arXiv:1010.5773 · Open Physics

High-order connected moments expansion for the Rabi Hamiltonian

Paolo Amore, Francisco Marcelo Fernández, Martin Rodriguez-Vega

Published Nov 11, 2011• 3 citations

Abstract

Abstract We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large-order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.

DOI: 10.2478/s11534-011-0101-9

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arXiv:1010.5773 · Open Physics

High-order connected moments expansion for the Rabi Hamiltonian

Paolo Amore, Francisco Marcelo Fernández, Martin Rodriguez-Vega

Published Nov 11, 2011• 3 citations

arXiv HTML PDF

Abstract

DOI: 10.2478/s11534-011-0101-9

Related papers

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Jerzy Ciosłowski

Physical Review AOct 1, 198719 citations

The

t

-expansion method for calculating ground-state energies of Hamiltonian systems is generalized to excited states. We introduce quantities

{M}_{n}(t)

and

{D}_{n}(t)

which for $t\ensuremath{\rightarrow}\ensuremath{\infty}$ converge to ${\ensuremath{\Sigma}}_{n}={E}_{0}+{E}_{1}+\dots{}+{E}_{n}$ and ${\ensuremath{\Delta}}_{n}={E}_{n+1}\ensuremath{-}{E}_{n}$, respectively. Like in the standard

t

-expansion, the

t

-series for

{M}_{n}(t)

and

{D}_{n}(t)

are constructed from moments of the Hamiltonian. The values of ${\ensuremath{\Sigma}}_{n}$ and ${\ensuremath{\Delta}}_{n}$ can then be estimated using (e.g.) a generalization of the connected-moment expansion of Cioslowski.