Abstract
Geometry, electrostatics, and single-electron tunneling contribute to the nonlinearity in the quantum dot embedded nanomechanical resonator, while “Duffing term” is a kind of mathematics describing the third-order nonlinearity of the system as a whole. We study theoretically the influence of a variation of a mathematical parameter Fuffing term on the actual physical effect. The position probability distribution, the average current, and the displacement fluctuation spectrum with the different Duffing parameter and electromechanical coupling are obtained through numerically calculating the Fokker Planck equation. The mechanical bistability has been described by these quantities under different electromechanical coupling and Duffing parameters. We conclude that the nonlinearities of the nanotube resonator contribute to the mechanical bistability, which induces the asymmetry of the position probability distribution, compresses the current, and softens or stiffens the mechanical resonance frequency as the same as the electromechanical coupling to use it in mechanical engineering.
Highlights
Yue Wang,1 Ghulam Bary,1 Riaz Ahmad,1 Dameng Yin,1 Shiwei Xie,1 Qing Lu,1 Ilyas Khan,2 Nawa Alshammari,3 Nawaf N
People have found that strong coupling induces strong nonlinear signals in the mechanical resonance frequency and the mechanical noise in the single- or two-level quantum nanomechanical oscillator [22,23,24]. e strong coupling dominates the quadratic term in the restore force than the geometry, electrostatics, and single-electron tunneling. e nonlinear response of the system contains a mechanical resonator at nanoscale coupled to a transistor of single electron under the external drive which behaves like the Duffing oscillator [25]
We are interested to examine the characteristics of the position probability, mechanical noise, and average current which behaved meaningful significantly during the considered quantum systems at various energies and momenta, and we presume that the produced sources consist of the debris of frequencies that behave as the nanomechanical system to use in the thermal as well as in mechanical engineering
Summary
Yue Wang ,1 Ghulam Bary ,1 Riaz Ahmad ,1 Dameng Yin, Shiwei Xie, Qing Lu, Ilyas Khan ,2 Nawa Alshammari ,3 Nawaf N. Electrostatics, and single-electron tunneling contribute to the nonlinearity in the quantum dot embedded nanomechanical resonator, while “Duffing term” is a kind of mathematics describing the third-order nonlinearity of the system as a whole. We conclude that the nonlinearities of the nanotube resonator contribute to the mechanical bistability, which induces the asymmetry of the position probability distribution, compresses the current, and softens or stiffens the mechanical resonance frequency as the same as the electromechanical coupling to use it in mechanical engineering.
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