419 research outputs found

### 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

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

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?

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

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 $B_n$, plus a three-dimensional
spectrum of magnetic fluctuations $\delta {\bf B}$, which represents the
observed magnetic turbulence. The dawn-dusk electric field E$_y$ is also
included. A test particle simulation is performed using different values of
$\delta {\bf B}$, E$_y$ 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
($\delta B/B_0 = 0.0$ and $\delta B/B_0 \geq 0.4$, where B$_0$ is the constant
magnetic field in the magnetospheric lobes).Comment: 8 pages, 8 figures. J. Geophys. Res., in pres

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