Hypercontractivity for a family of quantum Ornstein-Uhlenbeck semigroups
Longfa Sun, Zhendong Xu, Hao Zhang
TL;DR
This paper proves hypercontractivity for a family of quantum Ornstein-Uhlenbeck semigroups and determines the optimal time order for elements with zero Gibbs state, using Meixiner polynomials.
Contribution
It establishes hypercontractivity for quantum Ornstein-Uhlenbeck semigroups and identifies the optimal time bounds, advancing understanding in quantum functional analysis.
Findings
Proved hypercontractivity for the quantum Ornstein-Uhlenbeck semigroups.
Determined the optimal order of the optimal time for certain elements.
Utilized Meixiner polynomials as a key proof ingredient.
Abstract
We show that a family of quantum Ornstein-Uhlenbeck semigroups is hypercontractive. We also obtain the optimal order of the optimal time up to a constant for those elements whose Gibbs state is zero. The main ingredient of our proof is Meixiner polynomials.
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Taxonomy
TopicsStochastic processes and financial applications · Advanced Thermodynamics and Statistical Mechanics · Quantum Information and Cryptography