Kink fluctuation asymptotics and zero modes

In this paper we propose a refinement of the heat-kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero-energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat-kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey–DeWitt heat-kernel expansion.     

Quantum kinks on the null plane

We consider the quantization of a 1+1 dimensional field theory with kink solutions on a null plane. We present a field expansion which diagonalizes the operatorM ²=2P ⁺ P ^? including first order quantum corrections, reobtaining thereby the well known result for the kink mass. The quantization scheme treats classical solutions of different rapidity on an equal footing and the translation mode cancels completely, at least in the order considered here.     

Correcting the kink gas double counting by an effective potential

We show how to improve the dilute-gas expansion by including terms that correct double counting erros. The 1D double-well system is studied in detail. The effective correction potential diverges as the kink-antikink distance goes to zero and in this way provides a repulsive core to cut off the kink-gas density. Comparisons with the kink mass give limits to the applicability of the uncorrected kink gas.     

On the quantization of moving extended objects in one space dimension

We consider the quantum expansion around a classical moving extended object using as a specific example the moving kink solution of the spontaneously broken φ⁴ theory in one space dimension. The quantization is carried out using canonical methods similar to those employed by Creutz for the static kink. The main difference with the paper of Christ and Lee consists in the treatment of the translation mode. The quantum state corresponding to a moving kink has the correct relativistic energy momentum relation including first-order quantum corrections. Renormalization effects are discussed in detail.     

Cecotti-Fendley-Intriligator-Vafa index in a box

The Cecotti-Fendley-Intriligator-Vafa (CFIV) index in two-dimensional N=(2,2) models is revisited. We address the problem of “elementary” (nontopological) excitations over a kink solution, in the one-kink sector (using the Wess-Zumino or Landau-Ginzburg models with two vacua as examples). In other words, we limit ourselves to the large-β limit. The excitation spectrum over the BPS-saturated at the classical level kink is discretized through a large box with judiciously chosen boundary conditions. The boundary conditions are designed in such a way that half of supersymmetry is preserved as well as the BPS kink itself, and relevant zero modes. The excitation spectrum acquires a mass gap. All (discretized) excited states enter in four-dimensional multiplets (two bosonic states + two fermionic). Their contribution to indCFIV vanishes level-by-level. The ground state contribution produces |indCFIV|=1.     

Exact solutions of semiclassical non-characteristic Cauchy problems for the sine-Gordon equation

The use of the sine-Gordon equation as a model of magnetic flux propagation in Josephson junctions motivates studying the initial-value problem for this equation in the semiclassical limit in which the dispersion parameter ε tends to zero. Assuming natural initial data having the profile of a moving −2π kink at time zero, we analytically calculate the scattering data of this completely integrable Cauchy problem for all ε>0 sufficiently small, and further we invert the scattering transform to calculate the solution for a sequence of arbitrarily small ε. This sequence of exact solutions is analogous to that of the well-known N-soliton (or higher-order soliton) solutions of the focusing nonlinear Schrödinger equation. We then use plots obtained from a careful numerical implementation of the inverse-scattering algorithm for reflectionless potentials to study the asymptotic behavior of solutions in the semiclassical limit. In the limit ε↓0 one observes the appearance of nonlinear caustics, i.e. curves in space-time that are independent of ε but vary with the initial data and that separate regions in which the solution is expected to have different numbers of nonlinear phases.In the appendices, we give a self-contained account of the Cauchy problem from the perspectives of both inverse scattering and classical analysis (Picard iteration). Specifically, Appendix A contains a complete formulation of the inverse-scattering method for generic L¹-Sobolev initial data, and Appendix B establishes the well-posedness for L^p-Sobolev initial data (which in particular completely justifies the inverse-scattering analysis in Appendix A).     

Asymptotics for kink propagation in the discrete Sine-Gordon equation

The evolution of a propagating kink in a Sine-Gordon lattice is studied asymptotically using an averaged Lagrangian formulation appropriately coupled to the effect of the radiation. We find that unlike the continuum case the interaction with the Goldstone mode is important to explain the acceleration of the kink as it hops along the lattice. We develop a discrete WKB type solution to study the interaction of the kink and the radiation. In particular using this solution we show how to calculate the effect of the Peyrard and Kruskal resonant radiation in the energy loss of the kink. We obtain a set of modulation equation which explains qualitatively the evolution of the kink with remarkable quantitative agreement.     

Internal mode dynamics in driven nonlinear Klein-Gordon systems

We study analytically and numerically the action of a constant force on the propagation of kinks in the φ⁴ and sine-Gordon systems, with and without dissipation. We specifically investigate the relation of the external force with the oscillations of the kink width due to excitation of its internal mode or quasimode. We demonstrate that both dc force and dissipation, either jointly or separately, damp the oscillations of the kink width. We further prove that, in contrast to earlier predictions, those oscillations can only arise if we use a distorted kink as initial condition for the evolution. Finally, we show that for the φ⁴ system the oscillations of the kink width come from the excitation of its internal mode, whereas in the sG equation they originate in the excitation of the lowest radiational modes and an internal mode induced by the discreteness of the numerical simulations. Received 6 June 2000     

Ion Viscosity Stabilization of Tokamak Resistive Internal Kink Modes

For most of small and medium sized Tokamaks, the unstable mode responsible for the sawtooth crash is the resistive internal kink mode. However, the plasma parameters can be in the ion kinetic regime. In this paper, we consider the dependence of the mode growth rate on the magnetic shear which is changeable during a sawtooth cycle and find that the ion viscosity effect can completely stabilize the mode only for shear smaller than some critical value, corresponding to the stable phase of the sawtooth evolution. This is consistent with one of the salient phenomena of the sawtooth, the sudden onset.     

离子动力参数区托卡马克电阻性内扭曲模稳定性分析

利用离子动力参数区的内扭曲模色散关系分析了托卡马克等离子体电阻性内扭曲模的频率和增长率随磁剪切量s₀的变化。我们发现:存在一个临界磁剪切量s_0c,只有当s₀>s_0c时,即中心安全因子q₀小于某个临界值q_0c时,电阻性内扭曲模才能被激发。另一方面,随着磁剪切量s₀的加大,增长率增大的趋势比相应的磁流体电阻性内扭曲模快得多,因而与锯齿的快崩裂有内在的联系。所 关键词：     

Potts q-color field theory and scaling random cluster model

We study structural properties of the q-color Potts field theory which, for real values of q, describes the scaling limit of the random cluster model. We show that the number of independent n-point Potts spin correlators coincides with that of independent n-point cluster connectivities and is given by generalized Bell numbers. Only a subset of these spin correlators enters the determination of the Potts magnetic properties for q integer. The structure of the operator product expansion of the spin fields for generic q is also identified. For the two-dimensional case, we analyze the duality relation between spin and kink field correlators, both for the bulk and boundary cases, obtaining in particular a sum rule for the kink-kink elastic scattering amplitudes.     

Localization of five-dimensional Elko spinors on dS/AdS thick branes

Owing to the special structure of a five-dimensional Elko spinor, its localization on a brane with codimension one becomes completely different from that of a Dirac spinor. By introducing the coupling between the Elko spinor and the scalar field that can generate the brane, we have two types of localization mechanism for the five-dimensional Elko spinor zero mode on a brane. One is the Yukawa-type coupling, and the other is the non-minimal coupling. In this study, we investigate the localization of the Elko zero mode on de Sitter and Anti-de Sitter thick branes with the two localization mechanisms, respectively. The results show that both the mechanisms can achieve localization. The forms of the scalar coupling function in both localization mechanisms have similar properties, and they play a similar role in localization.     

Onset and saturation of the kink instability in a current-carrying line-tied plasma

An internal kink instability is observed to grow and saturate in a line-tied screw pinch plasma. Detailed measurements show that an ideal, line-tied kink mode begins growing when the safety factor q = (4pi2r2B(z))/(mu0I(p)(r)L) drops below 1 inside the plasma; the saturated state corresponds to a rotating helical equilibrium. In addition to the ideal mode, reconnection events are observed to periodically flatten the current profile and change the magnetic topology.     

Translationally invariant kink solutions of discrete ϕ<Superscript>4</Superscript> models

The properties of translationally invariant kinks in two discrete ϕ⁴ models are compared with those of the kinks in a classical discrete model. The translationally invariant kink solutions can be found randomly with respect to the lattice sites, i.e., their Peierls–Nabarro potential is exactly equal to zero. It is shown that these solutions have a Goldstone mode, that is, they can move along the lattice at vanishingly small velocities. Thus, the translationally invariant kink is not trapped by the lattice and can be accelerated by an arbitrary small external field and, having an increased mobility, can transfer a range of physical quantities: matter, energy, momentum, etc.     

The 1/r expansion for the critical multiple well problem

We consider the critical multiple well problem $$H = - \Delta + \sum\limits_{i = 1}^n {V(x - rx_i )} ,$$ where ?Δ+V(x) has a zero energy resonance. We prove that all eigenvalues and resonances ofH tending to zero as 1/r ² are analytic in 1/r. We give an explicit equation for the lowest nonvanishing coefficient in the 1/r expansion for any of these eigenvalues or resonances and observe thatH has infinitely many resonances tending to zero. Forn=2 andn=3, we compute the coefficients explicitly and forn=2, we also give the next coefficient in the 1/r expansion.     

<Emphasis Type="Italic">Q</Emphasis> kink of the nonlinear <Emphasis Type="Italic">O</Emphasis>(3) <Emphasis Type="Italic">σ</Emphasis> model involving an explicitly broken symmetry

The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S ¹, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range ω ∈ [−1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.     

Evaluation of the neutron background in CsI target for WIMP direct detection when using a reactor neutrino detector as a neutron veto system

In this work we show that universal gauge vector fields can be localized on the recently proposed 5D thick tachyonic braneworld which involves a de Sitter cosmological background induced on the 3-brane. Namely, by performing a suitable decomposition of the vector field, the resulting 4D effective action corresponds to a massive gauge field, while the profile along the extra dimension obeys a Schrödinger-like equation with a Pöschl–Teller potential. It turns out that the massless zero mode of the gauge field is bound to the expanding 3-brane and allows us to recover the standard 4D electromagnetic phenomena of our world. Moreover, this zero mode is separated from the continuum of Kaluza–Klein (KK) modes by a mass gap determined by the scale of the expansion parameter. We also were able to analytically solve the corresponding Schrödinger-like equation for arbitrary mass, showing that KK massive modes asymptotically behave like plane waves, as expected.     

A renormalized perturbation theory for problems with non-trivial boundary conditions or backgrounds in two space–time dimensions

We discuss the effects of non-trivial boundary conditions or backgrounds, including non-perturbative ones, on the renormalization program for systems in two dimensions. We present an alternative renormalization procedure in which these non-perturbative conditions can be taken into account in a self-contained and, we believe, self-consistent manner. These conditions have profound effects on the properties of the system, in particular all of its n-point functions. To be concrete, we investigate these effects in the λ φ ⁴ model in two dimensions and show that the mass counterterms turn out to be proportional to the Green’s functions which have a non-trivial position dependence in these cases. We then compute the difference between the mass counterterms in the presence and absence of these conditions. We find that in the case of non-trivial boundary conditions this difference is minimum between the boundaries and infinite on them. The minimum approaches zero when the boundaries go to infinity. In the case of non-trivial backgrounds, we consider the kink background and show that the difference is again small and localized around the kink.     

Anomalous exponents at the onset of an instability

Critical exponents are calculated exactly at the onset of an instability, by using asymptotic expansion techniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous; i.e., the mode amplitude X scales with departure from onset μ as ∝μ(β) with an exponent β different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability, and our results provide a possible explanation for recent experimental observations.     

Three-dimensional massive scalar field theory and the derivative expansion of the renormalization group

We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum — without using bare actions or any tuning procedure. As an example, we estimate the universal couplings of the non-perturbative three-dimensional one-component massive scalar field theory in the Ising model universality class, by using a derivative expansion (and no other approximation). These are compared to the recent results from other methods. At order derivative-squared approximation, the four-point coupling at zero momentum is better determined by other methods, but factoring this out appropriately, all our other results are in very close agreement with the most powerful of these methods. In addition we provide for the first time, estimates of the n-point couplings at zero momentum, with n = 12, 14, and the order momentum-squared parts with n = 2,…, 10.