Back and forth from Fock space to Hilbert space: a guide for commuters

被引：7

作者：

Beggi, Andrea ^{[1
]}

Siloi, Ilaria ^{[2
]}

Benedetti, Claudia ^{[3
]}

Piccinini, Enrico ^{[4
]}

Razzoli, Luca ^{[5
]}

Bordone, Paolo ^{[5
]}

Paris, Matteo G. A. ^{[3
,6
]}

机构：

[1] IIS Primo Levi, I-41058 Vignola, Italy

[2] Univ North Texas, Dept Phys, Denton, TX 76201 USA

[3] Univ Milan, Quantum Technol Lab, Dipartimento Fis Aldo Pontremoli, I-20133 Milan, Italy

[4] Univ Bologna, Dipartimento Ingn Energia Elettr & Informaz Gugli, I-40136 Bologna, Italy

[5] Univ Modena & Reggio Emilia, Dipartimento Sci Fis Informat & Matemat, I-41125 Modena, Italy

[6] Inst Math Sci, CIT Campus, Madras 600113, Tamil Nadu, India

来源：

EUROPEAN JOURNAL OF PHYSICS | 2018年 / 39卷 / 06期

关键词：

identical particles; Fock space; Hilbert space; SYMMETRIZATION POSTULATE; SMALL VIOLATIONS; QUANTUM; PARTICLES; SEARCH; MODEL;

D O I：

10.1088/1361-6404/aad760

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

Quantum states of systems made of many identical particles, e.g. those described by Fermi-Hubbard and Bose-Hubbard models, are conveniently depicted in the Fock space. However, in order to evaluate some specific observables or to study system dynamics, it is often more effective to employ the Hilbert space description. Moving effectively from one description to the other is thus a desirable feature, especially when a numerical approach is needed. Here we recall the construction of the Fock space for systems of indistinguishable particles, and then present a set of recipes and advice for students and researchers with the need to commute back and forth from one description to the other. The two-particle case is discussed in some detail, and a few guidelines for numerical implementations are given.

引用

页数：19

共 30 条

[1] Probing the sign of the Hubbard interaction by two-particle quantum walks [J].