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Related Concept Videos

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Updated: Jun 23, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Dynamical typicality of quantum expectation values.

Christian Bartsch1, Jochen Gemmer

  • 1Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, D-49069 Osnabrück, Germany. cbartsch@uos.de

Physical Review Letters
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

Pure quantum states with similar observable values at one time exhibit similar values later in high-dimensional systems. This finding suggests individual quantum dynamics can be accurately represented by ensemble averages, simplifying theoretical analysis.

Related Experiment Videos

Last Updated: Jun 23, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Theoretical physics

Background:

  • Quantum systems in high-dimensional Hilbert spaces exhibit complex dynamics.
  • Understanding the long-term behavior of expectation values is crucial for quantum theory.

Purpose of the Study:

  • To investigate the temporal stability of expectation values for pure states in quantum dynamics.
  • To determine if individual quantum state evolution can be approximated by ensemble averages.

Main Methods:

  • Utilizing the Hilbert space average method for analytical investigation.
  • Performing numerical simulations via exact diagonalization of the time-dependent Schrödinger equation.
  • Analyzing a pertinent, abstract Hamiltonian model.

Main Results:

  • The vast majority of pure states with a common expectation value for a generic observable at a given time show very similar values at later times.
  • Individual dynamics of expectation values are typically well described by the ensemble average.
  • The Hilbert space average method provides a robust framework for this analysis.

Conclusions:

  • Quantum dynamics in high-dimensional Hilbert spaces exhibit a high degree of predictability for expectation values.
  • The ensemble average serves as a reliable descriptor for individual quantum dynamics in these systems.
  • Implications for projection operator methods and the nature of irreversibility in quantum mechanics are discussed.