Suzuki type estimates for exponentiated sums and generalized Lie-Trotter formulas in JB-algebras

被引：2

作者：

Chehade, Sarah ^{[1
]}

Wang, Shuzhou ^{[2
]}

Wang, Zhenhua ^{[2
,3
]}

机构：

[1] Oak Ridge Natl Lab, Computat Sci & Engn Div, Quantum Computat Sci Grp, Oak Ridge, TN 37831 USA

[2] Univ Georgia, Dept Math, Athens, GA 30602 USA

[3] Alabama A&M Univ, Dept Phys Chem & Math, Normal, AL 35762 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2024年 / 680卷

关键词：

Lie-Trotter formula; Suzuki approximation; JB-algebra; Jordan-Banach algebra;

D O I：

10.1016/j.laa.2023.10.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Lie-Trotter-Suzuki product formulas are ubiquitous in quantum mechanics, computing, and simulations. Approximating exponentiated sums with such formulas are investigated in the JB-algebraic setting. We show that the Suzuki type approximation for exponentiated sums holds in JB-algebras, we give explicit estimation formulas, and we deduce three generalizations of Lie-Trotter formulas for arbitrary number elements in such algebras. We also extended the Lie-Trotter formulas in a Jordan Banach algebra from three elements to an arbitrary number of elements. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：156 / 169

页数：14

共 7 条

[1]

Alfsen E. M., 2003, MATH THEORY

[2]

Escolano GM, 2023, Arxiv, DOI arXiv:2305.05530

[3]

Hanche-Olsen H., 1984, Jordan operator algebras

[4] TRANSFER-MATRIX METHOD AND MONTE-CARLO SIMULATION IN QUANTUM SPIN SYSTEMS [J].

SUZUKI, M .

PHYSICAL REVIEW B, 1985, 31 (05) :2957-2965

[5] GENERALIZED TROTTERS FORMULA AND SYSTEMATIC APPROXIMANTS OF EXPONENTIAL OPERATORS AND INNER DERIVATIONS WITH APPLICATIONS TO MANY-BODY PROBLEMS [J].

SUZUKI, M .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1976, 51 (02) :183-190

[6]

von Neumann J., 1993, The Collected Works of Eugene Paul Wigner: Part A: The Scientific Papers, P298

[7]

WRIGHT JDM, 1977, MICH MATH J, V24, P291

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