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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Diverging equilibration times in long-range quantum spin models.

Michael Kastner1

  • 1National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa. kastner@sun.ac.za

Physical Review Letters
|April 27, 2011
PubMed
Summary
This summary is machine-generated.

Quantum Ising models with long-range interactions rarely reach equilibrium in large systems. Equilibration occurs too slowly to be observed, meaning system properties remain near their initial values over accessible timescales.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Understanding the approach to thermal equilibrium is crucial in quantum many-body systems.
  • Long-range interactions in quantum Ising models (decaying as r(-α)) present unique challenges to equilibration dynamics.
  • Previous studies have explored equilibration in systems with varying interaction ranges.

Purpose of the Study:

  • To investigate the time evolution and approach to equilibrium in long-range quantum Ising models.
  • To analytically determine the conditions under which these models equilibrate.
  • To assess the practical observability of equilibrium in such systems.

Main Methods:

  • Analytical calculation of time evolution for expectation values of observables.
  • Focus on quantum Ising models with interactions decaying as r(-α), where α is less than or equal to the lattice dimension.
  • Consideration of a broad range of observables and initial states.

Main Results:

  • Demonstrated that for large system sizes (N), expectation values of certain observables remain practically unchanged from their initial values.
  • Proved analytically that equilibration is effectively absent on experimentally accessible timescales for large N.
  • The rate of equilibration is strongly dependent on the system size and interaction exponent α.

Conclusions:

  • Large quantum Ising models with long-range interactions exhibit extremely slow equilibration.
  • Equilibration occurs on timescales far beyond experimental reach, rendering it practically unobservable.
  • The findings have significant implications for simulating and understanding quantum dynamics in such systems.