A linear response function for zonal flows is obtained by solving the gyro-kinetic equation. This is an extension of a previous work which adopted the method of ＂integrating along particle orbit＂ to solve the drift ...A linear response function for zonal flows is obtained by solving the gyro-kinetic equation. This is an extension of a previous work which adopted the method of ＂integrating along particle orbit＂ to solve the drift kinetic equation. The formula derived in this paper is used to calculate the dispersion relation of geodesic acoustic mode, which is then compared with that of the gyro-kinetic analytic formula.展开更多
Let W be a real symplectic space and(G,G')an irreducible dual pair in Sp(W),in the sense of Howe,with G compact.Let G be the preimage of G in the metaplectic group Sp(W).Given an irreducible unitary representation...Let W be a real symplectic space and(G,G')an irreducible dual pair in Sp(W),in the sense of Howe,with G compact.Let G be the preimage of G in the metaplectic group Sp(W).Given an irreducible unitary representation II of G that occurs in the restriction of the Weil representation to G,let On denote its character.We prove that,for a suitable embedding T of Sp(W)in the space of tempered distributions on W,the distribution T(On)admits an asymptotic limit,and the limit is a nilpotent orbital integral.As an application,we compute the wave front set of II',the representation of G dual to II,by elementary means.展开更多
基金partially supported by the JSPS-CAS Core-University program in the field of 'Plasma and Nuclear Fusion'
文摘A linear response function for zonal flows is obtained by solving the gyro-kinetic equation. This is an extension of a previous work which adopted the method of ＂integrating along particle orbit＂ to solve the drift kinetic equation. The formula derived in this paper is used to calculate the dispersion relation of geodesic acoustic mode, which is then compared with that of the gyro-kinetic analytic formula.
基金the University of Oklahoma for hospitality and financial supporthospitality and financial support from the Université de Lorraine+1 种基金partial support from NSA (Grant No. H98230-13-1-0205)NSF (Grant No. DMS-2225892)
文摘Let W be a real symplectic space and(G,G')an irreducible dual pair in Sp(W),in the sense of Howe,with G compact.Let G be the preimage of G in the metaplectic group Sp(W).Given an irreducible unitary representation II of G that occurs in the restriction of the Weil representation to G,let On denote its character.We prove that,for a suitable embedding T of Sp(W)in the space of tempered distributions on W,the distribution T(On)admits an asymptotic limit,and the limit is a nilpotent orbital integral.As an application,we compute the wave front set of II',the representation of G dual to II,by elementary means.
