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Title: Boundary scattering in the Φ$$^{4}$$ model

Abstract

Here, we study boundary scattering in the $$\phi^4$$ model on a half-line with a one-parameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends previously-studied behaviour on the full line to include regimes of near-elastic scattering, the restoration of a missing scattering window, and the creation of a kink or oscillon through the collision-induced decay of a metastable boundary state. We also study the decay of the vibrational boundary mode, and explore different scenarios for its relaxation and for the creation of kinks.

Authors:
 [1]; ORCiD logo [2];  [3];  [4];  [5]
  1. Durham Univ. (United Kingdom). Dept. of Mathematical Sciences
  2. Belarusian State Univ. (BSU), Minsk (Belarus). Dept. of Theoretical Physics and Astrophysics; Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
  3. Durham Univ. (United Kingdom). Dept. of Mathematical Sciences; Deloitte MCS Limited, London (United States)
  4. Jagiellonian Univ., Krakow (Poland). Inst. of Physics
  5. Belarusian State Univ. (BSU), Minsk (Belarus). Dept. of Theoretical Physics and Astrophysics; Joint Inst. for Nuclear Research (JINR), Dubna (Russian Federation). Bogoliubov Lab. of Theoretical Physics (BLTP); Oldenburg Univ. (Germany). Inst. of Physics
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Russian Foundation for Basic Research; German Research Foundation (DFG)
OSTI Identifier:
1371841
Report Number(s):
DCPT-15-51; arXiv:1508.02329; FERMILAB-PUB-17-227-APC
Journal ID: ISSN 1029-8479; 1387352
Grant/Contract Number:
AC02-07CH11359; ST/L000407/1; 317089; 16-52 -12012; LE 838/12-2
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 5; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Field Theories in Lower Dimensions; Nonperturbative Effects; Solitons Monopoles and Instantons

Citation Formats

Dorey, Patrick, Halavanau, Aliaksei, Mercer, James, Romanczukiewicz, Tomasz, and Shnir, Yasha. Boundary scattering in the Φ$^{4}$ model. United States: N. p., 2017. Web. doi:10.1007/JHEP05(2017)107.
Dorey, Patrick, Halavanau, Aliaksei, Mercer, James, Romanczukiewicz, Tomasz, & Shnir, Yasha. Boundary scattering in the Φ$^{4}$ model. United States. doi:10.1007/JHEP05(2017)107.
Dorey, Patrick, Halavanau, Aliaksei, Mercer, James, Romanczukiewicz, Tomasz, and Shnir, Yasha. Fri . "Boundary scattering in the Φ$^{4}$ model". United States. doi:10.1007/JHEP05(2017)107. https://www.osti.gov/servlets/purl/1371841.
@article{osti_1371841,
title = {Boundary scattering in the Φ$^{4}$ model},
author = {Dorey, Patrick and Halavanau, Aliaksei and Mercer, James and Romanczukiewicz, Tomasz and Shnir, Yasha},
abstractNote = {Here, we study boundary scattering in the $\phi^4$ model on a half-line with a one-parameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends previously-studied behaviour on the full line to include regimes of near-elastic scattering, the restoration of a missing scattering window, and the creation of a kink or oscillon through the collision-induced decay of a metastable boundary state. We also study the decay of the vibrational boundary mode, and explore different scenarios for its relaxation and for the creation of kinks.},
doi = {10.1007/JHEP05(2017)107},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2017,
place = {United States},
year = {Fri May 19 00:00:00 EDT 2017},
month = {Fri May 19 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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Citation Metrics:
Cited by: 2works
Citation information provided by
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  • We study 1+1 dimensional Φ 4 theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C≤C max, we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along themore » full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.« less
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  • We obtain exact solutions for kinks in Φ⁸, Φ¹⁰, and Φ¹² field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order Φ⁴ and Φ⁶ theories. Additionally, we construct distinct kinks withmore » equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a Φ¹² potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the Φ¹⁰ field theory, which is a quasi-exactly solvable (QES) model akin to Φ⁶, we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.« less