Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in or
create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision |
Your text |
Line 1: |
Line 1: |
| 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): | | The '''Trotter formula''' is given by |
| :<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. This formula is used in the [[path integral formulation]]. | | where <math>H_0</math> and <math>V</math> are self-adjoint operators. |
| ==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/0202003 Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]
| |
| [[Category: Mathematics]] | | [[Category: Mathematics]] |