Laminar and turbulent dynamos in chiral magnetohydrodynamics-I: Theory

The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (\emph{chiral magnetic effect}). We present a self-consistent treatment of the \emph{chiral MHD equations}, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfv\'{e}n wave for incompressible flows, increases the frequencies of the Alfv\'{e}n wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark--gluon plasma.Comment: 23 pages, 4 figure

Travelling-wave nuclear magnetic resonance

Nuclear magnetic resonance (NMR) is one of the most versatile experimental methods in chemistry, physics and biology, providing insight into the structure and dynamics of matter at the molecular scale. Its imaging variant-magnetic resonance imaging (MRI)-is widely used to examine the anatomy, physiology and metabolism of the human body. NMR signal detection is traditionally based on Faraday induction in one or multiple radio-frequency resonators that are brought into close proximity with the sample. Alternative principles involving structured-material flux guides, superconducting quantum interference devices, atomic magnetometers, Hall probes or magnetoresistive elements have been explored. However, a common feature of all NMR implementations until now is that they rely on close coupling between the detector and the object under investigation. Here we show that NMR can also be excited and detected by long-range interaction, relying on travelling radio-frequency waves sent and received by an antenna. One benefit of this approach is more uniform coverage of samples that are larger than the wavelength of the NMR signal-an important current issue in MRI of humans at very high magnetic fields. By allowing a significant distance between the probe and the sample, travelling-wave interaction also introduces new possibilities in the design of NMR experiments and systems

Quantum spin systems at positive temperature

We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature $\beta$ and the magnitude of the quantum spins \CalS satisfy \beta\ll\sqrt\CalS. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with \CalS\gg1. The most notable examples are the quantum orbital-compass model on $\Z^2$ and the quantum 120-degree model on $\Z^3$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.Comment: 47 pages, version to appear in CMP (style files included

Further search for a neutral boson with a mass around 9 MeV/c2

Two dedicated experiments on internal pair conversion (IPC) of isoscalar M1 transitions were carried out in order to test a 9 MeV/c2 X-boson scenario. In the 7Li(p,e+e-)8Be reaction at 1.1 MeV proton energy to the predominantly T=0 level at 18.15 MeV, a significant deviation from IPC was observed at large pair correlation angles. In the 11B(d,n e+e-)12C reaction at 1.6 MeV, leading to the 12.71 MeV 1+ level with pure T=0 character, an anomaly was observed at 9 MeV/c2. The compatibility of the results with the scenario is discussed.Comment: 12 pages, 5 figures, 2 table

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

Rational sequences for the conductance in quantum wires from affine Toda field theories

We analyse the expression for the conductance of a quantum wire which is decribed by an integrable quantum field theory. In the high temperature regime we derive a simple formula for the filling fraction. This expression involves only the inverse of a matrix which contains the information of the asymptotic phases of the scattering matrix and the solutions of the constant thermodynamic Bethe ansatz equations. Evaluating these expressions for minimal affine Toda field theory we recover several sequences of rational numbers, which are multiples of the famous Jain sequence for the filling fraction occurring in the context of the fractional quantum Hall effect. For instance we obtain $\nu= 4 m/(2m +1)$ for $A_{4m-1}$-minimal affine Toda field theory. The matrices involved have in general non-rational entries and are not part of previous classification schemes based on integral lattices.Comment: 9 pages Latex, version to appear in Journal of Physics

Vortex Dynamics in Classical Non--Abelian Spin Models

We discuss the abelian vortex dynamics in the abelian projection approach to non-abelian spin models. We show numerically that in the three-dimensional SU(2) spin model in the Maximal Abelian projection the abelian off-diagonal vortices are not responsible for the phase transition contrary to the diagonal vortices. A generalization of the abelian projection approach to SU(N) spin models is briefly discussed.Comment: 7 pages, LaTeX, 1 figure, uses epsf.sty; Introduction is extended and a few references are added; to be published in JETP Let

Interaction of electric charges in (2+1)D magnetic dipole gas

The interaction of electrically charged particles in a dilute gas of point--like magnetic dipoles is studied. We show that the interaction potential at small distances has a linear piece due to overlap of the dipole clouds gathered near electric sources. At large distances the potential becomes of the Coulomb type with non-perturbatively renormalized charge of the test particle. The physical applications of these results are discussed.Comment: 23 pages, 12 EPS figures, RevTeX, uses epsfig.sty; misprints corrected (to appear in Phys.Rev.D

Decay of Superconducting and Magnetic Correlations in One- and Two-Dimensional Hubbard Models

In a general class of one and two dimensional Hubbard models, we prove upper bounds for the two-point correlation functions at finite temperatures for electrons, for electron pairs, and for spins. The upper bounds decay exponentially in one dimension, and with power laws in two dimensions. The bounds rule out the possibility of the corresponding condensation of superconducting electron pairs, and of the corresponding magnetic ordering. Our method is general enough to cover other models such as the t-J model.Comment: LaTeX, 8 pages, no figures. A reference appeared after the publication is adde