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We consider a classically chaotic system that is described by a Hamiltonian H (Q, P;x), where x is a constant parameter. Specifically, we discuss a gas particle inside a cavity, where x controls a deformation of the boundary or the position of a ``piston. '' The quantum eigenstates of the system are |n (x) 〉. We describe how the parametric kernel P (n) 0ex{0ex}=0ex{0ex}|〈n (x) (x₀) 〉|^2 evolves as a function of x{0ex{0ex}=0ex{0ex}x-x}₀. We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.
Cohen et al. (Mon,) studied this question.