Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems

Autor(en): Reimann, Peter
Gemmer, Jochen 
Stichwörter: Physics; Physics, Fluids & Plasmas; Physics, Mathematical; TYPICALITY
Erscheinungsdatum: 2019
Herausgeber: AMER PHYSICAL SOC
Journal: PHYSICAL REVIEW E
Volumen: 99
Ausgabe: 1
Zusammenfassung: 
We explore how the expectation values of a largely arbitrary observable A are distributed when normalized vectors vertical bar psi > are randomly sampled from a high-dimensional Hilbert space. Our analytical results predict that the distribution exhibits a very narrow peak of approximately Gaussian shape, while the tails significantly deviate from a Gaussian behavior. In the important special case that the eigenvalues of A satisfy Wigner's semicircle law, the expectation-value distribution for asymptotically large dimensions is explicitly obtained in terms of a large deviation function, which exhibits two symmetric nonanalyticities akin to critical points in thermodynamics.
ISSN: 24700045
DOI: 10.1103/PhysRevE.99.012126

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