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26 results on '"Lv, Cui-Hong"'

25. A New Kind of Integration Transformation in Phase Space Related to Two Mutually Conjugate Entangled-State Representations and Its Uses in Weyl Ordering of Operators

Author

Fan Hong-Yi and LV Cui-Hong

Subjects
Pure mathematics, General Physics and Astronomy, Inverse, State (functional analysis), law.invention, Convolution, Parseval's theorem, Transformation (function), Invertible matrix, law, Phase space, Quantum mechanics, Bipartite graph, Mathematics
Abstract

Based on the two mutually conjugate entangled state representations |ξ and |η, we propose an integration transformation in ξ — η phase space , and its inverse transformation, which possesses some well-behaved transformation properties, such as being invertible and the Parseval theorem. This integral transformation is a convolution, where one of the factors is fixed as a special normalized exponential function. We generalize this transformation to a quantum mechanical case and apply it to studying the Weyl ordering of bipartite operators, regarding to (Q1 – Q2) ↔ (P1 – P2) ordered and simultaneously (P1 + P2) ↔ (Q1 + Q2) ordered operators.

Published
2010

26. From fractional Fourier transformation to quantum mechanical fractional squeezing transformation.

Author

Li Dong-Wei, Lv Cui-Hong, and Fan Hong-Yi

Subjects
*FOURIER transforms, *UNITARY operators, *CRYSTALS, *QUADRATIC forms, *HYPERBOLIC functions, *NONLINEAR analysis, *GAUSSIAN quadrature formulas
Abstract

By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function, i.e., tan α → tanh α, sin α → sinh α, we find the quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within the ordered product of operators (IWOP) we derive the unitary operator responsible for the FrST, which is composite and is made of eiπa†a/2 and exp . The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches. [ABSTRACT FROM AUTHOR]

Published
2015
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