Trotter formula: Difference between revisions
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The '''Trotter formula''' is given by ( | The '''Trotter formula''' is given by (<ref>[http://www.jstor.org/stable/2033649 H. F. Trotter "On the Product of Semi-Groups of Operators", Proceedings of the American Mathematical Society '''10''' 545-551 (1959)]</ref> Eq. 5): | ||
:<math>e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n</math> | :<math>e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n</math> | ||
where <math>H_0</math> and <math>V</math> are self-adjoint operators. | where <math>H_0</math> and <math>V</math> are self-adjoint operators. This formula is used in the [[path integral formulation]]. | ||
==References== | ==References== | ||
<references/> | |||
'''Related reading''' | |||
*[http://dx.doi.org/10.1143/PTP.56.1454 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)] | |||
*[http://dx.doi.org/10.1103/PhysRevA.28.3575 Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A '''28''' 3575-3580 (1983)] | |||
*[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://arxiv.org/abs/physics/0202003Oscar Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)] | |||
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Revision as of 12:30, 10 July 2009
The Trotter formula is given by ([1] Eq. 5):
where and are self-adjoint operators. This formula is used in the path integral formulation.
References
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)