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The semiclassical density of states for the quantum asymmetric top
 Journal of Physics. A. Mathematical and Theoretical
"... In the quantization of a rotating rigid body, a top, one is concerned with the Hamiltonian operator Lα = α 2 0L 2 x + α 2 1L 2 y + α 2 2L 2 z, where α0 < α1 < α2. An explicit formula is known for the eigenvalues of Lα in the case of the spherical top (α1 = α2 = α3) and symmetrical top (α1 = α2 ̸= α3 ..."
Abstract

Cited by 2 (1 self)
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In the quantization of a rotating rigid body, a top, one is concerned with the Hamiltonian operator Lα = α 2 0L 2 x + α 2 1L 2 y + α 2 2L 2 z, where α0 < α1 < α2. An explicit formula is known for the eigenvalues of Lα in the case of the spherical top (α1 = α2 = α3) and symmetrical top (α1 = α2 ̸= α3) [LL]. However, for the asymmetrical top, no such explicit expression exists, and the study of the spectrum is much more complex. In this paper, we compute the semiclassical density of states for the eigenvalues of the family of operators Lα = α 2 0L 2 x+α 2 1L 2 y+α 2 2L 2 z for any α0 < α1 < α2. 1
ZETA FUNCTIONS FOR HYPERBOLIC SURFACES
, 2006
"... These are uncorrected notes from some informal lectures I gave in Manchester in May 2006. For more details (except on the last section) see [PP90] or the survey in [Ma04] (this has more recent things but not the most recent things). Closed Geodesics and Zeta Functions Let M = H 2 /Γ a “convex cocom ..."
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These are uncorrected notes from some informal lectures I gave in Manchester in May 2006. For more details (except on the last section) see [PP90] or the survey in [Ma04] (this has more recent things but not the most recent things). Closed Geodesics and Zeta Functions Let M = H 2 /Γ a “convex cocompact ” hyperbolic surface consisting of a compact core and, possibly, a finite number of infinite volume funnels. We do not allow M to have cusps. (More formally, Γ is convex cocompact if (convex.hull(LΓ))/Γ is compact, where LΓ is the limit set of Γ.) We exclude the possibility that Γ is elementary (i.e. virtually cyclic). The closed geodesics on M are is onetoone correspondence with the nontrivial conjugacy classes in π1M ∼ = Γ. Let CG denote the (countably infinite) set of closed geodesics on M and let PCG denote the set of prime closed geodesics on M (i.e. those which are not multiples of another closed geodesic. We write lγ for the length of γ ∈ CG. For each x ≥ 0, #{γ ∈ PCG (or CG) : lγ ≤ x} is finite. We shall consider the zeta function ζM (s) = γ∈PCG 1 − e
Nearestλqmultiple fractions
, 902
"... Abstract. We discuss the nearestλq–multiple continued fractions and their duals forλq = 2 cos () π q which are closely related to the Hecke triangle groups Gq, q=3, 4,.... They have been introduced in the case q=3 by Hurwitz and for even q by Nakada. These continued fractions are generated by interv ..."
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Abstract. We discuss the nearestλq–multiple continued fractions and their duals forλq = 2 cos () π q which are closely related to the Hecke triangle groups Gq, q=3, 4,.... They have been introduced in the case q=3 by Hurwitz and for even q by Nakada. These continued fractions are generated by interval maps fq respectively f ⋆ q which are conjugate to subshifts over infinite alphabets. We generalize to arbitrary q a result of Hurwitz concerning the Gq and fqequivalence of points on the real line. The natural extension of the maps fq and f ⋆ q can be used as a Poincaré map for the geodesic flow on the Hecke surfaces Gq\H and allows to construct the transfer operator for this flow. Contents