Fermionic bound states in distinct kinklike backgrounds

Bazeia, D.; Mohammadi, Azadeh

doi:10.1140/epjc/s10052-017-4778-9

Cited by 23 publications

(27 citation statements)

References 22 publications

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“…Since the second derivative of the potential calculated at the static solution ϕ k (x) depends only on x, we can assume that δϕ has the form 15) and this allows us to obtain the eigenvalue problem of the type of the stationary Schrödinger equation, 16) where the operatorĤ (the Hamiltonian) iŝ 17) with the potential…”

Section: Topological Solitons In (11)-dimensional Modelsmentioning

confidence: 99%

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model

2018

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We consider the scattering of kinks of the sinhdeformed ϕ 4 model, which is obtained from the well-known ϕ 4 model by means of the deformation procedure. Depending on the initial velocity v in of the colliding kinks, different collision scenarios are realized. There is a critical value v cr of the initial velocity, which separates the regime of reflection (at v in > v cr ) and that of a complicated interaction (at v in < v cr ) with kinks' capture and escape windows. Besides that, at v in below v cr we observe the formation of a bound state of two oscillons, as well as their escape at some values of v in .

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Section: Topological Solitons In (11)-dimensional Modelsmentioning

confidence: 99%

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model

2018

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“…Many interesting and important results have been obtained in the (1+1)dimensional models with polynomial potentials: ϕ 4 , ϕ 6 , ϕ 8 , and so on [55][56][57][58][59][60][61][63][64][65][66][67][68][69][70]]. An impressive progress has been achieved in the studies of Q-balls [71][72][73][74][75][76][77][78], embedded topological defects, e.g., a skyrmion on a domain wall [79,80], a Q-lump on a domain wall [81], fermionic states on a domain wall [82][83][84][85][86][87], etc. [88][89][90][91][92][93].…”

Section: Introductionmentioning

confidence: 99%

Scattering of the φ8 kinks with power-law asymptotics

Belendryasova

Gani

2019

Communications in Nonlinear Science and Numerical Simulation

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We study the scattering of the ϕ 8 kinks off each other, namely, we consider those ϕ 8 kinks that have power-law asymptotics. The slow power-law fall-off leads to a long-range interaction between the kink and the antikink. We investigate how the scattering scenarios depend on the initial velocities of the colliding kinks. In particular, we observe the 'escape windows' -the escape of the kinks after two or more collisions, explained by the resonant energy exchange between the translational and vibrational modes. In order to elucidate this phenomenon, we also analyze the excitation spectra of a solitary kink and of a composite kink+antikink configuration.

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“…The system composed of a fermion interacting with background φ 4 kink is analytically solvable and exhibits bound states as well as scattering states [6][7][8]. The properties of fermion-kink systems, such as the fermion energy spectrum and Casimir energy, have been studied for many different models [9][10][11][12][13][14]. In these systems, it is also possible to consider the back-reaction of the fermion on the soliton, which modifies the kink profile, especially for strong coupling constants [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Fermions on wobbling kinks: normal versus quasinormal modes

Campos

Mohammadi

2021

J. High Energ. Phys.

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The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in quantum mechanics. To do so, we compute the transition probabilities between states given in terms of the Bogoliubov coefficients. We derive Fermi’s golden rule for the model, which allows the transition to the continuum at a constant rate if the fermion-kink coupling constant is smaller than the wobbling frequency. Moreover, we study the system replacing the shape mode with a quasinormal mode. In this case, the transition rate to continuum decays in time due to the leakage of the mode, and the final transition probability decreases sharply for large coupling constants in a way that is analogous to Fermi’s golden rule. Throughout the paper, we compare the perturbative results with numerical simulations and show that they are in good agreement.

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Fermionic bound states in distinct kinklike backgrounds

Cited by 23 publications

References 22 publications

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model

Scattering of the φ8 kinks with power-law asymptotics

Fermions on wobbling kinks: normal versus quasinormal modes

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