Symmetry breaking, phase transitions, and hydrodynamic attractors

Buza, Guri (author), Grozdanov, Sašo (mentor), Soloviev, Alexander (comentor)

Recent theoretical studies of an expanding quark-gluon plasma, utilizing the Müller-Israel-Stewart formalism, have given rise to the concept of hydrodynamic attractors in relativistic viscous hydrodynamics. In parallel, the Son-Nicolis framework has elucidated the relation between fields and thermodynamical variables in an effective field theory. Expanding upon the incorporation of both approaches, we study the theory of an effective action for a complex scalar field, charged under a $U(1)$ global symmetry with a temperature-dependent symmetry-breaking potential, giving rise to a phase transition, in expanding background metrics. In particular, we examine the evolution of this superfluid within the contexts of Bjorken flow, Gubser flow, and the Friedmann-Lemaître-Robertson-Walker background, with special emphasis on the estimation of the hydrodynamic attractor timescale and the oscillatory behavior across these scenarios.

• Language: English
• Keywords: relativistic hydrodynamics, hydrodynamic attractors, order parameter, symmetry-breaking potential, superfluids, Bjorken flow, Gubser flow, FLRW background, Müller-Israel-Stewart formalism, Son-Nicolis framework
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-162763
• COBISS.SI-ID: 209045763
• Publication date in RUL: 27.09.2024

Secondary language

• Language: Slovenian
• Title: Zlom simetrije, fazni prehodi in hidrodinamski atraktorji

Abstract

Teoretični opisi kvark gluon plazme, ki temeljijo na Müller-Israel-Stewart formalizmu, uvedejo pojem hidrodinamskega atraktorja v relativistični hidrodinamiki. Po drugi strani lahko v efektivni teoriji polja povežemo termodinamske količine in dinamična polja s pomočjo Son-Nicolis teorije. V tem delu nadgradimo oba pristopa na primeru efektivne akcije kompleksnega skalarnega polja, nabitega pod globalno U(1) simetrijo, ob prisotnosti temperaturno odvisnega potenciala, ki simetrijo zlomi in posledično inducira fazni prehod v razširjajočem se ozadju. Obravnavamo predvsem časovno dinamiko te supertekočine v primerih Bjorkenovega in Gubserjevega toka ter FLRW ozadja, s posebnim poudarkom na oceni časovne skale hidrodinamskega atratkorja ter oscilatornimi pojavi v teh ozadjih.

• Keywords: relativistična hidrodinamika, hidrodinamski atraktorji, ureditveni parameter, potencial zloma simetrije, superfluidnost, Bjorkenov tok, Gubserjev tok, FLRW ozadje, Müller-Israel-Stewartov formalizem, Son-Nicolisova teorija.