126 research outputs found
Time evolution of a small reactive system
We investigate the irreversible evolution of a small system in which a
chemical reaction takes place. We have two main goals: the first requires to
find an equation to produce a time-irreversible behavior,the second consists in
introducing a simple exactly solvable model in order to understand basic facts
in chemical kinetics. Our basic tool is the transition function counting the
number of paths joining two points in the reactive coordinates system. An exact
quantum Smoluchowski equation is derived for the reactive system in vacuum, in
the presence of a solvent in equilibrium at any time with the reactive system a
new Smoluchowski equation is obtained. The transition from a quantum regime to
a classical one is discussed. The case of a reactive system not in equilibrium
with its neighborhood is investigated in terms of path integral and via a
partial differential function. Memory effects and closure assumptions are
discussed. Using a simple potential model, the chemical rate constant is
exactly calculated and questions such as the meaning of the activation energy
or the physical content of the so-called prefactor are investigated.Comment: 13 page
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