Quantum linear kicked rotor

This thesis primarily discusses the linear quantum kicked rotor and its energy growth over long periods of time. The linear kicked rotor is a useful model due to being exactly solvable. It has the Hamiltonian $H=2\pi \alpha p + V(\theta)\sum^\infty_{-\infty} \delta(t-n),\space (0\leq\theta\leq2\pi)$ as written by Berry [Physica D 10 (1984) 369–378]. The quasi-energy eigenstates of the system are localized in $p$ if $\alpha$ is irrational and extended in $p$ if $\alpha$ is rational. The re-derivations of the quasi-energy eigenstates, wave-function and kinetic energy expectation aim at reproducing previous results. The result in Berry's paper is for the pure momentum initial state, where the energy grows quadratically in time when $\alpha$ is rational and remains bounded when $\alpha$ is irrational. A new derivation generalizes the kinetic energy expectation and momentum expectation for arbitrary initial states. The generalized result reduces to Berry's in the case of a pure momentum initial state. Without a pure momentum initial state, the energy growth behaviour over long times still remains the same as Berry's.