Trotter formula: Difference between revisions

Revision as of 18:44, 23 October 2008

The Trotter formula is given by (Ref.1 Eq. 5):

e^{-\beta (H_{0}+V)}=\lim _{n\rightarrow \infty }(e^{-\beta H_{0}/n}e^{-\beta V/n})^{n}

where $H_{0}$ and $V$ are self-adjoint operators.

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-The '''Trotter formula''' is given by
+The '''Trotter formula''' is given by (Ref.1 Eq. 5):
 :<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.
+==References==
+#H. F. Trotter "On the Product of Semi-Groups of Operators", Proceedings of the American Mathematical Society '''10''' 545-551 (1959)
+#[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://arxiv.org/abs/physics/0202003Oscar Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]
 [[Category: Mathematics]]