 05135 Sheldon Goldstein, Joel L. Lebowitz, Roderich Tumulka, Nino Zanghi
 On the Distribution of the Wave Function for Systems in Thermal
Equilibrium
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Apr 13, 05

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Abstract. A density matrix that is not pure can arise, via averaging, from many
different distributions of the wave function. This raises the question,
which distribution of the wave function, if any, should be regarded as
corresponding to systems in thermal equilibrium as represented, for
example, by the density matrix $\rho_\beta = (1/Z) \exp( \beta H)$ of
the canonical ensemble. To answer this question, we construct, for any
given density matrix $\rho$, a measure on the unit sphere in Hilbert
space, denoted GAP($\rho$), using the Gaussian measure on Hilbert space
with covariance $\rho$. We argue that GAP($\rho_\beta$) corresponds to
the canonical ensemble.
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