Equilibrium dynamics of continuous unbounded spin systems
Equilibrium dynamics of continuous unbounded spin systems
View/Type of Scholarly Publication
DissertationDate of Exam
09.05.2011Date of Publication
25.05.2011Advisor
Otto, FelixCo-Referee
Müller, StefanMetadata
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Abstract
The relaxation properties of the Glauber and Kawasaki dynamics are studied for large lattice systems of unbounded continuous spins. For this purpose the logarithmic Sobolev inequality is deduced for the canonical ensemble in two cases. In the first case, the Hamiltonian consists of a sum of superquadratic single-site potentials. In the second case, the Hamiltonian also has a weak two-body interaction. For technical reasons, the single-site potential is a perturbation of a quadratic potential in this case. The scaling of the logarithmic Sobolev constant is optimal in the system size and independent of the boundary data of the system.
Subjects
Spin System, Kawasaki dynamics, Logarithmic Sobolev inequality, Canonical, ensemble, Coarse-graining, Weak interaction
Classification (DDC)
510 MathematikMenz, Georg: Equilibrium dynamics of continuous unbounded spin systems. - Bonn, 2011. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-25331
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-25331
@phdthesis{handle:20.500.11811/4979,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-25331,
author = {{Georg Menz}},
title = {Equilibrium dynamics of continuous unbounded spin systems},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2011,
month = may,
note = {The relaxation properties of the Glauber and Kawasaki dynamics are studied for large lattice systems of unbounded continuous spins. For this purpose the logarithmic Sobolev inequality is deduced for the canonical ensemble in two cases. In the first case, the Hamiltonian consists of a sum of superquadratic single-site potentials. In the second case, the Hamiltonian also has a weak two-body interaction. For technical reasons, the single-site potential is a perturbation of a quadratic potential in this case. The scaling of the logarithmic Sobolev constant is optimal in the system size and independent of the boundary data of the system.},
url = {https://hdl.handle.net/20.500.11811/4979}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-25331,
author = {{Georg Menz}},
title = {Equilibrium dynamics of continuous unbounded spin systems},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2011,
month = may,
note = {The relaxation properties of the Glauber and Kawasaki dynamics are studied for large lattice systems of unbounded continuous spins. For this purpose the logarithmic Sobolev inequality is deduced for the canonical ensemble in two cases. In the first case, the Hamiltonian consists of a sum of superquadratic single-site potentials. In the second case, the Hamiltonian also has a weak two-body interaction. For technical reasons, the single-site potential is a perturbation of a quadratic potential in this case. The scaling of the logarithmic Sobolev constant is optimal in the system size and independent of the boundary data of the system.},
url = {https://hdl.handle.net/20.500.11811/4979}
}
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