TY - JOUR
T1 - Thermodynamic phase transitions and shock singularities
JF - Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719
Y1 - 2012
A1 - Giuseppe De Nittis
A1 - Antonio Moro
AB - We show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed.
PB - The Royal Society
UR - http://hdl.handle.net/1963/6090
U1 - 5978
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - RPRT
T1 - The geometry emerging from the symmetries of a quantum system
Y1 - 2010
A1 - Giuseppe De Nittis
A1 - Gianluca Panati
AB - We investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result.
UR - http://hdl.handle.net/1963/3834
U1 - 493
U2 - Mathematics
U3 - Mathematical Physics
ER -