Vacuum energy of the Bukhvostov-Lipatov model

Bukhvostov and Lipatov have shown that weakly interacting instantons and anti-instantons in the $O(3)$ 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

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 $O(3)$ 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

Wavelet analysis of magnetic turbulence in the Earth's plasma sheet

Recent studies provide evidence for the multi-scale nature of magnetic turbulence in the plasma sheet. Wavelet methods represent modern time series analysis techniques suitable for the description of statistical characteristics of multi-scale turbulence. Cluster FGM (fluxgate magnetometer) magnetic field high-resolution (~67 Hz) measurements are studied during an interval in which the spacecraft are in the plasma sheet. As Cluster passes through different plasma regions, physical processes exhibit non-steady properties on magnetohydrodynamic (MHD) and small, possibly kinetic scales. As a consequence, the implementation of wavelet-based techniques becomes complicated due to the statistically transitory properties of magnetic fluctuations and finite size effects. Using a supervised multi-scale technique which allows existence test of moments, the robustness of higher-order statistics is investigated. On this basis the properties of magnetic turbulence are investigated for changing thickness of the plasma sheet.Comment: 17 pages, 5 figure

Pressure and intermittency in passive vector turbulence

We investigate the scaling properties a model of passive vector turbulence with pressure and in the presence of a large-scale anisotropy. The leading scaling exponents of the structure functions are proven to be anomalous. The anisotropic exponents are organized in hierarchical families growing without bound with the degree of anisotropy. Nonlocality produces poles in the inertial-range dynamics corresponding to the dimensional scaling solution. The increase with the P\'{e}clet number of hyperskewness and higher odd-dimensional ratios signals the persistence of anisotropy effects also in the inertial range.Comment: 4 pages, 1 figur

Multi-scale magnetic field intermittence in the plasma sheet

This paper demonstrates that intermittent magnetic field fluctuations in the plasma sheet exhibit transitory, localized, and multi-scale features. We propose a multifractal based algorithm, which quantifies intermittence on the basis of the statistical distribution of the 'strength of burstiness', estimated within a sliding window. Interesting multi-scale phenomena observed by the Cluster spacecraft include large scale motion of the current sheet and bursty bulk flow associated turbulence, interpreted as a cross-scale coupling (CSC) process.Comment: 18 pages, 7 figure

Transient and localized processes in the magnetotail: a review

Many phenomena in the Earth's magnetotail have characteristic temporal scales of several minutes and spatial scales of a few Earth radii (<I>R<sub>E</sub></I>). Examples of such transient and localized mesoscale phenomena are bursty bulk flows, beamlets, energy dispersed ion beams, flux ropes, traveling compression regions, night-side flux transfer events, and rapid flappings of the current sheet. Although most of these observations are linked to specific interpretations or theoretical models they are inter-related and can be the different aspects of a physical process or origin. Recognizing the inter-connected nature of the different transient and localized phenomena in the magnetotail, this paper reviews their observations by highlighting their important characteristics, with emphasis on the new results from Cluster multipoint observations. The multi-point Cluster measurements have provided, for the first time, the ability to distinguish between temporal and spatial variations, and to resolve spatial structures. Some examples of the new results are: flux ropes with widths of 0.3 <I>R<sub>E</sub></I>, transient field aligned currents associated with bursty bulk flows and connected to the Hall current at the magnetic reconnection, flappings of the magnetotail current sheet with time scales of 100 s–10 min and thickness of few thousand km, and particle energization including velocity and time dispersed ion structures with the latter having durations of 1–3 min. The current theories of these transient and localized processes are based largely on magnetic reconnection, although the important role of the interchange and other plasma modes are now well recognized. On the kinetic scale, the energization of particles takes place near the magnetic X-point by non-adiabatic processes and wave-particle interactions. The theory, modeling and simulations of the plasma and field signatures are reviewed and the links among the different observational concepts and the theoretical frameworks are discussed. The mesoscale processes in the magnetotail and the strong coupling among them are crucial in developing a comprehensive understanding of the multiscale phenomena of the magnetosphere

Alfvén waves in the near-PSBL lobe: Cluster observations

Electromagnetic low-frequency waves in the magnetotail lobe close to the PSBL (Plasma Sheet Boundary Layer) are studied using the Cluster spacecraft. The lobe waves show Alfvénic properties and transport their wave energy (Poynting flux) on average toward the Earth along magnetic field lines. Most of the wave events are rich with oxygen (O+) ion plasma. The rich O+ plasma can serve to enhance the magnetic field fluctuations, resulting in a greater likelihood of observation, but it does not appear to be necessary for the generation of the waves. Taking into account the fact that all events are associated with auroral electrojet enhancements, the source of the lobe waves might be a substorm-associated instability, i.e. some instability near the reconnection site, or an ion beam-related instability in the PSBL

Renormalization group in the infinite-dimensional turbulence: third-order results

The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of construction of the 1/d expansion for the fully developed fluid turbulence beyond the scope of the standard epsilon expansion. It is shown that in the large-d limit the number of the Feynman diagrams for the Green function (linear response function) decreases drastically, and the technique of their analytical calculation is developed. The main ingredients of the renormalization group approach -- the renormalization constant, beta function and the ultraviolet correction exponent omega, are calculated to order epsilon^3 (three-loop approximation). The two-point velocity-velocity correlation function, the Kolmogorov constant C_K in the spectrum of turbulent energy and the inertial-range skewness factor S are calculated in the large-d limit to third order of the epsilon expansion. Surprisingly enough, our results for C_K are in a reasonable agreement with the existing experimental estimates.Comment: 30 pages with EPS figure

Spectral Duality Between Heisenberg Chain and Gaudin Model

In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.Comment: 36 page

Local structure of the magnetotail current sheet: 2001 Cluster observations

Thirty rapid crossings of the magnetotail current sheet by the Cluster spacecraft during July-October 2001 at a geocentric distance of 19 <i>R<sub>E</sub></i> are examined in detail to address the structure of the current sheet. We use four-point magnetic field measurements to estimate electric current density; the current sheet spatial scale is estimated by integration of the translation velocity calculated from the magnetic field temporal and spatial derivatives. The local normal-related coordinate system for each case is defined by the combining Minimum Variance Analysis (MVA) and the curlometer technique. Numerical parameters characterizing the plasma sheet conditions for these crossings are provided to facilitate future comparisons with theoretical models. Three types of current sheet distributions are distinguished: center-peaked (type I), bifurcated (type II) and asymmetric (type III) sheets. Comparison to plasma parameter distributions show that practically all cases display non-Harris-type behavior, i.e. interior current peaks are embedded into a thicker plasma sheet. The asymmetric sheets with an off-equatorial current density peak most likely have a transient nature. The ion contribution to the electric current rarely agrees with the current computed using the curlometer technique, indicating that either the electron contribution to the current is strong and variable, or the current density is spatially or temporally structured