Browsing by Subject "Canonical transformation"
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Item Open Access Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems(IEEE, 2014) Özaktaş, Haldun M.; Öktem, F. S.We study the degrees of freedom of optical systems and signals based on space-frequency (phase-space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with multiple apertures, and give conditions for lossless transfer. Moreover, we focus on the degrees of freedom of signals in relation to the space-frequency support and provide a sub-Nyquist sampling approach to represent signals with arbitrary space-frequency support. Implications for simulating optical systems are also discussed.Item Open Access Quantum canonical transformations in star-product formalism(IOP, 2013) Dereli, T.; Hakioğlu, Tuğrul; Temen, A.We study construction of the star-product version of three basic quantum canonical transformations which are known as the generators of the full canonical algebra. By considering the fact that star-product of c-number phase-space functions is in complete isomorphism to Hilbert-space operator algebra, it is shown that while the constructions of gauge and point transformations are immediate, generator of the interchanging transformation deforms this isomorphism. As an alternative approach, we study all of them within the deformed form. How to transform any c-number function under linear-nonlinear transformations and the intertwining method are shown within this argument as the complementary subjects of the text.