%0 Journal Article %T Contraction semigroups of elliptic quadratic differential operators %A Karel Pravda-Starov %J Mathematics %D 2007 %I arXiv %X We study the contraction semigroups of elliptic quadratic differential operators. Elliptic quadratic differential operators are the non-selfadjoint operators defined in the Weyl quantization by complex-valued elliptic quadratic symbols. We establish in this paper that under the assumption of ellipticity, as soon as the real part of their Weyl symbols is a non-zero non-positive quadratic form, the norm of contraction semigroups generated by these operators decays exponentially in time. %U http://arxiv.org/abs/0705.0950v1