Decoherence quantum-classical correspondence

It is remarkable that the exceptional point Eq. 1.79 corresponds to the celebrated Laplace-Schwarzschild radius r = 2/i = Rls (given that M is confined inside a sphere with radius Rls). Note that the present result is a universal property of the present formulation in contrast to the classical Schwartzschild singularity , which depends on the choice of coordinate system. Stated in a different way decoherence to classical reality might take place for 0 < rc(r) < whilst potential quantum like structures appears inside Rls for j < K(r) < 1. 

These interference patterns are wonderful manifestations of wave function behavior, and are not found in classical electronics or electrodynamics. Since the correspondence principle tells us that quantum and classical systems should behave similarly in the limit of Planck s constant vanishing, we suspect that adequate decoherence effects will change the quantum equation into classical kinetics equations, and so issues of crosstalk and interference would vanish. This has been... 

The surface-hopping trajectories obtained in the adiabatic representation of the QCLE contain nonadiabatic transitions between potential surfaces including both single adiabatic potential surfaces and the mean of two adiabatic surfaces. This picture is qualitatively different from surface-hopping schemes [2,56] which make the ansatz that classical coordinates follow some trajectory, R(t), while the quantum subsystem wave function, expanded in the adiabatic basis, is evolved according to the time dependent Schrodinger equation. The potential surfaces that the classical trajectories evolve along correspond to one of the adiabatic surfaces used in the expansion of the subsystem wavefunction, while the subsystem evolution is carried out coherently and may develop into linear combinations of these states. In such schemes, the environment does not experience the force associated with the true quantum state of the subsystem and decoherence by the environment is not automatically taken into account. Nonetheless, these methods have provided com-... 

In the Poisson case, the decoherence theory affords a more satisfactory justification for the correspondence principle [20]. Adopting the Wigner formalism, it is possible to express quantum mechanical problems in terms of the classical phase space, and the Wigner quasi-probability is expected to remain positive definite until the instant at which a quantum transition occurs, according to the estimate of Ref. 120, at the time... 

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