Multiplying the eigenvector equation for ϕα on the right by ψβj and summing over j, and multiplying the eigenvector equation for ψβ on the left by \(\phi^\alp...Multiplying the eigenvector equation for ϕα on the right by ψβj and summing over j, and multiplying the eigenvector equation for ψβ on the left by ϕαi and summing over i, and subtracting the two results yields
Thus, while a complete description of a (classical) system would require us to account for \CO(1023) evolving degrees of freedom, with respect to the physical quantities in which we are...Thus, while a complete description of a (classical) system would require us to account for \CO(1023) evolving degrees of freedom, with respect to the physical quantities in which we are interested, the details of the initial conditions are effectively forgotten over some microscopic time scale τ, called the collision time, and over some microscopic distance scale, ℓ, called the mean free path 1 . The equilibrium state is time-independent.
