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Quantum Simulation

Quantum Boltzmann equation for spin-dependent reactions in the kinetic regime

arXiv

Authors: Martin L. R. Fürst, Markus Kotulla, Christian B. Mendl, Herbert Spohn

Year

2014

Paper ID

46537

Status

Preprint

Abstract Read

~2 min

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Abstract

We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-frac{1}{2} particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 times 2 spin-density ("Wigner") matrix. We show that density and energy conservation laws as well as the H-theorem hold, and enumerate additional conservation laws depending on the interaction. The conserved quantities characterize the t → infty thermal (Fermi-Dirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.

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We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-frac12 particles...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1411.2576 [2] arXiv https://arxiv.org/abs/1411.2576 [3] Publisher https://arxiv.org/abs/1411.2576

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