Quasi-ergodicity

Figure 8.16 from Frantz, D D, D L Freeman and J D DoU 1990. Reducing quasi-ergodic behavior in Monte Carlo simulations by J-walking applications to atomic clusters. The Journal of Chemical Physics 93 2769-2784. 

DD Frantz, DL Freeman, ID Doll. Reducing quasi-ergodic behavior m Monte Carlo simulations by J-waUcmg Applications to atomic clusters. I Chem Phys 93 2769-2784, 1990. 

A similar theorem is called the quasi-ergodic theorem by Brennan. See footnote 5. 

Frantz, D.D. Freeman, D.L. Doll, J.D., Reducing quasi-ergodic behavior in Monte Carlo simulation by J-walking Applications to atomic clusters, J. Chem. Phys. 1990, 93, 2769... 

A. Julg, From Atoms and Molecules to the Cosmos A Quasi-Ergodic Interpretation of Quantum Mechanics, Springer, Berlin, 1998. 

If, for the time being, we call systems satisfying requirement (I) of note 98 "quasi-ergodic, then, instead of statements 1), 2), and 3) in the text, we must Bay that for a "quasi-ergodic system on each surface E(q, p) =E there will be a continuum of oo different (7-paths with different values of the constants ct, , ... 

The Hamiltonian has radial (Kr) and angular Ka,Ke) kinetic energy operators in addition to the potential V (10.44). By treating these on par with V R,6fs,ot) and by assuming an initial quasi-ergodic distribution in phase space of the escape trajectories as they enter the Coulomb zone, Wannier was able to show that at threshold (small E) the total ionisation cross section was dominated by the instability in the escape trajectories and was given by... 

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