Topological theory of phase transitions

Year: 2022

Authors: Gori M., Franzosi R., Pettini G., Pettini M.

Autors Affiliation: Howard Univ, Quantum Biol Lab, 2400 6th St NW, Washington, DC 20059 USA; Univ Luxembourg, Dept Phys & Sci Mat, Luxembourg, Luxembourg; Univ Siena, DSFTA, Via Roma 56, I-53100 Siena, Italy; Ist Nazl Fis Nucl, Sez Perugia, I-06123 Perugia, Italy; CNR Ist Nazl Ott, QSTAR, Largo E Fermi 6, I-50125 Florence, Italy; Univ Firenze, Ist Nazl Fis Nucl, Sez Firenze, Dipartimento Fis, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy; Aix Marseille Univ, Univ Toulon, CNRS, Marseille, France; CNRS, Ctr Phys Theor, UMR7332, F-13288 Marseille, France; Ist Nazl Fis Nucl, Sez Firenze, I-50019 Sesto Fiorentino, Italy.

Abstract: The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase transitions. In fact, in correspondence of a phase transition there are peculiar geometrical changes of the mechanical manifolds that are found to stem from changes of their topology. These findings, together with two theorems, have suggested that a topological theory of phase transitions can be formulated to go beyond the limits of the existing theories. Among other advantages, the new theory applies to phase transitions in small N systems (that is, at nanoscopic and mesoscopic scales), and in the absence of symmetry-breaking. However, the preliminary version of the theory was incomplete and still falsifiable by counterexamples. The present work provides a relevant leap forward leading to an accomplished development of the topological theory of phase transitions paving the way to further developments and applications of the theory that can be no longer hampered.

Journal/Review: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Volume: 55 (37)      Pages from: 375002-1  to: 375002-34

More Information: This work has been done within the framework of the project MOLINT which has received funding from the Excellence Initiative of Aix-Marseille University-A*Midex, a French ’Investissements d’Avenir’ programme. This work was also partially supported by the European Union’s Horiz on 2020 Research and Innovation Programme under Grant Agreement No. 964203 (FET-Open LINkS project). Roberto Franzosi acknowledges support by the QuantERA ERA-NET Co-fund 731473 (Project Q-CLOCKS) and the support by the National Group of Mathematical Physics (GNFM-INdAM). Matteo Gori thanks the financial support of DARPA (USA) for his long term visit at Howard University at Washington D.C. during which part of this work was done.
KeyWords: phase transitions; topological methods; microcanonical ensemble
DOI: 10.1088/1751-8121/ac7f09

ImpactFactor: 2.100
Citations: 8
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-24
References taken from IsiWeb of Knowledge: (subscribers only)

Connecting to view paper tab on IsiWeb: Click here
Connecting to view citations from IsiWeb: Click here