- 05-320 Roderich Tumulka, Nino Zanghi
- Smoothness of Wave Functions in Thermal Equilibrium
Sep 14, 05
(auto. generated ps),
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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.