419 research outputs found

    Vacuum energy of the Bukhvostov-Lipatov model

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    Bukhvostov and Lipatov have shown that weakly interacting instantons and anti-instantons in the O(3)O(3) non-linear sigma model in two dimensions are described by an exactly soluble model containing two coupled Dirac fermions. We propose an exact formula for the vacuum energy of the model for twisted boundary conditions, expressing it through a special solution of the classical sinh-Gordon equation. The formula perfectly matches predictions of the standard renormalized perturbation theory at weak couplings as well as the conformal perturbation theory at short distances. Our results also agree with the Bethe ansatz solution of the model. A complete proof the proposed expression for the vacuum energy based on a combination of the Bethe ansatz techniques and the classical inverse scattering transform method is presented in the second part of this work [40].Comment: 28 pages, 10 figure

    Bukhvostov-Lipatov model and quantum-classical duality

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    The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1+1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O(3)O(3) non-linear sigma model. In our previous work [arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.Comment: 49 pages, 8 figure

    Evolution of kinklike fluctuations associated with ion pickup within reconnection outflows in the Earth's magnetotail

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    Magnetic reconnection (MR) in Earth's magnetotail is usually followed by a systemwide redistribution of explosively released kinetic and thermal energy. Recently, multispacecraft observations from the THEMIS mission were used to study localized explosions associated with MR in the magnetotail so as to understand subsequent Earthward propagation of MR outbursts during substorms. Here we investigate plasma and magnetic field fluctuations/structures associated with MR exhaust and ion-ion kink mode instability during a well documented MR event. Generation, evolution and fading of kinklike oscillations are followed over a distance of 70 000 km from the reconnection site in the midmagnetotail to the more dipolar region near the Earth. We have found that the kink oscillations driven by different ion populations within the outflow region can be at least 25 000 km from the reconnection site.Comment: 11 pages, 4 figure

    Is current disruption associated with an inverse cascade?

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    Current disruption (CD) and the related kinetic instabilities in the near-Earth magnetosphere represent physical mechanisms which can trigger multi-scale substorm activity including global reorganizations of the magnetosphere. Lui et al. (2008) proposed a CD scenario in which the kinetic scale linear modes grow and reach the typical dipolarization scales through an inverse cascade. The experimental verification of the inverse nonlinear cascade is based on wavelet analysis. In this paper the Hilbert-Huang transform is used which is suitable for nonlinear systems and allows to reconstruct the time-frequency representation of empirical decomposed modes in an adaptive manner. It was found that, in the Lui et al. (2008) event, the modes evolve globally from high-frequencies to low-frequencies. However, there are also local frequency evolution trends oriented towards high-frequencies, indicating that the underlying processes involve multi-scale physics and non-stationary fluctuations for which the simple inverse cascade scenario is not correct.Comment: 6 pages, 4 figure

    The role of oxygen ions in the formation of a bifurcated current sheet in the magnetotail

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    Cluster observations in the near-Earth magnetotail have shown that sometimes the current sheet is bifurcated, i.e. it is divided in two layers. The influence of magnetic turbulence on ion motion in this region is investigated by numerical simulation, taking into account the presence of both protons and oxygen ions. The magnetotail current sheet is modeled as a magnetic field reversal with a normal magnetic field component BnB_n, plus a three-dimensional spectrum of magnetic fluctuations δB\delta {\bf B}, which represents the observed magnetic turbulence. The dawn-dusk electric field Ey_y is also included. A test particle simulation is performed using different values of δB\delta {\bf B}, Ey_y and injecting two different species of particles, O+^+ ions and protons. O+^+ ions can support the formation of a double current layer both in the absence and for large values of magnetic fluctuations (δB/B0=0.0\delta B/B_0 = 0.0 and δB/B00.4\delta B/B_0 \geq 0.4, where B0_0 is the constant magnetic field in the magnetospheric lobes).Comment: 8 pages, 8 figures. J. Geophys. Res., in pres