A Lie Algebraic Approach to Order Parameters

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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AutoMO: automatic inference of memory order parameters for C/C++11

Proceedings of the 2015 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications - OOPSLA 2015 ◽

10.1145/2814270.2814286 ◽

2015 ◽

Cited By ~ 3

Author(s):

Peizhao Ou ◽

Brian Demsky

Keyword(s):

Order Parameters ◽

Automatic Inference

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Target space entanglement in quantum mechanics of fermions and matrices

Journal of High Energy Physics ◽

10.1007/jhep08(2021)046 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Sotaro Sugishita

Keyword(s):

Mutual Information ◽

Ground State ◽

Entanglement Entropy ◽

Algebraic Approach ◽

Upper Bounds ◽

Wave Functions ◽

Target Space ◽

Single Interval ◽

Area Law ◽

Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

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