%0 Journal Article
%J Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719
%D 2012
%T Thermodynamic phase transitions and shock singularities
%A Giuseppe De Nittis
%A Antonio Moro
%X 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.
%B Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719
%I The Royal Society
%G en
%U http://hdl.handle.net/1963/6090
%1 5978
%2 Mathematics
%3 Mathematical Physics
%4 -1
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T11:53:22Z\\nNo. of bitstreams: 1\\n1107.0394v2.pdf: 610849 bytes, checksum: be0b8d83ff44e0468c3133f7ab3ca18d (MD5)
%R 10.1098/rspa.2011.0459
%0 Report
%D 2010
%T The geometry emerging from the symmetries of a quantum system
%A Giuseppe De Nittis
%A Gianluca Panati
%X 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.
%G en_US
%U http://hdl.handle.net/1963/3834
%1 493
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T16:38:34Z\\nNo. of bitstreams: 1\\n0911.5270v2.pdf: 578198 bytes, checksum: a06ef54ebf418d5d7b6d0a7c3410c054 (MD5)