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Dynamical Typicality for Initial States with a Preset Measurement Statistics of Several Commuting Observables

  • Ben N. BalzEmail author
  • Jonas Richter
  • Jochen Gemmer
  • Robin Steinigeweg
  • Peter Reimann
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 195)

Abstract

We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then propagated by the pertinent Schrödinger or von Neumann equation up to some later time point, and invoking a few additional, fairly weak and realistic assumptions, we show that most of them still entail very similar expectation values for any given observable. This so-called dynamical typicality property thus corroborates the widespread observation that a few macroscopic features are sufficient to ensure the reproducibility of experimental measurements despite many unknown and uncontrollable microscopic details of the system. We also discuss and exemplify the usefulness of our general analytical result as a powerful numerical tool.

Notes

Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under Grants No. RE 1344/10-1, RE 1344/12-1, GE 1657/3-1, STE 2243/3-1 within the Research Unit FOR 2692, Grant No. 355031190, and by the Studienstiftung des Deutschen Volkes.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ben N. Balz
    • 1
    Email author
  • Jonas Richter
    • 2
  • Jochen Gemmer
    • 2
  • Robin Steinigeweg
    • 2
  • Peter Reimann
    • 1
  1. 1.Fakultät für PhysikUniversität BielefeldBielefeldGermany
  2. 2.Department of PhysicsUniversity of OsnabrückOsnabrückGermany

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