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

Martin L.R. Fürst; Markus Kotulla; Christian B. Mendl; Herbert Spohn

doi:10.1088/1751-8113/48/9/095204

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

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

Research output: Contribution to journal › Article › peer-review

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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-1/2 particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 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 → ∞ thermal (FermiDirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.

Original language	English
Article number	095204
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	48
Issue number	9
DOIs	https://doi.org/10.1088/1751-8113/48/9/095204
State	Published - 2 Mar 2015

Keywords

kinetic regime
quantum Boltzmann equation
spin-dependent quantum processes
weak interaction

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10.1088/1751-8113/48/9/095204

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title = "Quantum Boltzmann equation for spin-dependent reactions in the kinetic regime",

abstract = "We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-1/2 particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 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 → ∞ thermal (FermiDirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.",

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AU - Fürst, Martin L.R.

AU - Kotulla, Markus

AU - Mendl, Christian B.

AU - Spohn, Herbert

PY - 2015/3/2

Y1 - 2015/3/2

N2 - We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-1/2 particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 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 → ∞ thermal (FermiDirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.

AB - We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-1/2 particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 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 → ∞ thermal (FermiDirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.

KW - kinetic regime

KW - quantum Boltzmann equation

KW - spin-dependent quantum processes

KW - weak interaction

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VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

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ER -

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

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