Generalization of the Lie-Trotter Product Formula for q-Exponential Operators

Abstract

The Lie-Trotter formula $e^{\hat{A}+\hat{B}}={\lim }_{N\to \infty }(e^{\hat{A}/N}{e}^{\hat{B}/N}{)}^N$ 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 $e_q(x)=[1+(1-q)x{]}^{(1/(1-q))}$ (with $e_1(x)=e^x$), and prove $e_q(\hat{A}+\hat{B}+(1-q)[\hat{A}\hat{B}+\hat{B}\hat{A}]/2)={\lim }_{N\to \infty }{[e_{1-(1-q)N}(\hat{A}/N)][e_{1-(1-q)N}(\hat{B}/N)]}^N$. This extended formula is expected to be similarly useful in the nonextensive situations

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References in corpus (1)

• Nonextensivity and multifractality in low-dimensional dissipative systems

Cited by in corpus (1)

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