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Full-Text Articles in Physical Sciences and Mathematics
Superoscillations And Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
Superoscillations And Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these special wave functions can be constructed also by computing the approximating sequence of the normalized Hermite functions. First, we start by treating the case when a superoscillating sequence is multiplied by the Gaussian function. Then, we extend these calculations to the case of normalized Hermite functions leading to interesting relations with Weyl operators. In particular, we show that the Segal-Bargmann transform maps superoscillating sequences onto …
Disorder And Synchronization In A Josephson Junction Plaquette, Adam S. Landsberg, Yuri Braiman, Kurt Wiesenfeld
Disorder And Synchronization In A Josephson Junction Plaquette, Adam S. Landsberg, Yuri Braiman, Kurt Wiesenfeld
WM Keck Science Faculty Papers
We describe the effects of disorder on the coherence properties of a 2 x 2 array of Josephson junctions (a "plaquette"). The disorder is introduced through variations in the junction characteristics. We show that the array will remain one-to-one frequency locked despite large amounts of the disorder, and determine analytically the maximum disorder that can be tolerated before a transition to a desynchronized state occurs. Connections with larger N x M arrays are also drawn.
Statistical Properties Of Schriidinger Real And Imaginary Cat States, Victor V. Dodonov, Serguei Y. Kalmykov, Vladimir I. Man'ko
Statistical Properties Of Schriidinger Real And Imaginary Cat States, Victor V. Dodonov, Serguei Y. Kalmykov, Vladimir I. Man'ko
Serge Youri Kalmykov
We study the photon statistics in the superpositions of coherent states |\alpha> and |\alpha*> named “Schroedinger real and imaginary cat states”. The oscillatory character of the photon distribution function (PDF) emerging due to the quantum interference between the two components is shown, and quadrature squeezing is observed for moderate values |\alpha| ~ 1. In spite of the quantity <\delta n^2> / tending to unity (like in the Poissonian PDF) at |\alpha| >> 1, the photon statistics is essentially non-Poissonian for all values of |\alpha|. The factorial moments and cumulants of the PDF are calculated, and oscillations of their ratio are demonstrated.