Roderich Tumulka, Nino Zanghi
Smoothness of Wave Functions in Thermal Equilibrium
(48K, LaTeX)

ABSTRACT.  We consider the thermal equilibrium distribution at inverse 
temperature $\beta$, or canonical ensemble, of the wave function 
$\Psi$ of a quantum system. Since $L^2$ spaces contain more 
nondifferentiable than differentiable functions, and since the 
thermal equilibrium distribution is very spread-out, one might 
expect that $\Psi$ has probability zero to be differentiable. 
However, we show that for relevant Hamiltonians the contrary is the 
case: with probability one, $\Psi$ is infinitely often 
differentiable and even analytic. We also show that with 
probability one, $\Psi$ lies in the domain of the Hamiltonian.