Out of any unitary representation of a group, positive-type functions on the group can be obtained. These functions allow one to construct positive semi-definite matrices that may be used to define new inequalities for higher moments of observables associated with classical probability distribution functions and density states of quantum systems. The inequalities stemming from the Heisenberg–Weyl group representations are considered in connection with Gaussian distributions. We obtain new inequalities for multi-variable Hermite polynomials.
Positive-type functions on groups andnew inequalities in classicaland quantum mechanics / V. I., Man’Ko; Marmo, Giuseppe; Simoni, Alberto; Ventriglia, Franco. - In: PHYSICA SCRIPTA. - ISSN 0031-8949. - STAMPA. - 82:3(2010), pp. 038114-038120. [10.1088/0031-8949/82/03/038114]
Positive-type functions on groups andnew inequalities in classicaland quantum mechanics
MARMO, GIUSEPPE;SIMONI, ALBERTO;VENTRIGLIA, FRANCO
2010
Abstract
Out of any unitary representation of a group, positive-type functions on the group can be obtained. These functions allow one to construct positive semi-definite matrices that may be used to define new inequalities for higher moments of observables associated with classical probability distribution functions and density states of quantum systems. The inequalities stemming from the Heisenberg–Weyl group representations are considered in connection with Gaussian distributions. We obtain new inequalities for multi-variable Hermite polynomials.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
