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Smoothness of Wave Functions in Thermal Equilibrium

Roderich Tumulka·Nino Zanghi
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Abstract

We consider the thermal equilibrium distribution at inverse temperature $β$, or canonical ensemble, of the wave function $Ψ$ 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 $Ψ$ has probability zero to be differentiable. However, we show that for relevant Hamiltonians the contrary is the case: with probability one, $Ψ$ is infinitely often differentiable and even analytic. We also show that with probability one, $Ψ$ lies in the domain of the Hamiltonian.

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Roderich Tumulka, Nino Zanghi. 2005-09-13. Smoothness of Wave Functions in Thermal Equilibrium. https://doi.org/10.1063/1.2109767

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