We study numerically and analytically the behavior of classical Yang–Mills color fields in a random one-dimensional potential described by the Anderson model with disorder. Above a certain threshold, the nonlinear interactions of Yang–Mills fields lead to chaos and deconfinement of color wavepackets with their subdiffusive spreading in space. The algebraic exponent of the second moment growth in time is found to be in the range of 0.3–0.4. Below the threshold, color wavepackets remain confined even if a very slow spreading at very long times is not excluded due to subtle nonlinear effects and the Arnold diffusion for the case when initially color packets are located in close vicinity. In the case of large initial separation of color wavepackets, they remain well confined and localized in space. We also present the comparison with the behavior of the one-component field model of discrete Anderson nonlinear Schrödinger equation with disorder.
REFERENCES
1.
C. N.
Yang
and R. L.
Mills
, “Conservation of isotopic spin and isotopic gauge invariance
,” Phys. Rev.
96
, 191
(1954
). 2.
A. M.
Polyakov
, “Particle spectrum in quantum field theory
,” Pis’ma Zh. Eksp. Teor. Fiz.
20
, 430
(1974
) [JETP Lett. 20, 194 (1974)].3.
A. M.
Polyakov
, “Isomeric states of quantum fields
,” Zh. Eksp. Teor. Fiz.
68
, 1975
(1975
) [Sov. Phys. JETP 41(6), 988 (1976)].4.
A. M.
Polyakov
, “Compact gauge fields and the infrared catastrophe
,” Phys. Lett. B
59
, 82
(1975
). 5.
A. A.
Belavin
, A. M.
Polyakov
, A. S.
Schwartz
, and Y. S.
Tyupkin
, “Pseudoparticle solutions of the Yang-Mills equations
,” Phys. Lett. B
59
, 85
(1975
). 6.
A. I.
Vainstein
, V. I.
Zakharov
, V. A.
Novikov
, and M. A.
Shifman
, “ABC of instantons
,” Sov. Phys. Usp.
25
, 195
(1982
). 7.
D. M.
Ostrovsky
, G. W.
Carter
, and E. V.
Shuryak
, “Forced tunneling and turning state explosion in pure Yang-Mills theory
,” Phys. Rev. D
66
, 036004
(2002
). 8.
S. G.
Matinyan
, G. K.
Savvidi
, and N. G.
Ter-Arutunyan-Savvidi
, “Classical Yang-Mills mechanics. Nonlinear color oscillations
,” Zh. Eksp. Teor. Fiz.
80
, 830
(1981
) [Sov. Phys. JETP 53(3), 421 (1981)].9.
B. V.
Chirikov
and D. L.
Shepelyanskii
, “Stochastic oscillations of classical Yang-Mills fields
,” Pis’ma Zh. Eksp. Teor. Fiz.
34
(4), 171
(1981
) [JETP Lett. 34, 163 (1981)].10.
S. G.
Matinyan
, G. K.
Savvidi
, and N. G.
Ter-Arutyunyan-Savvidi
, “Stochasticity of classical Yang-Mills mechanics and its elimination by using the Higgs mechanism
,” Pis’ma Zh. Eksp. Teor. Fiz.
34
(11) 613
(1981
) [JETP Lett. 34, 590 (1981)].11.
B. V.
Chirikov
and D. L.
Shepelyanskii
, “Dynamics of some homogeneous models of classical Yang-Mills fields
,” Yad. Fiz.
36
, 1563
(1982
) [Sov. J. Nucl. Phys. 36(6), 908 (1982)].12.
T. S.
Biro
, S. G.
Matinyan
, and B.
Muller
, Chaos and Gauge Field Theory
(World Scientific Publishing
, Singapore
, 1994
).13.
B. V.
Chirikov
, “A universal instability of many-dimensional oscillator systems
,” Phys. Rep.
52
, 263
(1979
). 14.
A.
Lichtenberg
and M.
Lieberman
, Regular and Chaotic Dynamics
(Springer
, New York
, 1992
).15.
V.
Arnold
and A.
Avez
, Ergodic Problems in Classical Mechanics
(Benjamin
, New York
, 1968
).16.
I. P.
Cornfeld
, S. V.
Fomin
, and Y. G.
Sinai
, Ergodic Theory
(Springer-Verlag
, New York
, 1982
).17.
D.
Berenstein
and D.
Kawai
, “Smallest matrix black hole model in the classical limit
,” Phys. Rev. D
95
, 106004
(2017
). 18.
T.
Akutagawa
, K.
Hashimoto
, T.
Sasaki
, and R.
Watanabe
, “Out-of-time-order correlator in coupled harmonic oscillators
,” J. High Energ. Phys.
2020
, 13
(2020
). 19.
G.
Savvidy
, “Maximally chaotic dynamical systems
,” Ann. Phys.
421
, 168274
(2020
). 20.
E. V.
Shuryak
, “Quantum chromodynamics and the theory of superdense matter
,” Phys. Rep.
61
, 71
(1980
). 21.
P.
Olesen
, “Confinement and random fluxes
,” Nucl. Phys. B
200
(FS4
), 381
(1982
). 22.
S. M.
Apenko
, D. A.
Kirzhnits
, and Y. E.
Lozovik
, “Dynamical chaos, Anderson localization, and confinement
,” Pis’ma Zh. Eksp. Teor. Fiz.
36
(5
), 172
(1982
) [JETP Lett. 36(5), 213 (1982)].23.
E. V.
Shuryak
and J. J. M.
Verbaarschot
, “Random matrix theory and spectral sum rules for the Dirac operator in QCD
,” Nucl. Phys. A
560
, 306
(1993
). 24.
P. W.
Anderson
, “Absence of diffusion in certain random lattices
,” Phys. Rev.
109
, 1492
(1958
). 25.
26.
E.
Akkermans
and G.
Montambaux
, Mesoscopic Physics of Electrons and Photons
(Cambridge University Press
, Cambridge
, 2007
).27.
F.
Evers
and A. D.
Mirlin
, “Anderson transitions
,” Rev. Mod. Phys.
80
, 1355
(2008
). 28.
D. L.
Shepelyansky
, “Delocalization of quantum chaos by weak nonlinearity
,” Phys. Rev. Lett.
70
, 1787
(1993
). 29.
M. I.
Molina
, “Transport of localized and extended excitations in a nonlinear Anderson model
,” Phys. Rev. B
58
, 12547
(1998
). 30.
A. S.
Pikovsky
and D. L.
Shepelyansky
, “Destruction of Anderson localization by a weak nonlinearity
,” Phys. Rev. Lett.
100
, 094101
(2008
). 31.
C.
Skokos
, D. O.
Krimer
, S.
Komineas
, and S.
Flach
, “Delocalization of wave packets in disordered nonlinear chains
,” Phys. Rev. E
79
, 056211
(2009
). 32.
S.
Flach
, D. O.
Krimer
, and C.
Skokos
, “Universal spreading of wave packets in disordered nonlinear systems
,” Phys. Rev. Lett.
102
, 209903
(2009
). 33.
M.
Mulansky
and A.
Pikovsky
, “Energy spreading in strongly nonlinear disordered lattices
,” New J. Phys.
15
, 053015
(2013
). 34.
T. V.
Lapteva
, M. I.
Ivanchenko
, and S.
Flach
, “Nonlinear lattice waves in heterogeneous media
,” J. Phys. A: Math. Theor.
47
, 493001
(2014
). 35.
I.
Garcia-Mata
and D. L.
Shepelyansky
, “Delocalization induced by nonlinearity in systems with disorder
,” Phys. Rev. E
79
, 026205
(2009
). 36.
C.
Skokos
and S.
Flach
, “Spreading of wave packets in disordered systems with tunable nonlinearity
,” Phys. Rev. E
82
, 016208
(2010
). 37.
L.
Ermann
and D. L.
Shepelyansky
, “Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions
,” J. Phys. A: Math. Theor.
47
, 335101
(2014
). 38.
I.
Vakulchyk
, M. V.
Fistul
, and S.
Flach
, “Wave packet spreading with disordered nonlinear discrete-time quantum walks
,” Phys. Rev. Lett.
122
, 040501
(2019
). 39.
B.
Many Manda
, B.
Senyange
, and C.
Skokos
, “Chaotic wave-packet spreading in two-dimensional disordered nonlinear lattices
,” Phys. Rev. E
101
, 032206
(2020
). 40.
T.
Schwartz
, G.
Bartal
, S.
Fishman
, and M.
Segev
, “Transport and Anderson localization in disordered two-dimensional photonic lattices
,” Nature (London)
446
, 52
(2007
). 41.
Y.
Lahini
, A.
Avidan
, F.
Pozzi
, M.
Sorel
, R.
Morandotti
, D. N.
Christodoulides
, and Y.
Silberberg
, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices
,” Phys. Rev. Lett.
100
, 013906
(2008
). 42.
J. E.
Lye
, L.
Fallani
, M.
Modugno
, D. S.
Wiersma
, C.
Fort
, and M.
Inguscio
, “Bose-Einstein condensate in a random potential
,” Phys. Rev. Lett.
95
, 070401
(2005
). 43.
E.
Lucioni
, B.
Deissler
, L.
Tanzi
, G.
Roati
, M.
Zaccanti
, M.
Modugno
, M.
Larcher
, F.
Dalfovo
, M.
Inguscio
, and G.
Modugno
, “Observation of subdiffusion in a disordered interacting system
,” Phys. Rev. Lett.
106
, 230403
(2011
). 44.
P.
Petreczky
, “Lattice QCD at non-zero temperature
,” J. Phys. G: Nucl. Part. Phys.
39
, 093002
(2012
). 45.
O.
Philipsen
, “The QCD equation of state from the lattice
,” Prog. Part. Nucl. Phys.
70
, 55
(2013
). 46.
U.
Reinosa
, J.
Serreau
, M.
Tissier
, and N.
Wchebor
, “Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study
,” Phys. Rev. D
91
, 045035
(2015
). 47.
B.
Kramer
and A.
MacKinnon
, “Localization: Theory and experiment
,” Rep. Prog. Phys.
56
, 1469
(1993
). 48.
D.
Basko
, “Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
,” Phys. Rev. E
89
, 022921
(2014
). 49.
B. V.
Chirikov
and V. V.
Vecheslavov
, “Arnold diffusion in large systems
,” Zh. Eksp. Teor. Fiz.
112
, 1132
(1997
) [JETP 85(3), 616 (1997)]. 50.
S.
Fishman
, Y.
Krivopalov
, and A.
Soffer
, “On the problem of dynamical localization in the nonlinear Schrödinger equation with a random potential
,” J. Stat. Phys.
131
, 843
(2008
). 51.
J.
Bourgain
and W.-M.
Wang
, “Quasi-periodic solutions of nonlinear random Schrödinger equations
,” J. Eur. Math. Soc.
10
, 1
(2008
). 52.
G. P.
Korchemsky
, “Review of AdS/CFT integrability, chapter IV.4: Integrability in QCD and SYM
,” Lett. Math. Phys.
99
, 425
(2012
). 53.
L.
Ermann
and D. L.
Shepelyansky
, “Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
,” New J. Phys.
15
, 12304
(2013
). 54.
M.
Mulansky
, K.
Ahnert
, A.
Pikovsky
, and D. L.
Shepelyansky
, “Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems
,” J. Stat. Phys.
145
, 1256
(2011
). 55.
D. L.
Shepelyansky
, “Coherent propagation of two interacting particles in a random potential
,” Phys. Rev. Lett.
73
, 2607
(1994
). 56.
Y.
Imry
, “Coherent propagation of two interacting particles in a random potential
,” Europhys. Lett.
30
(7
), 405
(1995
). 57.
K. M.
Frahm
, “Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
,” Eur. Phys. J. B
89
, 115
(2016
). 58.
B. V.
Chirikov
, “Research concerning the theory of nonlinear resonance and stochasticity,” Preprint N 267 (Institute of Nuclear Physics, Novosibirsk, 1969) [CERN Trans. 71-40, Geneva, October (1971)].59.
A. B.
Rechester
, M. N.
Rosenbluth
, and R. B.
White
, “Calculation of the Kolmogorov entropy for motion along a stochastic magnetic field
,” Phys. Rev. Lett.
42
, 1247
(1979
). 60.
K. M.
Frahm
and D. L.
Shepelyansky
, “Diffusion and localization for the Chirikov typical map
,” Phys. Rev. E
80
, 016210
(2009
). 61.
T.
Goldfriend
and J.
Kurchan
, “Quasi-integrable systems are slow to thermalize but may be good scramblers
,” Phys. Rev. E
102
, 022201
(2020
). 62.
M.
Mulansky
, K.
Ahnert
, A.
Pikovsky
, and D. L.
Shepelyansky
, “Dynamical thermalization of disordered nonlinear lattices
,” Phys. Rev. E
80
, 056212
(2009
). 63.
J.
Berges
, M. P.
Heller
, A.
Mazeliauskas
, and R.
Venugopalan
, “Thermalization in QCD: theoretical approaches, phenomenological applications, and interdisciplinary connections,” arXiv:2005.12299[hep-th] (2020).64.
K. M.
Frahm
and D. L.
Shepelyansky
, “Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole
,” Eur. Phys. J. B
91
, 257
(2018
). 65.
R. S.
MacKay
and S.
Aubry
, “Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
,” Nonlinearity
7
, 1623
(1994
). 66.
S.
Flach
and A. V.
Gorbach
, “Discrete breathers—Advances in theory and applications
,” Phys. Rep.
467
, 1
(2008
). 67.
G.
Kopidakis
, S.
Komineas
, S.
Flach
, and S.
Aubry
, “Absence of wave packet diffusion in disordered nonlinear systems
,” Phys. Rev. Lett.
100
, 084103
(2008
). 68.
S.
Iubini
and A.
Politi
, “Chaos and localization in the discrete nonlinear Schrödinger equation,” arXiv:2103.11041[nlin.CD] (2021).© 2021 Author(s). Published under an exclusive license by AIP Publishing
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