Nota de FísicaPublicado
Generalization of the Lie-Trotter Product Formula for q-Exponential Operators
A.K. Rajagopal; C. Tsallis
1999
Dados da publicação
- Autores
- A.K. Rajagopal; C. Tsallis
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 1999
- Descrição
- The Lie-Trotter formula <math> e^{\hat{A}+\hat{B}} = \lim _{N\rightarrow \infty} \left(e^{\hat{A}/N} e^{\hat{B}/N}\right)^N \ \,\!</math> is of great utility in a variety of quantum problems ranging from the theory of path integrals and Monte Carlo methods in theoretical chemistry, to many-body and thermostatistical calculations. We generalize it for the q-exponential function <math> e_q (x) = [1+ (1-q) x]^{(1/(1-q))} \ </math> with <math>(\,\!</math> <math> e_1(x)=e^x)\,\!</math>, and prove <math> e_q(\hat{A}+\hat{B}+(1-q) \,\!</math> <math>[\hat{A}\hat{B}+\hat{B}\hat{A}] /2) = \lim_{N\rightarrow \infty} \left\{\left[e_{1-(1-q)N}\left(\hat{A}/N\right)\right] \left[e_{1-(1-q)N}\left(\hat{B}/N\right)\right]\right\}^N \,\!</math>. This extended formula is expected to be similarly useful in the nonextensive situations.
- Ano
- 1999
- Número
- CBPF-NF-004/99
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não