Quantum quenches in Luttinger liquids
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It is common in physics to treat 1D system as a toy model in order to test a physical theory because it is easier to work with low dimensional systems and find analytical solutions. One naively will say that one-dimensional models serve as toy models and they do not apply in the real world. But, one-dimensional systems, e.g quantum wires, exists in nature and have quite different physics from higher dimensional systems. It is remarkable that, in 1D, an interacting fermionic problem can be turned to a free bosonic theory. An interesting question to ask is how the system evolves after a change in the systems internal parameters. This is called a quantum quench. In this thesis we investigate quantum quenches in the Luttinger liquid model, which is a 1D model and serves as the analog of the Fermi liquid theory in one dimension. More specifically, we study the kinetic energy, when we periodically drive the internal parameters of the system, and the two point correlation function, after a periodic quench of finite duration.