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Condensed Matter > Statistical Mechanics

Title: Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure

Authors: Peter Reimann
Abstract: Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator $\rho$ of low purity, $\tr\rho^2\ll 1$, and yielding the ensemble averaged expectation value $\tr(\rho A)$ for any observable $A$. Assuming that the given statistical ensemble $\rho$ is generated by randomly sampling pure states $|\psi>$ according to the corresponding so-called Gaussian adjusted projected measure $[$Goldstein et al., J. Stat. Phys. 125, 1197 (2006)$]$, the expectation value $<\psi|A|\psi>$ is shown to be extremely close to the ensemble average $\tr(\rho A)$ for the overwhelming majority of pure states $|\psi>$ and any experimentally realistic observable $A$. In particular, such a `typicality' property holds whenever the Hilbert space $\hr$ of the system contains a high dimensional subspace $\hr_+\subset\hr$ with the property that all $|\psi>\in\hr_+$ are realized with equal probability and all other $|\psi> \in\hr$ are excluded.
Comments: accepted for publication in J. Stat. Phys
Subjects: Statistical Mechanics (cond-mat.stat-mech)
Journal reference: J. Stat. Phys. 132, 921 (2008)
DOI: 10.1007/s10955-008-9576-1
Cite as: arXiv:0805.3102 [cond-mat.stat-mech]
  (or arXiv:0805.3102v1 [cond-mat.stat-mech] for this version)

Submission history

From: Peter Reimann [view email]
[v1] Tue, 20 May 2008 15:24:23 GMT (15kb)

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