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Abstract

In this thesis, we explore the role of quasiparticles in two problems that have integrability at their core: the entanglement content of excited states and the out-of-equilibrium dynamics in the presence of unstable excitations. In the first part, we consider the one-dimensional massive free boson and different partitions of a ring. We compute entanglement entropies and logarithmic negativites in states composed of multiple particle excitations, in the limit of large volume and regions’ lengths. We find that the quasiparticle excitations give additive contributions to the vacuum entanglement that depend on very few properties of the state, namely the number of excitations and their (in) distinguishability, and that are independent of the connectivity of the regions. The results have a natural probabilistic interpretation as the entanglement of multi-qubit states where qubits represent the presence or absence of excitations in the regions of the partition. Such a simple structure suggests that the results obtained are universal, a suggestion that is further supported by both analytical and numerical evidence. At the heart of this universality there is the only basic assumption that particle excitations can be localised within the entanglement regions. In the second part of this thesis we apply the generalised hydrodynamic approach to study an integrable model possessing an unstable excitation in its spectrum. Because of the finite lifetime the dynamics of the unstable particle can be studied only indirectly, in terms of the constituent (stable) particles. We find that the out-of-equilibrium dynamics of the stable particles exhibits clear signatures of instability such as decay, creation of tails, and large-time stable populations of mutually interacting particles. We use these signatures to develop a more clear physical picture of the formation of the unstable excitation.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Departments:	Doctoral Theses School of Science & Technology School of Science & Technology > Mathematics

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