General mapping for bosonic and fermionic operators in Fock space

Alexej I. Streltsov, Ofir E. Alon, Lorenz S. Cederbaum

Research output: Contribution to journalArticlepeer-review


In this article, we provide an alternative and general way to construct the result of the action of any particle-conserving bosonic or fermionic operator represented in second quantized form on a state vector, without resorting to the matrix representation of operators or even its elements. This approach is based on our proposal to compactly enumerate the configurations (i.e., determinants for fermions, permanents for bosons) that are the elements of the state vector. This extremely simplifies the calculation of the action of an operator on a state vector. The computations of statical properties and the evolution dynamics of a system become much more efficient, and applications to systems made of more particles become feasible. Explicit formulations are given for spin-polarized fermionic systems and spinless bosonic systems, as well as to general (two-component) fermionic systems, two-component bosonic systems, and mixtures thereof.

Original languageEnglish
Article number022124
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
StatePublished - 26 Feb 2010
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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