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Characterization of Thermal Transport in One-dimensional Solid Materials
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Lower bounds on high-temperature diffusion constants from quadratically extensive almost-conserved operators.

Tomaž Prosen1

  • 1Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 4, 2014
PubMed
Summary
This summary is machine-generated.

We established a general theorem providing a strict lower bound for high-temperature diffusion constants in quantum lattice systems. This bound applies to systems with almost conserved quantities localized at boundaries.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Diffusion constants are crucial for understanding transport properties in quantum systems.
  • High-temperature approximations simplify complex quantum dynamics.
  • Green-Kubo formulas relate transport coefficients to equilibrium time-correlation functions.

Purpose of the Study:

  • To derive a general theorem for a strict lower bound on high-temperature diffusion constants.
  • To investigate the role of almost conserved quantities in bounding diffusion.
  • To apply the theorem to specific one-dimensional quantum models.

Main Methods:

  • Development of a general mathematical theorem.
  • Assumption of a quadratically extensive almost conserved quantity.
  • Localization of the commutator of the conserved quantity with the Hamiltonian to boundary sites.
  • Explicit computation of the bound in specific models.

Main Results:

  • A general theorem providing a strict lower bound on high-temperature diffusion constants is proven.
  • The existence of a localized almost conserved quantity is shown to be sufficient for this bound.
  • The bound is explicitly computed for the Heisenberg spin 1/2 chain and the fermionic Hubbard chain.

Conclusions:

  • The study provides a novel theoretical tool for bounding diffusion in quantum lattice systems.
  • The findings highlight the importance of boundary-localized conserved quantities in determining transport properties.
  • The explicit computations validate the theorem's applicability to important physical models.