On the Relationship between Large Order Graphs and Instantons for the Double Well Oscillator
نویسندگان
چکیده
The double well oscillator is used as a QCD-like model for studying the relationship between large order graphs and the instanton-antiinstanton solution. We derive an equation for the perturbative coefficients of the ground state energy when the number of 3 and/or 4-vertices is fixed and large. These coefficients are determined in terms of an exact “bounce” solution. When the number of 4-vertices is analytically continued to be near the negative of half the number of 3-vertices the bounce solution approaches the instantonantiinstanton solution and determines leading Borel singularity.
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 کاملSome Results on Forgotten Topological Coindex
The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...
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 کاملThe Effect of Structural Parameters on the Electronic States and Oscillator Strength of a Resonant Tunneling Quantum Well Infrared Photodetector
In this paper a resonant tunnelling quantum well infrared photodetector (RT-QWIP) is discussed. Each period of this photodetector structure comprises of a resonant tunnelling structure (AlAs/AlGaAs/AlAs) nearby a quantum well (AlGaAs/GaAs). In this photodetector, photocurrent is produced when an electron makes a transition from the ground state of the well to an excited state which is coupled t...
متن کاملSome New Analytical Techniques for Duffing Oscillator with Very Strong Nonlinearity
The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...
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 2000