Mass-sign duality of cubic oscillators
نویسنده
چکیده
In the light of the guiding methodical role of anharmonic oscillators in field theory we communicate the observation that their " first nontrivial " PT −symmetric cubic Hamiltonians H ± = p 2 ± m 2 x 2 + i f x 3 with opposite sign of mass term are, up to a constant shift, isospectral.
منابع مشابه
Power Series -Aftertreatment Technique for Nonlinear Cubic Duffing and Double-Well Duffing Oscillators
Modeling of large amplitude of structures such as slender, flexible cantilever beam and fluid-structure resting on nonlinear elastic foundations or subjected to stretching effects often lead to strongly nonlinear models of Duffing equations which are not amendable to exact analytical methods. In this work, explicit analytical solutions to the large amplitude nonlinear oscillation systems of cub...
متن کاملA Modified Energy Balance Method to Obtain Higher-order Approximations to the Oscillators with Cubic and Harmonic Restoring Force
This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equations are obtained. Higher-order nonlinear algebra...
متن کاملChanging the Behavior of Parametric Resonance in Mems Oscillators by Tuning the Effective Cubic Stiffness
Nonlinearity plays a critical role on the behavior of oscillators operating in the parametric resonance mode. Here, we study the effects of Effective Nonlinear Parameter, (effective cubic stiffness), γ3eff, on the behavior of parametric resonance in a micro electro mechanical oscillator. The value of γ3eff can be tuned by changing the amplitude of applied voltage. Varying the sign of γ3eff can ...
متن کاملFluidic Oscillators’ Applications, Structures and Mechanisms – A Review
Enhancement of heat and mass transfer and decrease of energy dissipation are great necessities of the evolution of fluid flow devices. Utilizing oscillatory or pulsatile fluid flow for periodic disturbing of velocity and thermal boundary layers is one of the methods with exciting results. Passive methods of generating oscillatory flow are preferred to active methods because of simplicity, no ne...
متن کاملOutput Feedback Adaptive Stabilization of aSecond - Order Systems
We consider output feedback adaptive stabilization for second-order systems. The assumptions we make are standard, namely, that the system has relative degree two and the sign of the high frequency gain is known. However, we complement the existing literature by deriving an explicit expression for the adaptive controller. The controller has the form of a 6th-order dynamic compensator with quadr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006