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Quantum hopping models for kinetic processes

Dasgupta1

  • 1Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Calcutta 700 009, India.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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We propose quantum operators can model classical steady states. Exact mass distributions for bosons in lattices reveal density peaks and exponential distributions, mirroring classical models.

Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Quantum operators typically describe system evolution.
  • Classical systems can exhibit steady-state dynamics.
  • Lattice models are fundamental in condensed matter physics.

Purpose of the Study:

  • To explore the potential of quantum operators in describing classical steady-state situations.
  • To determine the exact mass distribution for bosons in a hypercubic lattice.
  • To compare quantum and classical model mass distributions.

Main Methods:

  • Consideration of a specific Hamiltonian for single boson hopping.
  • Exact calculation of mass distribution for ground and first excited states.
  • Analysis of mass distribution in arbitrary dimensions.

Related Experiment Videos

  • Comparison with an analogous classical model.

    • Main Results:

    • The mass distribution for the ground and first excited states was exactly determined.
    • A peak in density was observed at a mass equal to the density.
    • A variant Hamiltonian yielded an exponential mass distribution for the ground state.
    • This exponential distribution was found to be identical to an analogous classical model.

    Conclusions:

    • Quantum operators can effectively represent classical dynamical (steady-state) situations.
    • The lattice boson model provides exact mass distributions with specific characteristics.
    • The study highlights a connection between quantum and classical models through mass distribution similarities.