Analytic exploration of the non-perturbative domain of asymptotic observables
Analytic exploration of the non-perturbative domain of asymptotic observables
Transseries expansions are natural extensions of ordinary power series and include non-perturbative monomials such as exponentials as additional basis elements. By using a range of highly accurate asymptotic methods an analytic understanding of the full non-perturbative domain of asymptotic observables can be obtained which can go far beyond the results of numerical computations. This is the focus of this thesis, where such asymptotic methods have proven crucial for the full non-perturbative understanding of observables in three separate research directions. The so-called transasymptotic summation is used to arrive at a novel analytic understanding of the bifurcation behaviour of discrete non-linear systems. It is shown that such transasymptotic summations can be used to naturally explain the emergence of so-called delayed bifurcations widely known as ’canards’ in singularly perturbed systems. In the context of relativistic hydrodynamics, several distinct summation techniques are used and compared to match the late time temperature evolution of an expanding fluid to its early time behaviour. The power of the transasymptotic summation method is further exploited to derive global analytical properties such as analytic approximations to the locations of square-root branch points. In the context of mathematical relativity, the exponentially decaying and oscillatory corrections to the perturbative WKB approximation of the quasinormal mode frequencies of a charged scalar field in an expanding charged black hole spacetime background (RNdS) are captured in a transseries and analysed using Borel techniques and new analytic properties are found. These approaches to study non-perturbative phenomena are quite generic and can be applied to a large class of problems.
non-perturbative, hydrodynamics, relativistic, black hole, quasinormal, transseries, Reissner, Nordstrom, de Sitter, logistic, mode, quark-gluon plasma, bifurcation, canards, Borel summation, hyperasymptotics, transasymptotics, resummation, exponential asymptotics, Stokes phenomenon, non-hydrodynamic, scales, attractor, conformal invariance, Bjorken, boost invariance
University of Southampton
Hasenbichler, Daniel
33471eb8-7e5c-4dd7-9062-6fed61ac9abe
2024
Hasenbichler, Daniel
33471eb8-7e5c-4dd7-9062-6fed61ac9abe
Aniceto, Ines
0061ca0c-1ad8-4510-9b12-008e5c27a7ea
Howls, Christopher
66d3f0f0-376c-4f7a-a206-093935e6c560
Hasenbichler, Daniel
(2024)
Analytic exploration of the non-perturbative domain of asymptotic observables.
University of Southampton, Doctoral Thesis, 221pp.
Record type:
Thesis
(Doctoral)
Abstract
Transseries expansions are natural extensions of ordinary power series and include non-perturbative monomials such as exponentials as additional basis elements. By using a range of highly accurate asymptotic methods an analytic understanding of the full non-perturbative domain of asymptotic observables can be obtained which can go far beyond the results of numerical computations. This is the focus of this thesis, where such asymptotic methods have proven crucial for the full non-perturbative understanding of observables in three separate research directions. The so-called transasymptotic summation is used to arrive at a novel analytic understanding of the bifurcation behaviour of discrete non-linear systems. It is shown that such transasymptotic summations can be used to naturally explain the emergence of so-called delayed bifurcations widely known as ’canards’ in singularly perturbed systems. In the context of relativistic hydrodynamics, several distinct summation techniques are used and compared to match the late time temperature evolution of an expanding fluid to its early time behaviour. The power of the transasymptotic summation method is further exploited to derive global analytical properties such as analytic approximations to the locations of square-root branch points. In the context of mathematical relativity, the exponentially decaying and oscillatory corrections to the perturbative WKB approximation of the quasinormal mode frequencies of a charged scalar field in an expanding charged black hole spacetime background (RNdS) are captured in a transseries and analysed using Borel techniques and new analytic properties are found. These approaches to study non-perturbative phenomena are quite generic and can be applied to a large class of problems.
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Published date: 2024
Keywords:
non-perturbative, hydrodynamics, relativistic, black hole, quasinormal, transseries, Reissner, Nordstrom, de Sitter, logistic, mode, quark-gluon plasma, bifurcation, canards, Borel summation, hyperasymptotics, transasymptotics, resummation, exponential asymptotics, Stokes phenomenon, non-hydrodynamic, scales, attractor, conformal invariance, Bjorken, boost invariance
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Local EPrints ID: 486358
URI: http://eprints.soton.ac.uk/id/eprint/486358
PURE UUID: 4e02f0fc-8b26-4f29-bbe3-e6461a5c3a9f
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Date deposited: 18 Jan 2024 19:23
Last modified: 18 Mar 2024 03:50
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Author:
Daniel Hasenbichler
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