General mapping for bosonic and fermionic operators in Fock space

• Verfasst von: Streltsov, Alexej Iwanowitsch [VerfasserIn]
• Verfasst von: Alon, Ofir E. [VerfasserIn]
• Verfasst von: Cederbaum, Lorenz S. [VerfasserIn]
• Titel: General mapping for bosonic and fermionic operators in Fock space
• Verf.angabe: Alexej I. Streltsov, Ofir E. Alon, and Lorenz S. Cederbaum
• E-Jahr: 2010
• Jahr: 26 February 2010
• Umfang: 12 S.
• Fussnoten: Gesehen am 01.09.2023
• Titel Quelle: Enthalten in: Physical review / A
• Ort Quelle: College Park, Md., 1970
• Jahr Quelle: 2010
• Band/Heft Quelle: 81(2010), 2, Artikel-ID 022124, Seite 1-12
• ISSN Quelle: 1094-1622
• DOI: doi:10.1103/PhysRevA.81.022124
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 185850564X

Abstract

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.