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Journal articles on the topic 'Quantum breathers'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Martinez-Galicia, R., and Panayotis Panayotaros. "Coherent states and localization in a quantized discrete NLS lattice." Journal of Nonlinear Optical Physics & Materials 25, no. 04 (December 2016): 1650047. http://dx.doi.org/10.1142/s0218863516500478.

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We study the evolution of a quantum discrete nonlinear Schrödinger (DNLS) system using as initial conditions coherent states corresponding to points in the vicinity of breather solutions of the classical system. We consider various examples of stable and unstable breathers and examine the distance between exactly evolved states and coherent states with parameters that evolve according to classical dynamics. Initial conditions near stable breathers and their vicinity are seen to lead to recurrences to small distances between the two evolving states. Similar recurrences are not observed for initial conditions near unstable breathers.

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2

Tang, Bing, De-Jun Li, and Yi Tang. "Quantum breathers in ferromagnetic chains with on-site easy axis anisotropy." Canadian Journal of Physics 91, no. 10 (October 2013): 788–92. http://dx.doi.org/10.1139/cjp-2013-0044.

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Quantum breathers in one-dimensional ferromagnetic chains with on-site easy axis anisotropy are investigated analytically. Based on the Hartree approximation, we can work out the case of quantum breathers with a large number of quanta. By using the multiple-scale method combined with the semidiscrete approximation, the nonlinear Schrödinger equation is derived. It is shown that quantum breathers can exist in the Heisenberg ferromagnetic chain. In addition, we obtain the energy level formula of quantum breathers, which indicates that the energy of such quantum breathers is quantized.

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3

Gutierrez, Hernan Oscar Cortez, Milton Milciades Cortez Gutierrez, Girady Iara Cortez Fuentes Rivera, Liv Jois Cortez Fuentes Rivera, and Deolinda Fuentes Rivera Vallejo. "Dark breather using symmetric Morse, solvent and external potentials for DNA breathing." Eclética Química Journal 43, no. 4 (December 5, 2018): 44. http://dx.doi.org/10.26850/1678-4618eqj.v43.4.2018.p43-48.

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We analyze the dynamics and the quantum thermodynamics of DNA in Symmetric-Peyrard-Bishop-Dauxois model (S-PBD) with solvent and external potentials and describe the transient conformational fluctuations using dark breather and the ground state wave function of the associate Schrodinger differential equation. We used the S-PBD, the Floquet theory, quantum thermodynamic and finite difference methods. We show that for lower coupling dark breather is present. We estimate the fluctuations or breathing of DNA. For the S-PBD model we have the stability of dark breather for k<0.004 and mobile breathers with coupling k=0.004. The fluctuations of the dark breather in the S-PBD model is approximately zero with the quantum thermodynamics. The viscous and external potential effect is direct proportional to hydrogen bond stretching.

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4

Gutierrez, Hernan Oscar Cortez, Milton Milciades Cortez Gutierrez, Girady Iara Cortez Fuentes Rivera, Liv Jois Cortez Fuentes Rivera, and Deolinda Fuentes Rivera Vallejo. "Dark breather using symmetric Morse, solvent and external potentials for DNA breathing." Eclética Química Journal 43, no. 4 (January 7, 2019): 44. http://dx.doi.org/10.26850/1678-4618eqj.v43.4.2018.p44-49.

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We analyze the dynamics and the quantum thermodynamics of DNA in Symmetric-Peyrard-Bishop-Dauxois model (S-PBD) with solvent and external potentials and describe the transient conformational fluctuations using dark breather and the ground state wave function of the associate Schrodinger differential equation. We used the S-PBD, the Floquet theory, quantum thermodynamic and finite difference methods. We show that for lower coupling dark breather is present. We estimate the fluctuations or breathing of DNA. For the S-PBD model we have the stability of dark breather for k<0.004 and mobile breathers with coupling k=0.004. The fluctuations of the dark breather in the S-PBD model is approximately zero with the quantum thermodynamics. The viscous and external potential effect is direct proportional to hydrogen bond stretching.

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5

MacKay, R. S. "Discrete breathers: classical and quantum." Physica A: Statistical Mechanics and its Applications 288, no. 1-4 (December 2000): 174–98. http://dx.doi.org/10.1016/s0378-4371(00)00421-0.

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6

Tang, Bing, and De-Jun Li. "Quantum breathers in XXZ ferromagnetic chains with on-site easy-plane anisotropy." International Journal of Modern Physics B 30, no. 17 (June 30, 2016): 1650100. http://dx.doi.org/10.1142/s0217979216501009.

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The existence and properties of quantum breathers in a one-dimensional XXZ ferromagnetic Heisenberg spin chain with single-ion easy-plane anisotropy are investigated analytically in the Hartree approximation. We show that the system can support the appearance of quantum breathers, and discuss their existence conditions and properties. In addition, our results show that, for quantum breathers in this system, both the corresponding energy and magnetic moment are quantized.

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7

Yu, Dang-Jun, and Jie-Fang Zhang. "Rogue Wave and Breather Structures with “High Frequency” and “Low Frequency” in 𝒫𝒯-Symmetric Nonlinear Couplers with Gain and Loss." Zeitschrift für Naturforschung A 71, no. 10 (October 1, 2016): 961–69. http://dx.doi.org/10.1515/zna-2016-0229.

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AbstractBased on the modified Darboux transformation method, starting from zero solution and the plane wave solution, the hierarchies of rational solutions and breather solutions with “high frequency” and “low frequency” of the coupled nonlinear Schrödinger equation in parity-time symmetric nonlinear couplers with gain and loss are constructed, respectively. From these results, some basic characteristics of multi-rogue waves and multi-breathers are studied. Based on the property of rogue wave as the “quantum” of pattern structure in rogue wave hierarchy, we further study the novel structures of the superposed Akhmediev breathers, Kuznetsov-Ma solitons and their combined structures. It is expected that these results may give new insight into the context of the optical communications and Bose-Einstein condensations.

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8

Dubinko, V. I. "Quantum tunneling in gap discrete breathers." Letters on Materials 5, no. 1 (2015): 97–104. http://dx.doi.org/10.22226/2410-3535-2015-1-97-104.

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9

Wang, W. Z., J. Tinka Gammel, A. R. Bishop, and M. I. Salkola. "Quantum Breathers in a Nonlinear Lattice." Physical Review Letters 76, no. 19 (May 6, 1996): 3598–601. http://dx.doi.org/10.1103/physrevlett.76.3598.

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10

Wang, W. Z., A. R. Bishop, J. T. Gammel, and R. N. Silver. "Quantum Breathers in Electron-Phonon Systems." Physical Review Letters 80, no. 15 (April 13, 1998): 3284–87. http://dx.doi.org/10.1103/physrevlett.80.3284.

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11

Adamashvili, Guram, and Andreas Knorr. "Optical breathers in semiconductor quantum dots." Optics Letters 31, no. 1 (January 1, 2006): 74. http://dx.doi.org/10.1364/ol.31.000074.

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12

Biswas, Arindam, Sutapa Adhikar, Kamal Choudhary, Reshmi Basu, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal. "Quantum breathers in lithium tantalate ferroelectrics." Applied Nanoscience 3, no. 4 (June 6, 2012): 343–55. http://dx.doi.org/10.1007/s13204-012-0132-6.

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13

Schulman, L. S., D. Tolkunov, and E. Mihóková. "Structure and time-dependence of quantum breathers." Chemical Physics 322, no. 1-2 (March 2006): 55–74. http://dx.doi.org/10.1016/j.chemphys.2005.07.023.

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14

El-Rashidy, Khaled, Aly R. Seadawy, Saad Althobaiti, and M. M. Makhlouf. "Investigation of interactional phenomena and multi wave solutions of the quantum hydrodynamic Zakharov–Kuznetsov model." Open Physics 19, no. 1 (January 1, 2021): 91–99. http://dx.doi.org/10.1515/phys-2021-0009.

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Abstract The symbolic computation with the ansatz function and the logarithmic transformation method are used to obtain a formula for certain exact solutions of the ( 3 + 1 ) \left(3+1) Zakharov–Kuznetsov (Z–K) equation. We use homoclinic breather, three waves method, and double exponential. There is a conflict of results with considerably known results, which indicates the solutions found in this study are new. By selecting appropriate parameter values, 3d representations are plotted to establish W-shaped, multi-peak, and kinky breathers solutions.

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15

Proville, Laurent. "Quantum breathers in a nonlinear Klein Gordon lattice." Physica D: Nonlinear Phenomena 216, no. 1 (April 2006): 191–99. http://dx.doi.org/10.1016/j.physd.2005.12.019.

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16

Igumenshchev, Kirill, Misha Ovchinnikov, Panagiotis Maniadis, and Oleg Prezhdo. "Signatures of discrete breathers in coherent state quantum dynamics." Journal of Chemical Physics 138, no. 5 (February 7, 2013): 054104. http://dx.doi.org/10.1063/1.4788618.

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17

Braun, Hans-Benjamin, and Nadia Fettes. "From micromagnetics to quantum spin chains: Quantization of breathers." Journal of Applied Physics 85, no. 8 (April 15, 1999): 5648–50. http://dx.doi.org/10.1063/1.369828.

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18

Fleurov, V. "Discrete quantum breathers: What do we know about them?" Chaos: An Interdisciplinary Journal of Nonlinear Science 13, no. 2 (June 2003): 676–82. http://dx.doi.org/10.1063/1.1541151.

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19

Feng, Wenhui, Lanjun Wu, Bing Tang, and Ke Deng. "Quantum Breathers in a Two-Dimensional Hexangular Heisenberg Ferromagnet." International Journal of Theoretical Physics 60, no. 4 (April 2021): 1438–54. http://dx.doi.org/10.1007/s10773-021-04769-1.

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20

Tang, Bing. "Quantum breathers and two-breathers in the β-Fermi-Pasta-Ulam chain with the second-neighbor coupling." Communications in Nonlinear Science and Numerical Simulation 48 (July 2017): 361–75. http://dx.doi.org/10.1016/j.cnsns.2017.01.010.

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21

Su, Wanhan, Jiayu Xie, Tianle Wu, and Bing Tang. "Modulational instability, quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field." Chinese Physics B 27, no. 9 (September 2018): 097501. http://dx.doi.org/10.1088/1674-1056/27/9/097501.

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22

Pinto, Ricardo A., Jean Pierre Nguenang, and Sergej Flach. "Boundary effects on quantum -breathers in a Bose–Hubbard chain." Physica D: Nonlinear Phenomena 238, no. 5 (March 2009): 581–88. http://dx.doi.org/10.1016/j.physd.2008.12.013.

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23

Martínez-Galicia, Ricardo, and Panayotis Panayotaros. "Classical breathers and quantum coherent states in discrete NLS systems." Physics Letters A 383, no. 2-3 (January 2019): 164–69. http://dx.doi.org/10.1016/j.physleta.2018.10.020.

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24

Tinka Gammel, J., W. Z. Wang, A. R. Bishop, and M. I. Salkola. "Quantum breathers in nonlinear phonon and coupled electron-phonon systems." Synthetic Metals 86, no. 1-3 (February 1997): 2215–16. http://dx.doi.org/10.1016/s0379-6779(97)81098-3.

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25

Asano, T., H. Nojiri, Y. Inagaki, Y. Ajiro, L. P. Regnault, and J. P. Boucher. "Elementary Excitations in Quantum Antiferromagnetic Chains: Dyons, Spinons and Breathers." Molecular Crystals and Liquid Crystals 379, no. 1 (January 1, 2002): 121–30. http://dx.doi.org/10.1080/713738604.

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26

Flach, S., and V. Fleurov. "Tunnelling in the nonintegrable trimer - a step towards quantum breathers." Journal of Physics: Condensed Matter 9, no. 33 (August 18, 1997): 7039–61. http://dx.doi.org/10.1088/0953-8984/9/33/007.

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27

Tang, Bing, De-Jun Li, and Yi Tang. "Quantum breathers in Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction." Chaos: An Interdisciplinary Journal of Nonlinear Science 24, no. 2 (June 2014): 023113. http://dx.doi.org/10.1063/1.4875041.

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28

Djoufack, Z. I., A. Kenfack-Jiotsa, J. P. Nguenang, and S. Domngang. "Quantum signatures of breathers in a finite Heisenberg spin chain." Journal of Physics: Condensed Matter 22, no. 20 (April 30, 2010): 205502. http://dx.doi.org/10.1088/0953-8984/22/20/205502.

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29

Tang, Bing. "Quantum Breathers in Anisotropy Ferromagnetic Chains with Second-Order Coupling." International Journal of Theoretical Physics 55, no. 8 (March 28, 2016): 3657–71. http://dx.doi.org/10.1007/s10773-016-2995-x.

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30

CUEVAS, J., E. B. STARIKOV, J. F. R. ARCHILLA, and D. HENNIG. "MOVING BREATHERS IN BENT DNA WITH REALISTIC PARAMETERS." Modern Physics Letters B 18, no. 25 (October 30, 2004): 1319–26. http://dx.doi.org/10.1142/s0217984904007840.

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Recent papers have considered moving breathers (MB) in DNA models including long range interaction due to the dipole moments of the hydrogen bonds. We have recalculated the value of the charge transfer when hydrogen bonds stretch using quantum chemical methods which takes into account the whole nucleoside pairs. We explore the consequences of this value on the properties of MBs, including the range of frequencies for which they exist and their effective masses. They are able to travel through bending points with fairly large curvatures, provided that their kinetic energy is larger than a minimum energy which depends on the curvature. These energies and the corresponding velocities are also calculated in function of the curvature.

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31

Vakulchyk, I., M. V. Fistul, Y. Zolotaryuk, and S. Flach. "Almost compact moving breathers with fine-tuned discrete time quantum walks." Chaos: An Interdisciplinary Journal of Nonlinear Science 28, no. 12 (December 2018): 123104. http://dx.doi.org/10.1063/1.5060654.

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32

Mandal, Subhra Jyoti, Kamal Choudhary, Arindam Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal. "Quantum breathers in Klein-Gordon lattice: Non-periodic boundary condition approach." Journal of Applied Physics 110, no. 12 (December 15, 2011): 124106. http://dx.doi.org/10.1063/1.3666013.

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33

Tang, Bing. "Quantum Two-breathers Formed by Ultracold Bosonic Atoms in Optical Lattices." International Journal of Theoretical Physics 55, no. 6 (January 7, 2016): 2697–710. http://dx.doi.org/10.1007/s10773-015-2903-9.

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34

GRACHEV, D. D., L. A. SEVASTYANOV, K. P. LOVETSKIY, A. A. GUSEV, S. I. VINITSKY, and V. L. DERBOV. "NONLINEAR SPIN WAVES IN GRAPHENE STRUCTURES." SPIN 04, no. 03 (September 2014): 1450005. http://dx.doi.org/10.1142/s2010324714500052.

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Basing on Dirac equation for interacting massless fermions, we propose a nonlinear model that describes a possible mechanism of ferromagnetism in graphene structures, resulting from electron–electron interaction and spontaneous breaking of spin symmetry of valence electrons. Qualitative predictions of the model are important for practical applications in spintronics. Localized kink–antikink patterns of valence electron spin density on the graphene surface are calculated, their interaction is described, and, finally, the formation of their quasi-bound metastable states (breathers) is investigated. The spectrum of breathers is calculated in both the analytical and the numerical form. Possible inverted population of the appropriate states may be used to generate quantum coherent nonlinear spin waves that can find practical applications in nanoelectronics and spintronics.

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35

Susanto, Hadi, Natanael Karjanto, Zulkarnain, Toto Nusantara, and Taufiq Widjanarko. "Soliton and Breather Splitting on Star Graphs from Tricrystal Josephson Junctions." Symmetry 11, no. 2 (February 20, 2019): 271. http://dx.doi.org/10.3390/sym11020271.

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We consider the interactions of traveling localized wave solutions with a vertex in a star graph domain that describes multiple Josephson junctions with a common/branch point (i.e., tricrystal junctions). The system is modeled by the sine-Gordon equation. The vertex is represented by boundary conditions that are determined by the continuity of the magnetic field and vanishing total fluxes. When one considers small-amplitude breather solutions, the system can be reduced into the nonlinear Schrödinger equation posed on a star graph. Using the equation, we show that a high-velocity incoming soliton is split into a transmitted component and a reflected one. The transmission is shown to be in good agreement with the transmission rate of plane waves in the linear Schrödinger equation on the same graph (i.e., a quantum graph). In the context of the sine-Gordon equation, small-amplitude breathers show similar qualitative behaviors, while large-amplitude ones produce complex dynamics.

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36

Mandal, Subhra Jyoti. "Effect of Poling Field and Non-linearity in Quantum Breathers in Ferroelectrics." IOSR Journal of Applied Physics 4, no. 5 (2013): 60–64. http://dx.doi.org/10.9790/4861-0456064.

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37

Igumenshchev, Kirill, Misha Ovchinnikov, and Oleg V. Prezhdo. "Herman–Kluk allows analysis of quantum discrete breathers in higher dimensional systems." Molecular Physics 110, no. 9-10 (May 10, 2012): 837–44. http://dx.doi.org/10.1080/00268976.2012.680513.

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38

Tang, Bing, De-Jun Li, Ke Hu, and Yi Tang. "Quantum Breathers in an Anisotropic Ferromagnetic Heisenberg Chain with Biquadratic Exchange Interaction." International Journal of Theoretical Physics 52, no. 11 (July 23, 2013): 4139–47. http://dx.doi.org/10.1007/s10773-013-1726-9.

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39

Tang, Bing, De-Jun Li, and Yi Tang. "Quantum Solitons and Breathers in an Anisotropic Ferromagnet with Octupole-Dipole Interaction." International Journal of Theoretical Physics 53, no. 2 (September 22, 2013): 359–69. http://dx.doi.org/10.1007/s10773-013-1816-8.

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40

Tang, Bing, De-Jun Li, and Yi Tang. "Controlling quantum breathers in Heisenberg ferromagnetic spin chains via an oblique magnetic field." physica status solidi (b) 251, no. 5 (March 31, 2014): 1063–68. http://dx.doi.org/10.1002/pssb.201350353.

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41

Djoufack, Z. I., J. P. Nguenang, and A. Kenfack-Jiotsa. "Quantum breathers and intrinsic localized excitations in an isotropic ferromagnet with octupole–dipole interaction." Physica B: Condensed Matter 598 (December 2020): 412437. http://dx.doi.org/10.1016/j.physb.2020.412437.

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42

Nhật, Lê Anh, Konstantin P. Lovetskiy, Leonid A. Sevastianov, and Dmitry S. Kulyabov. "Numerical modeling of stationary pseudospin waves on a graphene monoatomic films." Discrete and Continuous Models and Applied Computational Science 27, no. 4 (December 15, 2019): 365–77. http://dx.doi.org/10.22363/2658-4670-2019-27-4-365-377.

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For the first time, the theoretical model of the spin-electron structure of a singlelayer graphene film was proposed by Wallace. The literature also describes ferromagnetism generated by none of the three common causes: impurities, defects, boundaries. We believe that the source of ferromagnetism is the spontaneous breaking of spin symmetry in a graphene film. The classical field model describing spontaneously broken symmetry is necessarily non-linear. Among non-linear models, the simplest is the well-known 4 model. We believe that, as a first approximation, we can describe with its help all the characteristics of spin waves that interest us, their spectra, and the domain structure of ferromagnetism in graphene. The model admits kink and anti-kink exact solutions and a quasiparticle breather, which we modeled numerically. We use the kink-anti-kink interaction energy obtained numerically to solve the Schrödinger equation, which simulates the quantum dynamics of breathers, which underlies the description of spin waves. The solution of the Schrödinger equation by the Ritz method leads to a generalized problem of eigenvalues and eigenvectors, the solution of which is mainly devoted to this work.

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43

FUJII, TOSHIYUKI, MUNEHIRO NISHIDA, SATOSHI TANDA, and NORIYUKI HATAKENAKA. "TALKING BREATHER QUBITS." International Journal of Modern Physics B 23, no. 20n21 (August 20, 2009): 4352–64. http://dx.doi.org/10.1142/s0217979209063511.

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Breather is an elementary excitation regarded as a bound state of a fluxon and an antifluxon in a long Josephson junction. In quantum-mechanical regime, the breather energy is quantized so that the breather can be considered as an artificial moving atom. We propose a new type of fluxon qubit that is constructed by quantum-mechanical superposition of the breather's states. We describe quantum logic gates of breather qubit required for constructing quantum computer. In addition, our qubit can move in the system so that transfer of quntum information is possible between mobile qubits as well as stationary qubits. Our talking qubits support the global information sharing in quantum information networks.

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44

Zvyagin, Sergei. "Spin Dynamics in Quantum Sine-Gordon Spin Chains: High-Field ESR Studies." Applied Magnetic Resonance 52, no. 4 (February 24, 2021): 337–48. http://dx.doi.org/10.1007/s00723-021-01310-9.

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AbstractA spin-1/2 Heisenberg antiferromagnetic chain is one of the most important paradigmatic models in quantum magnetism. Its ground state is a spin singlet, while the excitation spectrum is formed by gapless fractional excitations, spinons. The presence of alternating g-tensors and/or the staggered Dzyaloshinskii-Moriya interaction results in opening the energy gap $$\varDelta \propto H^{2/3}$$ Δ ∝ H 2 / 3 , once the magnetic field H is applied. A fairly good understanding of this phenomenon was achieved in the framework of the sine-Gordon quantum-field theory, taking into account the effective transverse staggered field induced by the applied uniform field. The theory predicts solitons and antisolitons as elementary excitations, as well as their bound states, breathers. Here, I review recent high-field electron spin resonance spectroscopy studies of such systems, focusing on peculiarities of their spin dynamics in the sine-Gordon regime and beyond.

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45

Djoufack, Z. I., A. Kenfack-Jiotsa, and J. P. Nguenang. "Quantum signature of breathers in 1D ultracold bosons in optical lattices involving next-nearest neighbor interactions." International Journal of Modern Physics B 31, no. 20 (August 10, 2017): 1750140. http://dx.doi.org/10.1142/s0217979217501405.

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The dynamics and the energy spectrum of an ultracold gas of bosonic atoms in an optical lattice can be described by a Bose–Hubbard model for which the system parameters can be controlled by laser light. We study by means of the perturbation theory in addition to the numerical diagonalization, the energy spectrum and the related features of the band structures of the ultracold bosons in optical lattices containing a few number of quanta interacting with next-nearest neighbor interactions (NNNI) modeled by the Bose–Hubbard Hamiltonian. The energy spectra of such system display the bound states signature, which are analyzed in the first Brillouin zone for different wave numbers. The finding, i.e., quantum breathers, shows that their probabilities’ weight depends on the wave vector. The influence of NNNI on both the probabilities’ amplitude and the correlation function is also realized in case of a system with a small number of sites, respectively.

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46

Djoufack, Z. I., F. Fotsa-Ngaffo, E. Tala-Tebue, E. Fendzi-Donfack, and F. Kapche-Tagne. "Modulational instability in addition to discrete breathers in 2D quantum ultracold atoms loaded in optical lattices." Nonlinear Dynamics 98, no. 3 (October 15, 2019): 1905–18. http://dx.doi.org/10.1007/s11071-019-05295-w.

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47

Djoufack, Z. I., E. Tala-Tebue, and J.-P. Nguenang. "Quantum breathers and intrinsic localized excitation associated with the modulational instability in 1D Bose–Hubbard chain." Communications in Nonlinear Science and Numerical Simulation 69 (April 2019): 134–47. http://dx.doi.org/10.1016/j.cnsns.2018.07.018.

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48

Djoufack, Z. I., J. P. Nguenang, and A. Kenfack-Jiotsa. "Quantum breathers and modulational instability in quantum zigzag spin chains with alternative combination ferromagnetic and antiferromagnetic interactions in an external magnetic field." Journal of Magnetism and Magnetic Materials 489 (November 2019): 165385. http://dx.doi.org/10.1016/j.jmmm.2019.165385.

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49

YA. AREF'EVA, I. "SOLITONS EXPERIENCE FOR BLACK HOLE PRODUCTION IN ULTRARELATIVISTIC PARTICLE COLLISIONS." International Journal of Modern Physics B 26, no. 27n28 (September 18, 2012): 1243010. http://dx.doi.org/10.1142/s0217979212430102.

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We discuss the analogy between soliton scattering in quantum field theory and black hole/wormholes (BH/WH) production in ultrarelativistic particle collisions in gravity. It is a common wisdom of the current paradigm suggests that BH/WH formation in particles collisions will happen when a center-mass energy of colliding particles is sufficiently above the Planck scale (the transplanckian region) and the BH/WH production can be estimated by the classical geometrical cross section. We compare the background of this paradigm with the functional integral method to scattering amplitudes and, in particular, we stress the analogy of the BH production in collision of ultrarelativistic particle and appearance of breathers poles in the scattering amplitudes in the Sin–Gordon model.

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50

Volkov, A. V., and O. M. Parshkov. "Polarisation effects in the formation of optical breathers at the inhomogeneously broadenedJ= 0 →J= 1 quantum transition." Quantum Electronics 38, no. 9 (September 30, 2008): 862–68. http://dx.doi.org/10.1070/qe2008v038n09abeh013758.

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