99 research outputs found

### Bernstein modes in a weakly relativistic electron-positron plasma

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

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 $\gamma=5/3$ 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

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

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

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

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 $\varepsilon\ll 1$ controls the separation of time
scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in
which the slow and fast degrees of freedom decouple. At the same time
$\varepsilon\to 0$ 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 $\varepsilon^2$. 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

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
$m_{1/2}$, the universal scalar mass $m_0$ and the coupling $A$. 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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