CHEMISTRY: Odd Electron Chains

Normal form for odd periodic FPU chains

In this paper we prove that near the equilibirum position any periodic FPU chain with an odd number of particles admits a Birkhoff normal form up to order 4, and we obtain an explicit formula of the Hessian of its Hamiltonian at the fixed point.

Crystal chemistry of silica - rich barium silicates II : Electron microscopy of barium silicates containing multiple chains

The phases containing multiple chains in the series Ba",+1[Si2mOsm+d those with triple (m = 3), quadruple (m = 4) and quintuple (m = 5) tetrahedral chains were investigated by high resolution transmission electron microscopy. The resulting images could be correlated with the structures. Variations of the chain multiplicity (m) within single crystals were observed as well as faults in the packin...

Electron controlled chemistry

Effective chiral-spin Hamiltonian for odd-numbered coupled Heisenberg chains.

An L×∞ system of odd number of coupled Heisenberg spin chains is studied using a degenerate perturbation theory, where L is the number of coupled chains. An effective chain Hamiltonian is derived explicitly in terms of two spin half degrees of freedom of a closed chain of L sites, valid in the regime the inter-chain coupling is stronger than the intra-chain coupling. The spin gap has been calcu...

Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

H.E. Boos1 Institute for High Energy Physics Protvino, 142284, Russia V.E. Korepin 2 C.N. Yang Institute for Theoretical Physics State University of New York at Stony Brook Stony Brook, NY 11794{3840, USA Abstract Riemann zeta function is an important object of number theory. We argue that it is related to Heisenberg spin 1/2 anti-ferromagnet. In the XXX spin chain we study the probability of f...