalize the hard-thermal-loop effective action of the equilibrium quark-gluon plasma to a non-equilibrium system which is space-time homogeneous but for which the parton momentum distribution is anisotropic. We show that the manifestly gauge-invariant Braaten-Pisarski form of the effective action can be straightforwardly generalized and we verify that it then generates all n-point functions following from collisionless gauge-covariant transport theory for a homogeneous anisotropic plasma. On the other hand, the Taylor-Wong form of the hard-thermal-loop effective action has a more complicated generalization to the anisotropic case. Already in the simplest case of anisotropic distribution functions, it involves an additional term that is gauge invariant by itself, but nontrivial also in the static limit.Comment: 12 pages. Version 3: typo in (15) corrected, note added discussing metric conventions use

    Small BGK waves and nonlinear Landau damping

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    Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

    Semiclassical approximations for Hamiltonians with operator-valued symbols

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    We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter 1\varepsilon\ll 1 controls the separation of time scales and the limit 0\varepsilon\to 0 corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time 0\varepsilon\to 0 is the semiclassical limit for the slow degrees of freedom. In this paper we show that the \varepsilon-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an \epsi-dependent classical Hamilton function and an \varepsilon-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order 2\varepsilon^2. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was remove

    Neutralino Dark Matter in a Class of Unified Theories

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    The cosmological significance of the neutralino sector is studied for a class of models in which electroweak symmetry breaking is seeded by a gauge singlet. Extensive use is made of the renormalisation group equations to significantly reduce the parameter space, by deriving analytic expressions for all the supersymmetry-breaking couplings in terms of the universal gaugino mass m1/2m_{1/2}, the universal scalar mass m0m_0 and the coupling AA. The composition of the LSP is determined exactly below the W mass, no approximations are made for sfermion masses, and all particle exchanges are considered in calculating the annihilation cross-section; the relic abundance is then obtained by an analytic approximation. We find that in these models, stable neutralinos may make a significant contribution to the dark matter in the universe.Comment: 24 Pages, OUTP-92-10
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