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Allan I. Solomon

Publications and source records attributed to Allan I. Solomon.

23 records · Page 2Linked to original sources
arXiv2002

Combinatorics of Boson Normal Ordering: the Dobinski Formula Revisited

We derive explicit formulas for the normal ordering of powers of arbitrary monomials of boson operators. These formulas lead to generalisations of conventional Bell and Stirling numbers and to appropriate generalisations of the Dobinski relations. These new combinatorial numbers are shown to be coherent state matrix elements of powers of the monomials in question. It is further demonstrated that such Bell-type numbers, when considered as power moments, give rise to positive measures on the positive half-axis, which in many cases can be written in terms of known functions.

quant-ph↗
arXiv1997

Dynamical Group for the Quantum Hall Effect

A dynamical group for the single-particle (non-interacting) Quantum Hall Effect is found, and used to describe the Landau levels and determine the transverse (Hall) current.

cond-mat.mes-hall↗
arXiv1997

Coherent pairing states for the Hubbard model

We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the $η$-pairing operators introduced by C.N.Yang, and define coherent pairing states, which are combinations of eigenfunctions of $η$-operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing ODLRO to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.

cond-mat.str-el↗
arXiv1997

Optimal Signal-to-Quantum Noise Ratio for Nonclassical Number States

We analyze the properties of nonclassical number states, specifically squeezed number states D(a)S(z)|n >, and find their maximum signal-to-quantum noise ratio. It is shown that the optimal signal-to-quantum noise ratio for these states decreases as 1/(2n+1)2, where n is the photon number, from the optimal value as derived by Yuen.

quant-ph↗