Bovo, Filippo (2015). Thermal dynamics of one-dimensional quantum systems. University of Birmingham. Ph.D.
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Bovo15PhD.pdf
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Abstract
In this work we examine the dynamics of one-dimensional systems. We present a continuum approach to the construction of the non-equilibrium Keldysh functional integral and derive a relation between the classical and quantum fields of the Keldysh formalism and the occupation of a state. Using the Keldysh formalism, we give a self-contained presentation of bosonization and refermionisation of fermionic and bosonic interacting particles. We derive the first two non-linear corrections to linear bosonization due to the fermionic spectrum curvature using the functional integral formalism. Using the previous results, we study the thermal dynamics of one-dimensional systems. We consider both the phonons, coming from bosonization, and fermionic quasiparticles, coming from refermionisation, in a single theory. Having them in a single theory is justified by a scale separation between them. Studying the dynamical structure factor we find three regimes. From higher to lower energies we have a ballistic and a collisional regimes of fermionic quasiparticles and a hydrodynamical regime of non-linear phonons. The phase field of the non-linear bosons satisfies the Kardar-Parisi-Zhang equation, thereby linking the dynamics of one-dimensional quantum systems to the universality class of surface growth. The time-scale separating the phononic and fermionic quasiparticle regimes is very long for up-to-date experiments, meaning that the ballistic regime of fermionic quasiparticles is the only one likely to be observed. Since this approach has a limited range of validity for weakly interacting bosons, we derive their dynamical structure factor using a semiclassical approach.
Type of Work: | Thesis (Doctorates > Ph.D.) | ||||||
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Award Type: | Doctorates > Ph.D. | ||||||
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College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | ||||||
School or Department: | School of Physics and Astronomy | ||||||
Funders: | None/not applicable | ||||||
Subjects: | Q Science > QC Physics | ||||||
URI: | http://etheses.bham.ac.uk/id/eprint/6320 |
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