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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
Correction published on 8 July 2016, see Math. Comput. Appl. 2016, 21(3), 28.

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Math. Comput. Appl. 2011, 16(1), 290-300;

Amplitude Noise Reduction in a Nano-Mechanical Oscillator

Dept. of Elec. and Electronics Engineering, Gediz University, Hurriyet Bulv. No:16/1, Cankaya, Izmir, Turkey
Published: 1 April 2011
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We study the quantum properties of a nano-mechanical oscillator via the squeezing of the oscillator amplitude. The static longitudinal compressive force 0 F close to a critical value at the Euler buckling instability leads to an anharmonic term in the Hamiltonian and thus the squeezing properties of the nano-mechanical oscillator are to be obtained from the Hamiltonian of the form H = a+a + β(a+ + a) / 4 . This Hamiltonian has no exact solution unlike the other known models of nonlinear interactions of the forms a+2 a2, (a2a)2 and a+4 + a4 - (a+2 a2 + a2 a+2 ) previously employed in quantum optics to study squeezing. Here we solve the Schrodinger equation numerically and show that in-phase quadrature gets squeezed for both vacuum and coherent states. The squeezing can be controlled by bringing F0 close to or far from the critical value Fc. We further study the effect of the transverse driving force on the squeezing in nano-mechanical oscillator.
Keywords: Squeezing; Nano-mechanical Systems; Quantum Noise Squeezing; Nano-mechanical Systems; Quantum Noise
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Kolkiran, A. Amplitude Noise Reduction in a Nano-Mechanical Oscillator. Math. Comput. Appl. 2011, 16, 290-300.

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