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Canonical transformation

About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.


Papers
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Journal ArticleDOI
Ko Aizu1
TL;DR: In this paper, it was shown that if a linear multistep formula applied to numerical integration of hamiltonian systems is also to be a canonical transformation, it must essentially be a two-term formula.

7 citations

Journal ArticleDOI
TL;DR: In this article, the underlying covariant canonical transformation framework invokes a dynamical spacetime Hamiltonian consistence, which is used to solve cosmological solutions for covariant canonically gauge theories of gravity.
Abstract: Cosmological solutions for covariant canonical gauge theories of gravity are presented. The underlying covariant canonical transformation framework invokes a dynamical spacetime Hamiltonian consist...

7 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that a Hamiltonian p ∈ C1(TRn) is locally integrable near a non-degenerate critical point �0 of the energy, provided that the fundamental matrix at �0 has rationally independent eigenvalues, none purely imaginary.
Abstract: We prove that a Hamiltonian p ∈ C1(TRn) is locally integrable near a non-degenerate critical point �0 of the energy, provided that the fundamental matrix at �0 has rationally independent eigenvalues, none purely imaginary. This is done by using Birkhoff normal forms, which turn out to be convergent in the C 1 sense. We also give versions of the Lewis-Sternberg normal form near a hyperbolic fixed point of a canonical transformation. Then we investigate the complex case, showing that when p is holomorphic near �0 ∈ TC n , then Re p becomes integrable in the complex domain for real times, while the Birkhoff series and the Birkhoff transforms may not converge, i.e., p may not be integrable. These normal forms also hold in the semi-classical frame.

7 citations

Journal ArticleDOI
15 May 2014
TL;DR: In this paper, a generalization of the improved Zakharov equation for the "almost" 2-D water waves at the surface of deep water is presented, which is very suitable for analytic study as well as for numerical simulation.
Abstract: In the paper [1] authors applied canonical transformation to water wave equation not only to remove cubic nonlinear terms but to simplify drastically fourth order terms in Hamiltonian. After the transformation well-known but cumbersome Zakharov equation is drastically simplified and can be written in X-space in compact way. This new equation is very suitable for analytic study as well as for numerical simulation At the same time one of the important issues concerning this system is the question of its integrability. The first part of the work is devoted to numerical and analytical study of the integrability of the equation obtained in [1]. In the second part we present generalization of the improved Zakharov equation for the "almost" 2-D water waves at the surface of deep water. When considering waves slightly inhomogeneous in transverse direction, one can think in the spirit of Kadomtsev-Petviashvili equation for Korteveg-de-Vries equation taking into account weak transverse diffraction. Equation can be written instead of classical variables η(x,y,t) and ψ(x,y,t) in terms of canonical normal variable b(x,y,t). This equation is very suitable for robust numerical simulation. Due to specific structure of nonlinearity in the Hamiltonian the equation can be effectively solved on the computer. It was applied for simulation of sea surface waving including freak waves appearing.

7 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the interaction between a two-level atom and three types of interaction of three quantized modes of a quantized field, namely: two parametric amplifiers and a frequency converter.
Abstract: In this paper, we study the interaction between a two-level atom and three types of interaction of three quantized modes of a quantized field, namely: two parametric amplifiers and a frequency converter. The SU(1, 1) algebra is used to represent the combination of the interacting modes. A canonical transformation is used to cast the Hamiltonian into a tangible form. The solution of the Schrodinger equation for the wave function is given analytically. Using this solution we discuss numerically the atomic inversion, the degree of entanglement through the linear entropy and the variance entropy for chosen values of the detuning and coupling parameters. It is shown that the atomic inversion can be controlled through the rotation angle α and the atomic angle θ as well as the Bargmann index k. The degree of entanglement is affected by both α and θ in addition to the ratio ϵ. Variance squeezing is sensitive to changes in the atomic and the phase angles besides the parameter k. For entropy squeezing, the effective parameters are α, θ and k.

7 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202218
202158
202042
201932
201829