Travaglino, Riccardo
(2023)
On the generalized hydrodynamics of integrable quantum field theories with irrelevant deformations.
[Laurea magistrale], Università di Bologna, Corso di Studio in
Physics [LM-DM270]
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Abstract
The purpose of this Master Thesis is to study the Generalized Hydrodynamics
(GHD) of Integrable Quantum Field Theories perturbed by the famous TTbar deformation and its generalizations. These deformations are irrelevant, and therefore
alter dramatically the UV structure of the theory and are not renormalizable, but
are still considered consistent and interesting theories since they preserve the integrable structure of the underlying model. The specific focus of the work is to
find the average densities and currents related to conserved charges of generic spin,
which describe the flow of energy, momentum, and higher charges, between two
semi-infinite slabs prepared in two different states and placed in contact in the
origin, in the setup known as partitioning protocol. From a theoretical point of
view this is the most important protocol in out of equilibrium physics, since it is
simple enough to have an analytical description and in some situations to have an
analytical solution, but at the same time it is complex enough to gain practical
knowledge on the effect of inhomogeneities on integrable systems. In particular,
through a convenient way of rewriting the Thermodynamic Bethe Ansatz (TBA)
equations, I found exact expressions for the currents and densities in the conformal
limit, generalizing previously known results in several directions, with excellent numerical validation. I have also performed an in-depth study of possible extensions
of the results out of the conformal point in the simplest possible theory, the free
fermion, obtaining interesting expressions for the lowest order corrections in terms
of special functions. Finally, I have performed numerical simulations which give
a perfect confirmation of the analytical results, and allow to gain insight on some
interesting aspects of the models which are not accessible analytically.
Abstract
The purpose of this Master Thesis is to study the Generalized Hydrodynamics
(GHD) of Integrable Quantum Field Theories perturbed by the famous TTbar deformation and its generalizations. These deformations are irrelevant, and therefore
alter dramatically the UV structure of the theory and are not renormalizable, but
are still considered consistent and interesting theories since they preserve the integrable structure of the underlying model. The specific focus of the work is to
find the average densities and currents related to conserved charges of generic spin,
which describe the flow of energy, momentum, and higher charges, between two
semi-infinite slabs prepared in two different states and placed in contact in the
origin, in the setup known as partitioning protocol. From a theoretical point of
view this is the most important protocol in out of equilibrium physics, since it is
simple enough to have an analytical description and in some situations to have an
analytical solution, but at the same time it is complex enough to gain practical
knowledge on the effect of inhomogeneities on integrable systems. In particular,
through a convenient way of rewriting the Thermodynamic Bethe Ansatz (TBA)
equations, I found exact expressions for the currents and densities in the conformal
limit, generalizing previously known results in several directions, with excellent numerical validation. I have also performed an in-depth study of possible extensions
of the results out of the conformal point in the simplest possible theory, the free
fermion, obtaining interesting expressions for the lowest order corrections in terms
of special functions. Finally, I have performed numerical simulations which give
a perfect confirmation of the analytical results, and allow to gain insight on some
interesting aspects of the models which are not accessible analytically.
Tipologia del documento
Tesi di laurea
(Laurea magistrale)
Autore della tesi
Travaglino, Riccardo
Relatore della tesi
Correlatore della tesi
Scuola
Corso di studio
Indirizzo
THEORETICAL PHYSICS
Ordinamento Cds
DM270
Parole chiave
Statistical Field Theory,Nonequilibrium Physics,TTbar,Integrability,Generalized Hydrodynamics,TBA,Generalized Gibbs Ensemble,Irrelevant Perturbations,Conformal Field Theory
Data di discussione della Tesi
29 Settembre 2023
URI
Altri metadati
Tipologia del documento
Tesi di laurea
(NON SPECIFICATO)
Autore della tesi
Travaglino, Riccardo
Relatore della tesi
Correlatore della tesi
Scuola
Corso di studio
Indirizzo
THEORETICAL PHYSICS
Ordinamento Cds
DM270
Parole chiave
Statistical Field Theory,Nonequilibrium Physics,TTbar,Integrability,Generalized Hydrodynamics,TBA,Generalized Gibbs Ensemble,Irrelevant Perturbations,Conformal Field Theory
Data di discussione della Tesi
29 Settembre 2023
URI
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