Neravnotežna dinamika međudjelujućih višečestičnih sustava zanimljiva je u kontekstu jednodimenzionalnih bozonskih plinova iz više razloga: (i) ovi su sustavi eksperimentalno realizirani, (ii) modeli kojima opisujemo ovakve sustave, npr. Lieb-Liniger model, egzaktno su rješivi u nekim slučajevima i (iii) kvantni efekti pojačani su u sustavima reduciranih dimenzija. Naš je cilj opis neravnotežne dinamike korištenjem egzaktnih metoda što je od posebnog značaja kada se sustav približava jako koreliranom režimu. U okviru Lieb-Liniger modela, gdje jakost interakcije varira od slabo do jako interagirajućeg režima, koristimo metodu koja daje egzaktna vremenski ovisna višečestična rješenja, a izvorno ju je uveo Gaudin. Također, u jako interagirajućem limesu Tonks-Girardeau plina proučili smo pojavu Andersonove lokalizacije.

Nonequilibrium dynamics of interacting many-body systems is extremely interesting in the context of one-dimensional (1D) bosonic gases for many reasons: (i) these systems are experimentally realized with atoms trapped in 1D atomic waveguides, (ii) models which describe such systems, e.g. the Lieb-Liniger model, are exactly solvable in some non-equilibrium situations, and (iii) quantum effects are enhanced in systems of reduced dimensionality. Our aim is to describe dynamics of a many-body system by employing exact methods, which is of particular importance when the system approaches strongly correlated regime, when the usual mean-field treatment is not applicable. We have studied nonequilibrium dynamics within the framework of the Lieb-Liniger model, where interaction strength varies from weakly to strongly interacting regime, using an exact approach, originally introduced by Gaudin. Furthermore, in the strongly interacting limit of the Tonks-Girardeau gas we have studied the phenomenon of Anderson localization.