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This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.
This paper considers the $$ \mathcal{P}\mathcal{T} $$ -symmetric extensions of the equations examined by Cooper, Shepard and Sodano. From the scaling properties of the $$ \mathcal{P}\mathcal{T} $$ -symmetric equations a general theorem relating the energy, momentum and velocity of any solitarywave solution of the generalized KdV equation is derived. We also discuss the stability of the compacton...
The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time to perform the measurement. This paper considers the possibility that ΔE, the uncertainty in the energy, may be complex. To understand the effect of a particle having a complex energy, the behaviour of a classical particle in a one-dimensional periodic potential V(x) = −cos(x) is studied. On the...
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