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New Convenient Way for Deriving Exponential Operators' Disentangling Formulas and Their Applications

Fan Hong-Yi, Liyun Hu

We recommend a new convenient method for disentangling some exponential operators and derive a set of new operator identities. Especially, we derive the normal odering form of exp [fa † a + ga †2 + ka 2 ] without appealing to Lie algebra method. Application of these formulas in solving some dynamic Hamiltonian is presented.

Communications in Theoretical PhysicsFeb 1, 200913 citations

Algebra of the Exponential Operator

Ravinder Rupchand Puri

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 20011 citation

Study of correction terms for higher-order decompositions of exponential operators

Hiroto Kobayashi, Naomichi Hatano, Masuo Suzuki

Physica A Statistical Mechanics and its ApplicationsNov 1, 199414 citations

New Convenient Way for Disentangling Exponential Operator Composed of Angular Momentum Operators

Hongqi Li, Xing-Lei Xu, Fan Hong‐Yi

In the preceding paper ( Commun. Theor. Phys. 51 (2009) 321 ) we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators composed of angular momentum operators. We mainly disentangle the form of exp[2hJ z + gJ + + kJ − ] as the ordering exp(...J + )exp(...J z )exp(...J − ), we employ the Schwinger Bose realization J − = b † a, J + = a † b, J z = (a † a − b † b)/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator's disentangling is different from its decomposition in normal ordering.In the preceding paper ( Commun. Theor. Phys. 51 (2009) 321 ) we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators composed of angular momentum operators. We mainly disentangle the form of exp[2hJ z + gJ + + kJ − ] as the ordering exp(...J + )exp(...J z )exp(...J − ), we employ the Schwinger Bose realization J − = b † a, J + = a † b, J z = (a † a − b † b)/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator's disentangling is different from its decomposition in normal ordering.

Communications in Theoretical PhysicsMay 1, 20112 citations

Matrices, Exponential Operators and Physical Applications

WORLD SCIENTIFIC eBooksOct 1, 20190 citations

New Convenient Way for Deriving Exponential Operators' Disentangling Formulas and Their Applications (II)

Fan Hong‐Yi, Liyun Hu

In the preceding paper [Commun. Theor. Phys. 51 (2009) 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B + C}, trying to find an operator A that satisfies [A, B] = C, and [A,[A,B]] = 0, then from the Baker–Hausdorff formula we have exp{B + C} = exp{B+[A, B]} = e A e B e −A . After arranging e A e B = e B e A e W , the disentangling exp{B + C} = e B e W is obtained. In this work we use this method to two-mode case, especially, derive the normal ordering form of exp[h(a † a + b † b) + ga † b † + kab] without appealing to Lie algebra method.In the preceding paper [Commun. Theor. Phys. 51 (2009) 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B + C}, trying to find an operator A that satisfies [A, B] = C, and [A,[A,B]] = 0, then from the Baker–Hausdorff formula we have exp{B + C} = exp{B+[A, B]} = e A e B e −A . After arranging e A e B = e B e A e W , the disentangling exp{B + C} = e B e W is obtained. In this work we use this method to two-mode case, especially, derive the normal ordering form of exp[h(a † a + b † b) + ga † b † + kab] without appealing to Lie algebra method.

Communications in Theoretical PhysicsMar 1, 200912 citations

A new simple approach for disentangling some exponential operators

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A new simple approach for disentangling some exponential operators

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