Comparing periodic-orbit theory to perturbation theory in the asymmetric infinite square well

Comparing periodic-orbit theory to perturbation theory in the asymmetric infinite square well.

An infinite square well with a discontinuous step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits. This system is analyzed using both time-independent perturbation theory (PT) and periodic-orbit theory and the approximate formulas for the energy eigenvalues derived from these two approaches are compared. The periodic orbits of the system can be divided into...

Analytic Equation of State for the Square-well Plus Sutherland Fluid from Perturbation Theory

Analytic expressions were derived for the compressibility factor and residual internal energy of the square-well plus Sutherland fluid. In this derivation, we used the second order Barker-Henderson perturbation theory based on the macroscopic compressibility approximation together with an analytical expression for radial distribution function of the reference hard sphere fluid. These properties...

Periodic Orbit Theory

Beyond the periodic orbit theory

The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory appr...

Does orbit-averaged theory require a scale separation between periodic orbit size and perturbation correlation length?

Canonical perturbation theory shows that orbit-averaged theory only requires the time-scale separation between equilibrium and perturbed motions and verifies the conventional concept that orbit averaging effects greatly reduce the transport of energetic particles by microturbulence in tokamak. Thereafter, a recent claim [Phys. Rev. Lett. 102, 075004 (2009); 107, 239502 (2011)] of the orbit-aver...