The authors have presented [1] a subdynamics theory in which quantities characteristic of irreversible behaviour - such as that of a collision process - appear in the generator of kinetic evolution. This theory is applied to the simple case of potential scattering. The original dynamics is first widened after incoming, outgoing and intermediate degrees of freedom are distinguished. An extended concept of vacuum state is introduced by reference to the observational situation of interest. The redundant degrees of freedom are then constrained by the requirement that the physi¬ cal evolution takes place entirely in the subdynamics associated with that vacuum. The relationship with previous treatments of the same system is analysed in some detail. PACS numbers : 05.30 ; 02.90 ; 11.20.
The authors have presented [1] a subdynamics theory in which quantities characteristic of irreversible behaviour - such as that of a collision process - appear in the generator of kinetic evolution. This theory is applied to the simple case of potential scattering. The original dynamics is first widened after incoming, outgoing and intermediate degrees of freedom are distinguished. An extended concept of vacuum state is introduced by reference to the observational situation of interest. The redundant degrees of freedom are then constrained by the requirement that the physi¬ cal evolution takes place entirely in the subdynamics associated with that vacuum. The relationship with previous treatments of the same system is analysed in some detail. PACS numbers : 05.30 ; 02.90 ; 11.20.
A subdynamics theory has been presented recently in which quan¬ tities characteristic of an irreversible behaviour, such as that of a collision process, appear in the generator of evolution. The original dynamics, with degrees of freedom in large number, is first widened once self-energy parts have been recognized. The redundancies are then constrained by the requirement that the evolution takes place entirely in a subdynamics associated with a vacuum defined by reference to the observational situation of interest. This scheme, resulting in no loss of physical information, is examined in detail in the simple case of potential scattering, after that incoming, outgoing and intermediate degrees of freedom are distinguished. The relation with previous approaches is analysed.
The compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics requires an extension of the latter. Such an extension of a reversible formalism is made possible by the presence of self-energy processes (already found in quantum electrodynamics), which allows for the widening of the dynamics through the introduction of specific additional variables leading to the recognition of such processes. A projection technique modeled on that introduced long ago by the Brussels group defines a subdynamics that is shown to contain the starting formulation in its entirety. (It corresponds to a restricted class of initial conditions, namely the reversible ones.) A new kinetic description is obtained in which, e.g., collision processes for privileged components arise from the original interaction. This method is applied successively to various models, and we focus in this paper on the possible presence of temporal behaviour excluded in ordinary quantum mechanics. Among the differences between this framework and that of ordinary quantum mechanics, the possibility appears for the purely exponential decay of a particle, while ordinary quantum mechanics requires long time tails associated with the finite lower bound in the spectrum of the Hamiltonian.
The compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics is a challenging problem. Our solution requires an extension of the latter. Such an extension of a reversible formalism is made possible by the presence of self‐energy processes (already found in quantum electrodynamics) which enables the widening of the dynamics by the introduction of specific additionnal variables leading to the recognition of such processes. A projection technique modeled on the one introduced long ago by the Brussels group defines a subdynamics which is shown to contain entirely the starting formulation (it corresponds now to a restricted class of initial conditions, namely the reversible one). A new kinetic description is obtained in which e.g. collision processes for privileged components arise from the original interaction. This method is applied successively to various models and we focus in this paper on the possible presence of temporal behaviours excluded in ordinary quantum mechanics. Among those differences, the possibility appears of a purely exponential decay for a particle while ordinary quantum mechanics requires long time tails associated with the finite lower bound in the spectrum of the Hamiltonian.
An approach to the description of subdynamics inside the nonrelativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory derivation of the subdynamics of a microsystem interacting through collisions with a macrosystem is given, leading to a master equation expressed in terms of the operator-valued dynamic structure factor, a two-point correlation function which compactly takes the statistical mechanics properties of the macrosystem into account. For the case of a free quantum gas the dynamic structure factor can be exactly calculated and in the long wavelength limit a Fokker–Planck equation for the description of quantum dissipation and in particular quantum Brownian motion is obtained, where peculiar corrections due to quantum statistics can be put into evidence.
Scattering theory is extended to the description of processes during collision. Indeed, for large wave packets we may consider situations where time t, while large with respect to characteristic frequencies, is still smaller than the duration of the collision tc. This leads to an asymptotic theory which is different from the usual S-matrix approach. There appear intermediate states with scattering cross sections which result from secular effects for ttc, but differ from the values obtained for t\ensuremath{\gtrsim}tc in the S-matrix theory. The consideration of such intermediate time scales is the normal procedure in many-body situations as realized, for example, in chemical reactions. Our method is closely connected to our work on the extension of quantum theory beyond the Hilbert space for large Poincar\'e systems. This theory applies to persistent scattering using delocalized density matrices (an example is plane waves). For this case, the S-matrix theory is not valid, while the results of our asymptotic approach remain valid for all times. Our theoretical predictions have been validated by numerical simulations. \textcopyright{} 1996 The American Physical Society.