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We study theoretically the exchange of angular momentum between electromagnetic and electrostatic waves in a plasma, due to the stimulated Raman and Brillouin backscattering processes. Angular momentum states for plasmon and phonon fields are introduced for the first time. We demonstrate that these states can be excited by nonlinear wave mixing, associated with the scattering processes. This could be relevant for plasma diagnostics, both in laboratory and in space. Nonlinearly coupled paraxial equations and instability growth rates are derived. PACS numbers:It is well known that the angular momentum of electromagnetic radiation contains two distinct parts, one associated with its polarization state, or photon spin, the other being the external or orbital photon angular momentum (OAM). With the advent of laser beams, an increasing interest is being given to the study of photon OAM, and various optical experimental configurations have been considered [1,2,3,4]. It is now well understood that collimated electromagnetic beams, such as laser or radio wave beams, can be described by LaguerreGaussian functions, which provide a natural orthonormal basis for a generic beam representation. Utilization of photon OAM states in the low frequency (≤ GHz) radio wave domain was also recently proposed in Ref. 5, as a new method for studying and characterizing radio sources in astrophysics.The possibility of remote study of space plasma vorticity by measuring the OAM of radio beams interacting with vortical plasmas was pointed out in Ref. 6, and a more detailed theoretical analysis was given recently by studying the electromagnetic wave scattering from the plasma medium, with the associated OAM exchanges between the plasma and probing photon beams [7]. A more speculative work was also recently published where the strong similarities between photon and neutrino dispersion relations were explored, and OAM states of neutrino beams interacting with dense plasmas were considered [8].Here we consider the important problem of stimulated Raman and Brillouin backscattering of collimated electromagnetic beams with finite OAM in a plasma. This also leads us to consider, to our knowledge for the first * Electronic address: titomend@ist.utl.pt † Also at LOIS Space Centre, Växjö University, SE-351 95 Växjö, Sweden time, the possible existence of plasmon and phonon states with finite orbital angular momentum. Raman and Brillouin scattering instabilities are well known in the context of laser fusion [9], as possible sources of anomalous plasma reflectivity. Raman backscattering is now recognized as a dominant process for ultra-intense laser plasma interactions, in the context of inertial fusion research [10]. In all these studies, angular momentum in general, and photon OAM in particular, have been systematically ignored. On the other hand, there seems to be experimental evidence of OAM dependence in Brillouin scattering of radio waves in the ionosphere [11], which awaits for a deeper theoretical understanding. In contrast with the traditional t...

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nanoscale system from one equilibrium state to another in finite time, Schmiedl and Seifert ͓T. Schmiedl and U. Seifert, Phys. Rev. Lett. 98, 108301 ͑2007͔͒ found the Euler-Lagrange equation to be a nonlocal integrodifferential equation of correlation functions. For two linear examples, we show how this integrodifferential equation can be solved analytically. For nonlinear physical systems we show how the optimal protocol can be found numerically and demonstrate that there may exist several distinct optimal protocols simultaneously, and we present optimal protocols that have one, two, and three jumps, respectively.

We analyse the anisotropy of the cosmic microwave background (CMB) in hyperbolic universes possessing a non-trivial topology with a fundamental cell having an infinitely long horn. The aim of this paper is twofold. On the one hand, we show that the horned topology does not lead to a flat spot in the CMB sky maps in the direction of the horn as stated in the literature. On the other, we demonstrate that a horned topology having a finite volume could explain the suppression of the lower multipoles in the CMB anisotropy as observed by 98.70.Vc, 98.80.Es

For any square-free integer N such that the "moonshine group" Γ 0 (N ) + has genus zero, the Monstrous Moonshine Conjectures relate the Hauptmoduli of Γ 0 (N ) + to certain McKay-Thompson series associated to the representation theory of the Fischer-Griess monster group. In particular, the Hauptmoduli admits a q-expansion which has integer coefficients. In this article, we study the holomorphic function theory associated to higher genus moonshine groups Γ 0 (N ) + . For all moonshine groups of genus up to and including three, we prove that the corresponding function field admits two generators whose q-expansions have integer coefficients, has lead coefficient equal to one, and has minimal order of pole at infinity. As corollary, we derive a polynomial relation which defines the underlying projective curve, and we deduce whether i∞ is a Weierstrass point. Our method of proof is based on modular forms and includes extensive computer assistance, which, at times, applied Gauss elimination to matrices with thousands of entries, each one of which was a rational number whose numerator and denominator were thousands of digits in length.

We derive a fluctuation theorem for generalized work distributions, related to bijective mappings of the phase spaces of two physical systems, and use it to derive a two-sided constraint maximum likelihood estimator of their free-energy difference which uses samples from the equilibrium configurations of both systems. As an application, we evaluate the chemical potential of a dense Lennard-Jones fluid and study the construction and performance of suitable maps.

In this paper we study, both analytically and numerically, questions involving the distribution of eigenvalues of Maass forms on the moonshine groups Γ 0 (N ) + , where N > 1 is a square-free integer. After we prove that Γ 0 (N ) + has one cusp, we compute the constant term of the associated non-holomorphic Eisenstein series. We then derive an "average" Weyl's law for the distribution of eigenvalues of Maass forms, from which we prove the "classical" Weyl's law as a special case. The groups corresponding to N = 5 and N = 6 have the same signature; however, our analysis shows that, asymptotically, there are infinitely more cusp forms for Γ 0 (5) + than for Γ 0 (6) + . We view this result as being consistent with the Phillips-Sarnak philosophy since we have shown, unconditionally, the existence of two groups which have different Weyl's laws. In addition, we employ Hejhal's algorithm, together with recently developed refinements from [31], and numerically determine the first 3557 of Γ 0 (5) + and the first 12474 eigenvalues of Γ 0 (6) + . With this information, we empirically verify some conjectured distributional properties of the eigenvalues.

Abstract. We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r = 40000. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130millionth eigenvalue.