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4 results on '"ϕ4 theory"'

1. Quadratic Klein-Gordon equations with a potential in one dimension

Author

Pierre Germain and Fabio Pusateri

Subjects
nonlinear Klein-Gordon equation, distorted Fourier transform, scattering theory, kink solutions, ϕ4 theory, relativistic Ginzburg-Landau, 43A32, 42B37, 35P25, 35Q56, Mathematics, QA1-939
Abstract

This paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier transform at the nonlinear level; it does not rely only on Strichartz or virial estimates and is therefore able to treat low-power nonlinearities (hence also nonlocalised solitons) and capture the global (in space and time) behaviour of solutions.

Published
2022
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2. Wobbling kinks and shape mode interactions in a coupled two-component [formula omitted] theory.

Author

Alonso-Izquierdo, A., Miguélez-Caballero, D., and Nieto, L.M.

Subjects
*MODE shapes, *VIBRATIONAL spectra, *COUPLING constants, *SCALAR field theory
Abstract

The dynamics of a wobbling kink in a two-component coupled ϕ 4 scalar field theory (with an excited orthogonal shape mode) is addressed. For this purpose, the vibration spectrum of the second order small kink fluctuation is studied in order to find the corresponding vibration modes associated to the first (longitudinal) and second (orthogonal) field components. By means of this analysis, it was found that the number of possible shape modes depends on the value of the coupling constant. It is notable that when one of the orthogonal field shape modes is initially triggered, the unique shape mode of the longitudinal field is also activated. This coupling causes the kink to emit radiation with twice the frequency of excited mode in the first field component. Meanwhile, in the orthogonal channel we find radiation with two different frequencies: one is three times the frequency of the orthogonal wobbling mode and another is the sum of the frequencies of the longitudinal shape mode and the triggered mode. All the analytical results obtained in this study have been successfully contrasted with those obtained through numerical simulations. • The dynamics of a wobbler in a two component field theory is studied. • The number of shape modes is shown to depend on the value of the coupling constant. • When one orthogonal mode is triggered, the mode of the first field is activated. • The kink emits radiation with twice the frequency of the excited mode in the first component. • In the orthogonal channel radiation with two different frequencies appear. [ABSTRACT FROM AUTHOR]

Published
2024
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3. ANALYSIS OF CRITICAL SHORT-TIME LANGEVIN DYNAMICS IN TWO-DIMENSIONAL ϕ4 THEORY ON THE BASIS OF A HIGHER-ORDER ALGORITHM.

Author

OTOBE, TSUYOSHI, NAKAZATO, HIROMICHI, OKANO, KEISUKE, YUASA, KAZUYA, and HATTORI, NOZOMU

Subjects
*LANGEVIN equations, *ALGORITHMS, *ANALYSIS of variance, *CONTINUUM mechanics, *MAGNETISM
Abstract

We investigate the critical short-time scaling of the two-dimensional lattice ϕ4 field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed, through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents θ, z and the static exponent β/ν are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-known second-order form of discretized Langevin equation works well to investigate the short-time dynamics. [ABSTRACT FROM AUTHOR]

Published
2009
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4. Dynamics of numerical stochastic perturbation theory

Author

Garofalo, Marco, Kennedy, Anthony, Horsley, Roger, and Science and Technology Facilities Council (STFC)

Subjects
Langevin equation, Instantaneous Stochastic Perturbation Theory, Numerical Stochastic Perturbation theory, ϕ4 theory, lattice quantum field theory
Abstract

Numerical Stochastic Perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice quantum field theory. The standard algorithm based on the Langevin equation, however, suffers from several limitations which in practice restrict the potential of this technique: first of all it is not exact, a sequence of simulations with finer and finer discretization of the relevant equations have to be performed in order to extrapolate away the systematic errors in the results; and, secondly, the numerical simulations suffer from critical slowing down as the continuum limit of the theory is approached. In this thesis I investigate some alternative methods which improve upon the standard approach. In particular, I present a formulation of Numerical Stochastic Perturbation theory based on the Generalised Hybrid Molecular Dynamics algorithm and a study of the recently proposed Instantaneous Stochastic Perturbation Theory. The viability of these methods is investigated in ϕ4 theory.

Published
2018

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