27,621 research outputs found
Finiteness of irreducible holomorphic eta quotients of a given level
We show that for any positive integer N, there are only finitely many holomorphic eta quotients of level N, none of which is a product of two holomorphic eta quotients other than 1 and itself. This result is an analog of Zagier’s conjecture/Mersmann’s theorem which states that of any given weight, there are only finitely many irreducible holomorphic eta quotients, none of which is an integral rescaling of another eta quotient. We construct such eta quotients for all cubefree levels. In particular, our construction demonstrates the existence of irreducible holomorphic eta quotients of arbitrarily large weights
Stereochemical properties of the OH molecule in combined electric and magnetic fields: analytic results
The stereochemical properties of the ultracold ground state OH molecule in
the presence of electric and magnetic fields are currently of considerable
interest. For example, relevant quantities such as molecular alignment and
orientation, calculated numerically by using large basis sets, have lately
appeared in the literature. In this work, based on our recent exact solution to
an effective eight-dimensional matrix Hamiltonian for the molecular ground
state, we present analytic expressions for the stereochemical properties of OH.
Our results require the solution of algebraic equations only, agree well with
the aforementioned fully numerical calculations, provide compact expressions
for simple field geometries, allow ready access to relatively unexplored
parameter space, and yield straightforwardly higher moments of the molecular
axis distribution.Comment: 8 pages, 9 figure
Characterization of soft stripe-domain deformations in Sm-C and Sm-C* liquid-crystal elastomers
The neoclassical model of Sm-C (and Sm-C*) elastomers developed by Warner and Adams predicts a class of “soft” (zero energy) deformations. We find and describe the full set of stripe domains—laminate structures in which the laminates alternate between two different deformations—that can form between pairs of these soft deformations. All the stripe domains fall into two classes, one in which the smectic layers are not bent at the interfaces, but for which—in the Sm-C* case—the interfaces are charged, and one in which the smectic layers are bent but the interfaces are never charged. Striped deformations significantly enhance the softness of the macroscopic elastic response
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