We study positivity and contractivity properties for semigroups on M2(C), compute the optimal log-Sobolev constant and prove hypercontractivity for the class of positive semigroups leaving invariant both subspaces generated by the Pauli matrices σ0, σ3 and σ1, σ2. The optimal log-Sobolev constant turns out to be bigger than the usual one arising in several commutative and noncommutative contexts when the semigroup acts on the off-diagonal matrices faster than on diagonal matrices. These results are applied to the semigroup of the Wigner–Weisskopf atom.
Optimal log-Sobolev inequality and hypercontractivity for semigroups on M_2(C)
CARBONE, RAFFAELLA
2004-01-01
Abstract
We study positivity and contractivity properties for semigroups on M2(C), compute the optimal log-Sobolev constant and prove hypercontractivity for the class of positive semigroups leaving invariant both subspaces generated by the Pauli matrices σ0, σ3 and σ1, σ2. The optimal log-Sobolev constant turns out to be bigger than the usual one arising in several commutative and noncommutative contexts when the semigroup acts on the off-diagonal matrices faster than on diagonal matrices. These results are applied to the semigroup of the Wigner–Weisskopf atom.File in questo prodotto:
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