Trotter formula: Difference between revisions
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*[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)] | *[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)] | ||
*[http://dx.doi.org/10.1016/0375-9601(93)90701-Z Masuo Suzuki "Improved Trotter-like formula", Physics Letters A '''180''' pp. 232-234 (1993)] | *[http://dx.doi.org/10.1016/0375-9601(93)90701-Z Masuo Suzuki "Improved Trotter-like formula", Physics Letters A '''180''' pp. 232-234 (1993)] | ||
*[http://arxiv.org/abs/physics/ | *[http://arxiv.org/abs/physics/0202003 Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)] | ||
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Latest revision as of 11:39, 10 July 2009
The Trotter formula is given by ([1] Eq. 5):
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_0} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} are self-adjoint operators. This formula is used in the path integral formulation.
References[edit]
Related reading
- Masuo Suzuki "Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems - Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations", Progress of Theoretical Physics 56 pp. 1454-1469 (1976)
- Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A 28 3575-3580 (1983)
- R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General 19 1551-1554 (1986)
- Masuo Suzuki "Improved Trotter-like formula", Physics Letters A 180 pp. 232-234 (1993)
- Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)