In the setting of the Weyl quantization on the flat torus Tn , we exhibit a class of wave functions with uniquely associated Wigner probability measure, invariant under the Hamiltonian dynamics and with support contained in weak KAM tori in phase space. These sets are the graphs of Lipschitz-continuous weak KAM solutions of negative type of the stationary Hamilton-Jacobi equation. Such Wigner measures are, in fact, given by the Legendre transform of Mather’s minimal probability measures. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.
Alberto Parmeggiani, Lorenzo Zanelli (2014). Wigner measures supported on weak KAM tori. JOURNAL D'ANALYSE MATHEMATIQUE, 123(1), 107-137 [10.1007/s11854-014-0015-8].
Wigner measures supported on weak KAM tori
PARMEGGIANI, ALBERTO;
2014
Abstract
In the setting of the Weyl quantization on the flat torus Tn , we exhibit a class of wave functions with uniquely associated Wigner probability measure, invariant under the Hamiltonian dynamics and with support contained in weak KAM tori in phase space. These sets are the graphs of Lipschitz-continuous weak KAM solutions of negative type of the stationary Hamilton-Jacobi equation. Such Wigner measures are, in fact, given by the Legendre transform of Mather’s minimal probability measures. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
