Exact trace formulas for a class of one-dimensional ray-splitting systems

Exact trace formulae for a class of one-dimensional ray-splitting systems

Based on quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman et al. (Phys. Rev. A 46, 6193 (1992)) is exact for a class of one-dimensional ray-splitting systems. Important applications in combinatorics are suggested. PACS: 05.45.+b,03.65.Sq,72.15.Rn

A CNF Class Generalizing Exact Linear Formulas

Combinatorial identities for binary necklaces from exact ray-splitting trace formulae

Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (Pólya necklaces). 02.10.Eb, 02.30.Lt, 05.45.+b Typeset using REVTEX 1

Trace formulas and class number sums

We specialize the Eichler-Selberg trace formula to obtain trace formulas for the prime-to-level Hecke action on cusp forms for certain congruence groups of arbitrary level. As a consequence, we determine the asymptotic in the prime p of the number of (weighted) SL2(Z)-conjugation orbits of 2 × 2 matrices of determinant p whose reductions modulo N lie in a given conjugacy class in GL2(Z/NZ). Thi...

Exact results for anomalous transport in one-dimensional hamiltonian systems.

Anomalous transport in one-dimensional translation invariant hamiltonian systems with short range interactions is shown to belong in general to the Kardar-Parisi-Zhang universality class. Exact asymptotic forms for density-density and current-current time correlation functions and their Fourier transforms are given in terms of the Prähofer-Spohn scaling functions, obtained from their exact solu...