Soliton Mass Research Articles

Quantum Bright Soliton in a Disorder Potential

At very low temperature, a quasi-one-dimensional ensemble of atoms with attractive interactions tend to form a bright soliton. When exposed to a sufficiently weak external potential, the shape of the soliton is not modified, but its external motion is affected. We develop in detail the Bogoliubov approach for the problem, treating, in a non-perturbative way, the motion of the center of mass of the soliton. Quantization of this motion allows us to discuss its long time properties. In particular, in the presence of a disordered potential, the quantum motion of the center of mass of a bright soliton may exhibit Anderson localization, on a localization length which may be much larger than the soliton size and could be observed experimentally.

BPSZNstring tensions, sine law and Casimir scaling, and integrable field theories

We consider a Yang-Mills-Higgs theory with spontaneous symmetry breaking of the gauge group $G\ensuremath{\rightarrow}U(1{)}^{r}\ensuremath{\rightarrow}{C}_{G}$, with ${C}_{G}$ being the center of $G$. We study two vacua solutions of the theory which produce this symmetry breaking. We show that for one of these vacua, the theory in the Coulomb phase has the mass spectrum of particles and monopoles which is exactly the same as the mass spectrum of particles and solitons of two-dimensional affine Toda field theory, for suitable coupling constants. That result holds also for $\mathcal{N}=4$ super Yang-Mills theories. On the other hand, in the Higgs phase, we show that for each of the two vacua the ratio of the tensions of the BPS ${Z}_{N}$ strings satisfy either the Casimir scaling or the sine law scaling for $G=SU(N)$. These results are extended to other gauge groups: for the Casimir scaling, the ratios of the tensions are equal to the ratios of the quadratic Casimir constant of specific representations; for the sine law scaling, the tensions are proportional to the components of the left Perron-Frobenius eigenvector of Cartan matrix ${K}_{ij}$ and the ratios of tensions are equal to the ratios of the soliton masses of affine Toda field theories.

One-loop corrections to the mass of self-dual semi-local planar topological solitons

A formula is derived that allows the computation of one-loop mass shifts for self-dual semilocal topological solitons. These extended objects, which in three spatial dimensions are called semi-local strings, arise in a generalized Abelian Higgs model with a doublet of complex Higgs fields. Having a mixture of global, SU ( 2 ) , and local (gauge), U ( 1 ) , symmetries, this weird system may seem bizarre, but it is in fact the bosonic sector of electro-weak theory when the weak mixing angle is π 2 . The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.

Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory

The solitons and kinks of the generalized $sl(3, \IC)$ sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the {\sl tau} functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the $sl(3, \IC)$ affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized $sl(3, \IC)$ sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U(1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for "quark" confinement.

Two-dimensional dark soliton in the nonlinear Schrödinger equation

Two-dimensional gray solitons to the nonlinear Schroedinger equation are numerically created by two processes to show its robustness. One is transverse instability of a one-dimensional gray soliton, and another is a pair annihilation of a vortex and an antivortex. The two-dimensional dark solitons are anisotropic and propagate in a certain direction. The two-dimensional dark soliton is stable against the head-on collision. The effective mass of the two-dimensional dark soliton is evaluated from the motion in a harmonic potential.

Nonlinear Transport in Hydrogen-Bonded Systems with Asymmetric Double-Well Potential

We study the nonlinear transport and the motion of the bell-shape soliton in hydrogen-bonded chains with asymmetric double-well potential, based on the new two-component soliton model. Solution, momentum, effective mass, width and energy of bell-shape soliton are found. The theoretical reasults are estimated and compared with experimental ones. The agreement between them is good.

On the renormalization of the two-point Green function in the sine-Gordon model

We analyse the renormalizability of the sine-Gordon model using the two-point causal Green function. We show that all divergences can be removed by the renormalization of the dimensional coupling constant using the renormalization constant Z1, calculated in Faber and Ivanov (2003 J. Phys. A: Math. Gen. 36 7839) within the path-integral approach. We calculate the Gell-Mann–Low function and solve the Callan–Symanzik equation for the two-point Green function. We analyse the renormalizability of Gaussian fluctuations around a soliton. We show that Gaussian fluctuations around a soliton solution are renormalized like quantum fluctuations around the trivial vacuum and do not introduce any singularity to the sine-Gordon model at β2 = 8π. We calculate the correction to the soliton mass, caused by Gaussian fluctuations around a soliton, within the discretization procedure for various boundary conditions and find complete agreement with our result, obtained in continuous space–time.

Stable fermion bag solitons in the massive Gross-Neveu model: Inverse scattering analysis

Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We study this phenomenon non-perturbatively in the 1+1 dimensional Massive Gross-Neveu model, in the large $N$ limit. We find, applying inverse scattering techniques, that the extremal static bag configurations are reflectionless, as in the massless Gross-Neveu model. This adds to existing results of variational calculations, which used reflectionless bag profiles as trial configurations. Only reflectionless trial configurations which support a single pair of charge-conjugate bound states of the associated Dirac equation were used in those calculations, whereas the results in the present paper hold for bag configurations which support an arbitrary number of such pairs. We compute the masses of these multi-bound state solitons, and prove that only bag configurations which bear a single pair of bound states are stable. Each one of these configurations gives rise to an O(2N) antisymmetric tensor multiplet of soliton states, as in the massless Gross-Neveu model.

Chern–Simons soliton and a critical study of the energy momentum tensor in noncommutative field theory

We have shown unambiguously the existence of solitons in the non-commutative (NC) extension of Chern–Simons–Higgs model. The analysis is done at the classical level (since solitons are essentially classical objects) and in the first non-trivial order in θ, the only spatial noncommutativity parameter. At the same time, we have exposed an inadequacy in the conventional definitions of the energy momentum tensor (EMT) in the present context but this pathology appears to be generic to NC field theories. This is reflected in the fact that the BPS soliton equations (obtained from the EMT) are not compatible with the full variational equations of motion, requiring further imposition a restriction on the form of the Higgs field, contrary to the commutative spacetime case. Both in the Lagrangian and Hamiltonian formulations of the problem, we concentrate on the canonical and symmetric forms of the energy–momentum tensor. In the Hamiltonian scheme, constraint analysis and the induced Dirac brackets are derived. In fact the EMT behaves properly as the spacetime translation generators and their actions on the fields are discussed in detail. The effects of noncommutativity on the soliton solutions have been analyzed carefully and we have come up with some interesting results. Comparing the relative strengths of the noncommutative effects, we have shown that there is a universal character in the noncommutative correction to the magnetic field—it depends only on θ. On the other hand, in the cases of all other observables of physical interest, such as the potential profile, soliton mass or the electric field, the parameters θ as well as τ (the latter comprising solely of commutative Chern–Simons–Higgs model parameters) appear with similar weightage.

Skyrmions and pentaquarks in the quark–hadron continuity perspective

We argue that in the color-flavor-locking (CFL) superconducting phase classical soliton solutions can exist, whose excitations should be interpreted as states formed by a quark (or an antiquark) and condensed diquarks. This finding extends the picture of quark–hadron continuity showing the existence of a region, intermediate between the CFL and the hypernuclear phase, where chiral solitons and Nambu–Goldstone bosons can exist. We derive an expression of the soliton mass in terms of the QCD coupling, gs, and the Nambu Goldstone boson parameters. From the quark–hadron continuity we can draw an argument in favor of the interpretation of the Θ+(1540) particle in terms of a strange antiquark and two highly correlated ud pairs (diquarks).

Noncommutative Chern-Simons soliton

We have studied the noncommutative extension of the relativistic Chern-Simons-Higgs model, in the first non-trivial order in $\theta$, with only spatial noncommutativity. Both Lagrangian and Hamiltonian formulations of the problem have been discussed, with the focus being on the canonical and symmetric forms of the energy-momentum tensor. In the Hamiltonian scheme, constraint analysis and the induced Dirac brackets have been provided. The spacetime translation generators and their actions on the fields are discussed in detail. The effects of noncommutativity on the soliton solutions have been analysed thoroughly and we have come up with some interesting observations. Considering the {\it{relative}} strength of the noncommutative effects, we have shown that there is a universal character in the noncommutative correction to the magnetic field - it depends {\it{only}} on $\theta$. On the other hand, in the cases of all other observables of physical interest, such as the potential profile, soliton mass or the electric field, $\theta$ as well as $\tau$, (comprising solely of commutative Chern-Simons-Higgs model parameters), appear on similar footings. This phenomenon is a new finding which has come up in the present analysis. Lastly, we have pointed out a generic problem in the NC extension of the models, in the form of a mismatch between the BPS dynamical equation and the full variational equations of motion, to $O(\theta)$. This mismatch indicates that the analysis is not complete as it brings in to fore the ambiguities in the definition of the energy-momentum tensor in a noncommutative theory.

Exact soliton solution of spin chain with an external magnetic field in linear wave background

Employing a simple, straightforward Darboux transformation we construct exact N-soliton solution for anisotropic spin chain driven by an external magnetic field in linear wave background. As a special case the explicit one- and two-soliton solution dressed by the linear wave corresponding to magnon in quantum theory is obtained analytically and its property is discussed in detail. The dispersion law, effective soliton mass, and the energy of each soliton are investigated as well. Our result show that the stability criterion of soliton is related with anisotropic parameter and the amplitude of the linear wave.

Exact soliton solution of spin chain with an external magnetic field in linear wave background

Employing a simple, straightforward Darboux transformation we construct exact N-soliton solution for anisotropic spin chain driven by an external magnetic field in linear wave background. As a special case the explicit one- and two-soliton solution dressed by the linear wave corresponding to magnon in quantum theory is obtained analytically and its property is discussed in detail. The dispersion law, effective soliton mass, and the energy of each soliton are investigated as well. Our result show that the stability criterion of soliton is related with anisotropic parameter and the amplitude of the linear wave.

Duality in the color flavor locked spectrum

We analyze the spectrum of the massive states for the color flavor locked phase (CFL) of QCD. We show that the vector mesons have a mass of the order of the color superconductive gap Δ. We also see that the excitations associated with the solitonic sector of the CFL low energy theory have a mass proportional to F2π/Δ and hence are expected to play no role for the physics of the CFL phase for large chemical potential. Another interesting point is that the product of the soliton mass and the vector meson mass is independent of the gap. We interpret this behavior as a form of electromagnetic duality in the sense of Montonen and Olive. Our approach for determining the properties of the massive states is non-perturbative in nature and can be applied to any theory with multiple scales.

Quasisupersymmetric Solitons of Coupled Scalar Fields in Two Dimensions

We consider solitonic solutions of coupled scalar systems, whose Lagrangian has a potential term (quasisupersymmetric potential) consisting of the square of derivative of a superpotential. The most important feature of such a theory is that among soliton masses there holds a Ritz-like combination rule (e.g. M12+M23=M13), instead of the inequality (M12+M23<M13) which is a stability relation generally seen in N=2 supersymmetric theory. The promotion from N=1 to N=2 theory is considered.

Comment on: “One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models”: [Phys. Lett. B 542 (2002) 282

We refute the claim that previous works on the one-loop quantum mass of solitons had incorrectly dropped a surface term from a partial integration. Rather, the paper quoted in the title contains a fallacious derivation with two compensating errors. We also remark that the φ2cos2ln(φ2) model considered in that paper does not have solitons at the quantum level because at two-loop order the degeneracy of the vacua is lifted. This may be remedied, however, by a supersymmetric extension.

Nonlinear dust Bernstein–Greene–Kruskal modes in charge-varying dusty plasmas

Nonlinear dust Bernstein–Greene–Kruskal (BGK) modes are investigated in a charge-varying dusty plasma. It is found that highly localized structures, solely due to the dust charge variation, can exist. The dust BGK soliton suffers the well-known anomalous damping, the importance of which is roughly proportional to the dust grain velocity. This dissipation causes the soliton amplitude to decay algebraically and the conservation of “soliton mass” leads to the development of a noise tail.

Solitons in coupled Ablowitz–Ladik chains

A model of two coupled Ablowitz–Ladik (AL) lattices is introduced. While the system as a whole is not integrable, it admits reduction to the integrable AL model for symmetric states. Stability and evolution of symmetric solitons are studied in detail analytically (by means of a variational approximation) and numerically. It is found that there exists a finite interval of positive values of the coupling constant in which the symmetric soliton is stable, provided that its mass is below a threshold value. Evolution of the unstable symmetric soliton is further studied by means of direct simulations. It is found that the unstable soliton breaks up and decays into radiation, or splits into two counter-propagating asymmetric solitons, or evolves into an asymmetric pulse, depending on the coupling coefficient and the mass of the initial soliton.

One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models

The bare one loop soliton quantum mass corrections can be expressed in two ways: as a sum over the zero-point energies of small oscillations around the classical configuration, or equivalently as the (Euclidean) effective action per unit time. In order to regularize the bare one loop quantum corrections (expressed as the sum over the zero-point energies) we subtract and add from it the tadpole graph that appear in the expansion of the effective action per unit time. The subtraction renders the one loop quantum corrections finite. Next, we use the renormalization prescription that the added tadpole graph cancels with adequate counterterms, obtaining in this way a finite unambiguous expression for the one loop soliton quantum mass corrections. When we apply the method to the solitons of the sine-Gordon and φ 4 kink models we obtain results that agree with known results. Finally we apply the method to compute the soliton quantum mass corrections in the recently introduced φ 2cos 2ln( φ 2) model.

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac–Moody algebra sl 3( C) . It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions.