arXiv subjects

Danial Saadatmand

Publications and source records attributed to Danial Saadatmand.

At least 19 recordsLinked to original sources

arXiv2026

False-vacuum bubbles in sphaleron scattering

We investigate the collision dynamics of two bright sphalerons in a (1+1)-dimensional deformed $ϕ^6$ scalar field theory with a symmetric potential possessing false vacua. Two one-parameter realizations of the model, referred to as the barrier and well models, are considered and their static and linear instability properties are first reviewed. We then study head-on collisions of boosted sphalerons over a broad range of initial velocities and deformation parameters. The scattering dynamics exhibit a rich variety of final states, including the production of kink-antikink pairs, long-lived oscillons in true and false vacuum, multiple oscillons propagating in false-vacuum regions, and radiative decay. A particularly remarkable outcome is the emergence of a long-lived bubble of the false broken vacuum bounded by a kink-antikink pair, which repeatedly collapses and re-expands before eventually decaying into an oscillon. These results demonstrate that deformed $ϕ^6$ theories with false vacua exhibit considerably richer sphaleron dynamics than previously known and provide new insight into the role of unstable localized configurations in nonlinear field theories.

hep-th↗

arXiv2026

Deformation of sine-Gordon two-soliton solutions in $φ^4$ kink-antikink configurations

In this work, we construct analytical kink-antikink $(K\bar{K})$ configurations in the non-integrable $φ^4$ model by mapping exact solutions of the integrable sine-Gordon system via a field deformation. This procedure yields two distinct classes of configurations, parametrized by the initial half-separation and velocity. We compare these profiles with the standard additive superposition Ansatz in terms of vacuum structure and equation-of-motion residuals, deriving explicit closed-form expressions for the corresponding integrated squared residuals. For small separations, the mapped soliton-antisoliton configurations exhibit appreciably smaller residuals than the naive superposition Ansatz, which in turn performs better than the mapped two-soliton configurations. Although the mapped fields are not exact solutions of the $φ^4$ equation of motion, they provide mathematically consistent, topologically sound, and physically motivated initial data for numerical studies of kink-antikink scattering and resonance phenomena.

nlin.PS↗

arXiv2026

A resonance in phonons scattering off a kink in the absence of a Peierls-Nabarro potential

We investigate the interaction of small-amplitude waves called phonons, with an initially static kink in an exceptional discretization of the $ϕ^4$ model that is free of the Peierls-Nabarro potential. Phonons are generated by a localized harmonic source and scattered from one side of the kink. By computing the transmission and reflection coefficients over the entire phonon band, we demonstrate that the scattering properties depend strongly on the lattice spacing. In the weak-discreteness regime ($h<1$), the kink is nearly transparent and phonons are transmitted through it over most of the phonon spectrum. In contrast, for strong discreteness ($h>1$), significant reflection emerges even though the corresponding continuum $ϕ^4$ kink is reflectionless. We further show that depending on the frequency of the incoming phonons, the kink experiences negative radiation pressure and is accelerated toward the incoming phonons for all lattice spacings considered, and this effect is much stronger for the strong discretness. The frequency dependence of the kink velocity and energy transfer is explained in terms of resonances associated with Doppler-shifted phonon frequencies and extrema of the phonon group velocity. Our results reveal that strong lattice discreteness can qualitatively modify phonon-kink interactions even in systems where the static Peierls-Nabarro potential is absent.

nlin.PS↗

arXiv2026

Long-time behaviour of sphalerons in $ϕ^4$ models with a false vacuum

Evolution of sphalerons in a class of quartic Klein-Gordon models are studied under a growing perturbation. Sphalerons are unstable lump-like solutions that arise from a saddle point between true and false vacua in the energy functional. Numerical simulations are presented which show the sphaleron evolving into an accelerating kink-antikink pair whose separation increases in time and asymptotically approaches the speed of light. To explain this behaviour analytically, a nonlinear collective coordinate method is developed which has three dynamical parameters and leads to an explicit asymptotic solution using a power series expansion. The solution describes the emergence of a spreading tabletop profile whose height approaches the true vacuum while its flanks steepen and accelerate outward. In addition, the energy density is shown to concentrate at the flanks, indicating the onset of a gradient blow-up at large times. These results provide a detailed description of the long-time dynamics of positively perturbed sphalerons, and reveal a universal mechanism for the formation of relativistically expanding structures in nonlinear field theories.

hep-th↗

arXiv2024

Phonons scattering off discrete asymmetric solitons in the absence of a Peierls-Nabarro potential

We analyze the interaction of lattice vibrations (phonon wave-packets) with an asymmetric kink soliton initially at rest. We employ the $ϕ^6$ model in one space and one time dimensions for various lattice spacings and consider two different discretization prescriptions for the field potential that do not generate Peierls-Nabarro potentials, i.e. the kink can be placed anywhere along the lattice beyond discrete translational invariance. Since the $ϕ^6$ model kink is neither symmetric nor anti-symmetric under spatial reflections we simulate the cases where the wave-packet approaches the kink from negative or positive spatial infinity. We extract the energy transmission and reflection coefficients as functions of the central frequency of the phonon wave-packet for the different lattice spacings. For large lattice spacings the wave-packet is always fully reflected while for smaller spacing the amount of reflection and transmission depends on the central frequency. We also identify scenarios in which the target kink acquires a non-zero velocity from its interaction with the wave-packet.

nlin.PS↗

arXiv2023

Variational Approach to Excited Fermions on Kinks

We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink energy, the energy of valence fermions and the fermion vacuum polarization energy. The latter arises from the interaction of the kink with the Dirac sea and is required for consistency of the semi-classical expansion for the fermions. Earlier studies only considered the valence part and observed a substantial back-reaction. This was reflected by a sizable distortion of the kink profile. We find that this distortion is strongly mitigated when the Dirac sea is properly accounted for. As a result the back-reaction merely produces a slight squeeze or stretch of the kink profile.

hep-th↗

arXiv2023

Excited fermions on kinks and the Dirac sea

We study quantum effects of recently discovered kink solitons which are constructed self-consistently by coupling to a single, excited fermion bound state. Our studies are based on the observation that in a semi-classical expansion the energies of this single level and of the Dirac sea should be treated equally. For these kink solutions we compute the energy of the Dirac sea as the fermion vacuum polarization energy. We find it to be substantial and to typically outweigh the energy gain from binding the single level.

hep-th↗

arXiv2022

Scattering of the asymmetric $ϕ^6$ kinks from a $\mathcal{PT}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons

Interaction of asymmetric $ϕ^6$ kinks with a spatially localized $\mathcal{PT}$-symmetric perturbation is investigated numerically. It has been shown that when the kink (antikink) hits the defect from the gain side, a final velocity of the kink decreases (increases), while for the kink and antikink coming from the opposite direction their final velocities remain unchanged. It is also found that when the kink interacts with the defect from the gain side multiple pair of the kink-antikink are formed from small amplitude waves (phonons) in the final states depending on the initial velocity of the initial kink and parameter of the perturbation.

nlin.PS↗

arXiv2020

Collision of $ϕ^4$ kinks free of the Peierls-Nabarro barrier in the regime of strong discreteness

The two major effects observed in collisions of the continuum $ϕ^4$ kinks are (i) the existence of critical collision velocity above which the kinks always emerge from the collision and (ii) the existence of the escape windows for multi-bounce collisions with the velocity below the critical one, associated with the energy exchange between the kink's internal and translational modes. The potential merger (for sufficiently low collision speeds) of the kink and antikink produces a bion with oscillation frequency $ω_B$, which constantly radiates energy, since its higher harmonics are always within the phonon spectrum. Similar effects have been observed in the discrete $ϕ^4$ kink-antikink collisions for relatively weak discreteness. Here we analyze kinks colliding with their mirror image antikinks in the regime of strong discreteness considering an exceptional discretization of the $ϕ^4$ field equation where the static Peierls-Nabarro potential is precisely zero and the not-too-fast kinks can propagate practically radiating no energy. Several new effects are observed in this case, originating from the fact that the phonon band width is small for strongly discrete lattices and for even higher discreteness an inversion of the phonon spectrum takes place with the short waves becoming low-frequency waves. When the phonon band is narrow, not a bion but a discrete breather with frequency $ω_{DB}$ and all higher harmonics outside the phonon band is formed. When the phonon spectrum is inverted, the kink and antikink become mutually repulsive solitary waves with oscillatory tails, and their collision is possible only for velocities above a threshold value sufficient to overcome their repulsion.

nlin.PS↗

arXiv2019

Multi-kink scattering in the double sine-Gordon model

We study collisions of two, three, and four kinks of the double sine-Gordon model. The initial conditions are taken in a special form in order to provide collision of all kinks in one point. We obtain dependences of the maximal energy densities on the model parameter. We also analyze the final states observed in these collisions.

hep-th↗

arXiv2018

A new look at the double sine-Gordon kink-antikink scattering

We study the kink-antikink scattering within the double sine-Gordon model. In the numerical simulations we found a critical value $v_{cr}$ of the initial velocity $v_{in}$, which separates two different scenarios: at $v_{in} v_{cr}$ the kinks pass through each other and escape to infinities. We obtain non-monotonous dependence of $v_{cr}$ on the model parameter $R$. Besides that, at some initial velocities below $v_{cr}$ we observe formation and interaction of the so-called oscillons (new phenomenon), as well as escape windows (well-known phenomenon).

hep-th↗

arXiv2018

Scattering of the double sine-Gordon kinks

We study the scattering of kink and antikink of the double sine-Gordon model. There is a critical value of the initial velocity $v_{cr}$ of the colliding kinks, which separates different regimes of the collision. At $v_{in}>v_{cr}$ we observe kinks reflection, while at $v_{in}<v_{cr}$ their interaction is complicated with capture and escape windows. We obtain the dependence of $v_{cr}$ on the parameter of the model. This dependence possesses a series of local maxima, which has not been reported by other authors. At some initial velocities below the critical value we observe a new phenomenon -- the escape of two oscillons in the final state. Besides that, at $v_{in}<v_{cr}$ we found the initial kinks' velocities at which the oscillons do not escape, and the final configuration looks like a bound state of two oscillons.

hep-th↗

arXiv2018

Graphene Nanoribbon as an Elastic Damper

Heterostructures composed of dissimilar two-dimensional nanomaterials can have nontrivial physical and mechanical properties promising for many applications. Interestingly, in some cases, it is possible to create heterostructures composed of weakly and strongly stretched domains with the same chemical composition, as it has been demonstrated for some polymer chains, DNA, and intermetallic nanowires supporting this effect of two-phase stretching. These materials at relatively strong tension forces split into domains with smaller and larger tensile strain. Within this region, average strain increases at constant tensile force due to the growth of the domain with the larger strain in the expense of the domain with smaller strain. Here the two-phase stretching phenomenon is described for graphene nanoribbons with the help of molecular dynamics simulations. This unprecedented feature of graphene revealed in our study is related to the peculiarities of nucleation and motion of the domain walls separating the domains with different elastic strain. It turns out that the loading-unloading curves exhibit a hysteresis-like behavior due to the energy dissipation during the domain wall nucleation and motion. Here, we originally put forward the idea of implementing graphene nanoribbons as elastic dampers, efficiently converting mechanical strain energy into heat during cyclic loading-unloading through elastic extension where domains with larger and smaller strain coexist. Furthermore, in the regime of two-phase stretching, graphene nanoribbon is a heterostructure for which the fraction of domains with larger and smaller strain, and consequently its physical and mechanical properties, can be tuned in a controllable manner by applying elastic strain and/or heat.

cond-mat.mtrl-sci↗

arXiv2017

Discrete breathers assist energy transfer to ac driven nonlinear chains

One-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in six-order polynomial on-site potentials is considered. Power of the energy source in the form of single ac driven particles is calculated numerically for different amplitudes $A$ and frequencies $ω$ within the linear phonon band. The results for the on-site potentials with hard and soft nonlinearity types are compared. For the hard-type nonlinearity, it is shown that when the driving frequency is close to (far from) the {\em upper} edge of the phonon band, the power of the energy source normalized to $A^2$ increases (decreases) with increasing $A$. In contrast, for the soft-type nonlinearity, the normalized power of the energy source increases (decreases) with increasing $A$ when the driving frequency is close to (far from) the {\em lower} edge of the phonon band. Our further demonstrations indicate that, in the case of hard (soft) anharmonicity, the chain can support movable discrete breathers (DBs) with frequencies above (below) the phonon band. It is the energy source quasi-periodically emitting moving DBs in the regime with driving frequency close to the DBs frequency, that induces the increase of the power. Therefore, our results here support the mechanism that the moving DBs can assist energy transfer from the ac driven particle to the chain.

nlin.PS↗

arXiv2017

Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of $N$ slow kinks in the sine-Gordon model were calculated analytically (for $N=1,2$, and 3) and numerically (for $4\le N\le 7$). However, for many physical applications it is important to know not only the total potential energy density but also its two components (the on-site potential energy density and the elastic strain energy density) as well as the extreme values of the elastic strain, tensile (positive) and compressive (negative). In the present study we give (i) the two components of the potential energy density and (ii) the extreme values of elastic strain. Our results suggest that in multi-soliton collisions the main contribution to the potential energy density comes from the elastic strain, but not from the on-site potential. It is also found that tensile strain is usually larger than compressive strain in the core of multi-soliton collision.

nlin.PS↗

arXiv2017

Crossover from ballistic to normal heat transport in the $ϕ^{4}$ lattice: If nonconservation of momentum is the reason, what is the mechanism?

Anomalous (non-Fourier's) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier's) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving $ϕ^{4}$ model and present evidence that the mobile discrete breathers or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band can be responsible for that.

cond-mat.stat-mech↗

arXiv2017

Multi-kink collisions in the $ϕ^6$ model

We study simultaneous collisions of two, three, and four kinks and antikinks of the $ϕ^6$ model at the same spatial point. Unlike the $ϕ^4$ kinks, the $ϕ^6$ kinks are asymmetric and this enriches the variety of the collision scenarios. In our numerical simulations we observe both reflection and bound state formation depending on the number of kinks and on their spatial ordering in the initial configuration. We also analyze the extreme values of the energy densities and the field gradient observed during the collisions. Our results suggest that very high energy densities can be produced in multi-kink collisions in a controllable manner. Appearance of high energy density spots in multi-kink collisions can be important in various physical applications of the Klein-Gordon model.

hep-th↗

arXiv2016

Resonant interaction of $ϕ^4$ kink with spatially periodic $\mathcal{PT}$-symmetric perturbation

The resonant interaction of the $ϕ^4$ kink with a periodic $\mathcal{PT}$-symmetric perturbation is observed in the frame of the continuum model and with the help of a two degree of freedom collective variable model derived in PRA 89, 010102(R). When the kink interacts with the perturbation, the kink's internal mode is excited with the amplitude varying in time quasiperiodically. The maximal value of the amplitude was found to grow when the kink velocity is such that it travels one period of perturbation is nearly one period of the kink's internal mode. It is also found that the kink's translational and vibrational modes are coupled in a way that an increase in the kink's internal mode amplitude results in a decrease in kink velocity. The results obtained with the collective variable method are in a good qualitative agreement with the numerical simulations for the continuum model. The results of the present study suggest that kink dynamics in open systems with balanced gain and loss can have new features in comparison with the case of conservative systems.

nlin.PS↗