Quasilocality and equilibration in quantum systems

Medenjak, Marko (author), Prosen, Tomaž (mentor)

The primary area, on which we focus in the thesis, are the out-of-equilibrium properties of quantum and classical systems. The playground we use to study those properties, are interacting integrable and solitonic systems, whose structure enables us to perform analytical calculations. In the context of the out-of-equilibrium physics we focus on two questions. The first problem is related to the set of stationary states in quantum systems. The question is especially important in the context of the homogeneous quantum quenches, since it makes possible the calculations of expectation values of local observables. The building blocks of stationary states are quasilocal conserved quantities which constitute the information that is preserved under the time evolution. In the first part of the thesis we deal with the construction of quasilocal conserved quantities in one dimensional anisotropic Heisenberg model and bosonic models. Quasilocal charges are put in the context of the standard theory of integrability, which in turn allows for the calculation of physical quantities. The second question we deal with are the transport properties of one dimensional systems. The connection between the local integrals of motion and ideal transport was established in 90's. Here we extend the connection to the diffusive transport. This enables us to obtain explicit lower bound on diffusion constant in Heisenberg model, which proves that the Heisenberg model is not an insulator at finite temperatures. In the last chapter we deal with the transport properties of classical celular automata. The first example we consider is the gas of charged hard core interacting particles, and the second one the gas of interacting solitons. Explicit solution of the dynamics of local observables allows for the explicit calculation of transport coeffcients, and the solution of the inhomogeneous quench problem. Despite their simplicity, the models exhibit wide range of transport phenomena ranging from insulating, through diffusive to ballistic transport.

• Language: English
• Keywords: Nonequilibrium statistical physics, integrability, quasilocal integrals of motion, cellular automata, transport
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2018
• PID: 20.500.12556/RUL-101756
• COBISS.SI-ID: 3212388
• Publication date in RUL: 04.07.2018

Secondary language

• Language: Slovenian
• Title: Efektivna lokalnost in ekvilibracija v kvantnih sistemih

Abstract

Širše področje, ki ga obravnavamo v okviru doktorske disertacije sta neravnovesna kvantna in klasična fizika. Osrednja tema obravnave so integrabilni in solitonski interagirajoči sistemi, ki nam s svojo strukturo omogočajo analitično obravnavo. V okviru področja se osredotočimo na dve vprašanji. Prvo vprašanje zadeva stacionarna stanja v kvantnih sistemih. Karakterizacija vseh stacionarnih stanj nam omogoča izračun pričakovanih vrednosti lokalnih opazljivk, v okviru kvantnega homogenega začetnega problema. Gradniki stacionarnih stanj so efektivno lokalne ohranjene količine, ki predstavljajo informacijo, ki se ohrani v sistemu za vse čase. V prvem delu disertacije se posvetimo konstrukciji efektivno lokalnih ohranjenih količin v enodimenzionalnem anizotropnem Heisenbergovem modelu in bozonskih modelih. Efektivno lokalne ohranitvene zakone uvrstimo v okvir teorije integrabilnosti in kvazidelčnega opisa integrabilnih sistemov, ki omogoča neposreden izračun fizikalnih količin. Drugo vprašanje se nanaša na naravo transportnih lastnosti v enodimenzionalnih sistemih. Povezava med idealnim transportom in efektivno lokalnimi količinami je bila vzpostavljena v 90 letih. V disertaciji razširimo povezavo na normalni, oziroma difuzijski transport. Ta nam omogoča izračun spodnje meje na difuzijsko konstanto v Heisenbergovem modelu, s čimer pokažemo, da Heisenbergov model pri končnih temperaturah ni izolator. V zadnjem poglavju obravnavamo transportne lastnosti klasičnih celičnih avtomatov. Prvi model opisuje nabite delcev, ki se elastično sipajo, drugi pa ustreza dinamiki solitonov, pri katerih pride do faznega zamika ob sipanju. Eksplicitna rešitev dinamike lokalnih opazljivk nam omogoča analitičen izračun transportnih koefcientov, kot tudi rešitev nehomogenega začetnega problema. Kljub svoji preprostosti sta modela zanimiva zaradi svojih transportnih lastnosti. Izraženi so namreč kar trije transportni režimi, od izolatorskega, preko difuzijskega, pa vse do balističnega.

• Keywords: Neravnovesna statistična fizika, integrabilnost, efektivno lokalne ohranjene količine, celični avtomati, transport