On the chiral magnetic effect in Weyl superfluid <Superscript>3</Superscript>He-A

In the theory of the chiral anomaly in relativistic quantum field theories (RQFTs), some results depend on a regularization scheme at ultraviolet. In the chiral superfluid ³He-A, which contains two Weyl points and also experiences the effects of chiral anomaly, the “trans-Planckian” physics is known and the results can be obtained without regularization. We discuss this on example of the chiral magnetic effect (CME), which has been observed in ³He-A in the 1990s [1]. There are two forms of the contribution of the CME to the Chern–Simons term in free energy, perturbative and non-perturbative. The perturbative term comes from the fermions living in the vicinity of the Weyl point, where the fermions are “relativistic” and obey the Weyl equation. The non-perturbative term originates from the deep vacuum, being determined by the separation of the two Weyl points in momentum space. Both terms are obtained using the Adler–Bell–Jackiw equation for chiral anomaly, and both agree with the results of the microscopic calculations in the “trans-Planckian” region. Existence of the two nonequivalent forms of the Chern–Simons term demonstrates that the results obtained within the RQFT depend on the specific properties of the underlying quantum vacuum and may reflect different physical phenomena in the same vacuum.     

The role of strange sea quarks in chiral extrapolations on the lattice

Since the strange quark has a light mass of order , fluctuations of sea pairs may play a special role in the low-energy dynamics of QCD by inducing significantly different patterns of chiral symmetry breaking in the chiral limits N _f = 2 (m _u = m _d = 0, m _s physical) and N _f = 3 (m _u = m _d = m _s = 0). This effect of vacuum fluctuations of pairs is related to the violation of the Zweig rule in the scalar sector, described through the two O(p ⁴) low-energy constants L ₄ and L ₆ of the three-flavour strong chiral lagrangian. In the case of significant vacuum fluctuations, three-flavour chiral expansions might exhibit numerical competition between leading- and next-to-leading-order terms according to the chiral counting, and chiral extrapolations should be handled with special care. We investigate the impact of the fluctuations of pairs on chiral extrapolations in the case of lattice simulations with three dynamical flavours in the isospin limit. Information on the size of the vacuum fluctuations can be obtained from the dependence of the masses and decay constants of pions and kaons on the light quark masses. Even in the case of large fluctuations, corrections due to the finite size of spatial dimensions can be kept under control for large enough boxes ( fm).Received: 20 October 2004, Revised: 28 December 2004, Published online: 9 February 2005Laboratoire de Physique Théorique: LPT is an Unité Mixte de Recherche du CNRS et de lUniversité Paris-Sud 11 (UMR 8627).     

Chiral magnetic effect in SU(2) lattice gluodynamics at zero temperature

The chiral magnetic effect is the appearance of a quark electric current along a magnetic-field direction in topologically nontrivial gauge fields. There is evidence that this effect is observed in collisions between heavy ions at the RHIC collider. The features of the chiral magnetic effect in SU(2) lattice gluodynamics at zero temperature have been investigated. It has been found that the electric current increases in the magnetic-field direction owing to quantum fluctuations of gluon fields. Fluctuations of the local charge density and chirality also increase with the magnetic field strength, which is a signature of the chiral magnetic effect.     

Itinerant electron-driven chiral magnetic ordering and spontaneous quantum Hall effect in triangular lattice models

We study the Kondo Lattice and the Hubbard models on a triangular lattice. We find that at the mean-field level, these rotationally invariant models naturally support a noncoplanar chiral magnetic ordering. It appears as a weak-coupling instability at the band filling factor 3/4 due to the perfect nesting of the itinerant electron Fermi surface. This ordering is a triangular-lattice counterpart of the collinear Neel ordering that occurs on the half-filled square lattice. While the long-range magnetic ordering is destroyed by thermal fluctuations, the chirality can persist up to a finite temperature, causing a spontaneous quantum Hall effect in the absence of any externally applied magnetic field.     

Chiral magnetic soliton lattice on a chiral helimagnet

Using Lorenz microscopy and small-angle electron diffraction, we directly present that the chiral magnetic soliton lattice (CSL) continuously evolves from a chiral helimagnetic structure in small magnetic fields in Cr(1/3)NbS2. An incommensurate CSL undergoes a phase transition to a commensurate ferromagnetic state at the critical field strength. The period of a CSL, which exerts an effective potential for itinerant spins, is tuned by simply changing the field strength. Chiral magnetic orders observed do not exhibit any structural dislocation, indicating their high stability and robustness in Cr(1/3)NbS2.     

Chiral magnetic effect in lattice QCD with a chiral chemical potential

We perform a first lattice QCD simulation including a two-flavor dynamical fermion with a chiral chemical potential. Because the chiral chemical potential gives rise to no sign problem, we can exactly analyze a chirally imbalanced QCD matter by Monte Carlo simulation. By applying an external magnetic field to this system, we obtain a finite induced current along the magnetic field, which corresponds to the chiral magnetic effect. The obtained induced current is proportional to the magnetic field and to the chiral chemical potential, which is consistent with an analytical prediction.     

Spontaneous chiral symmetry breaking for a U(N) gauge theory on a lattice

We study the breakdown of chiral invariance by calculating, in the infinite coupling, large-N limit, the generating functional of a U(N) gauge theory with one fermion, expressed on a lattice with the naive, chiral symmetric action. We compute the link integral over the gauge fields and the expression obtained after the integration over the fermions is recast under the form of a generating functional for bosonic fields. Then, a saddle-point method allows the calculation of the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ for which a non-zero value signals the spontaneous breakdown of chiral symmetry. The analysis of the fluctuations around the saddle point allows one to exhibit the Goldstone modes corresponding to those global symmetries of the fermionic lattice action which are simultaneously broken.     

Resonant amplification of quantum fluctuations in a spinor gas

Bose-Einstein condensates of atoms with non-zero spin are known to constitute an ideal system to investigate fundamental properties of magnetic superfluids. More recently it was realized that they also provide the fascinating opportunity to investigate the macroscopic amplification of quantum and classical fluctuations. This is strikingly manifested in a sample initially prepared in the m _F = 0 state, where spin-changing collisions triggered by quantum fluctuations may lead to the creation of correlated pairs in m _F = ±1. We show that the pair creation efficiency is strongly influenced by the interplay between the external trapping potential and the Zeeman effect. It thus reflects the confinement-induced magnetic field dependence of elementary spin excitations of the condensate. Remarkably, pair production in our experiments is therefore characterized by a multi-resonant dependence on the magnetic field. Pair creation at these resonances acts as strong parametric matter-wave amplifier. Depending on the resonance condition, this amplification can be extremely sensitive or insensitive to the presence of seed atoms. We show that pair creation at a resonance which is insensitive to the presence of seed atoms is triggered purely by quantum fluctuations and thus the system acts as a matter-wave amplifier for the vacuum state.     

Floquet topological phase transitions and chiral edge states in a kagome lattice

The Floquet topological phases and chiral edge states in a kagome lattice under a circularly-polarized driving field are studied. In the off-resonant case, the system exhibits the similar character as the kagome lattice model with staggered magnetic fluxes, but the total band width is damped in oscillation. In the on-resonant case, the degeneracy splitting at the Γ point does not always result in a gap. The positions of the other two gaps are influenced by the flat band. With the field intensity increased, these two gaps undergo closing-then-reopening processes, accompanied with the changing of the winding numbers.     

A chiral theory of nucleons

We present arguments that QCD at low momenta is reduced to a simple theory given by a path integral over pion fields and quarks which obtain dynamical mass owing to chiral symmetry breaking. The dimensional quantities of this low-momenta theory are fixed through the Λ_QCD parameter. The effective chiral lagrangian is given by a quark determinant in a background chiral field. Its properties are investigated both for slowly and rapidly varying pion fields. Though it satisfies requirements known from theory and phenomenology, it does not possess non-trivial soliton solutions. However we show that, at large N_c, nucleons correspond not to the local minimum of the effective chiral lagrangian but to a minimum of a more subtle quantity. In general, different functionals of the chiral field should be minimized, depending on the baryon charge of the system.We obtain a quantitative picture of nucleons as localized states of “constituent” quarks bound by a self-consistent pion field. Its properties, such as electromagnetic form factors, etc., are investigated in detail. We get very reasonable numerical values for the nucleon static properties.     

Gauge cosmic chiral strings in general relativity

Cylindrically symmetric self-gravitating configurations of string (vortex) type are considered within the framework of the chiral SU(2) model with the inclusion of the Yang-Mills proper gauge field. In the approximation of the large topological charge n the solutions to the field equations are found, with the magnetic field of the vortex being longitudinal. The linear energy density of the vortex configuration is estimated. The text was submitted by the author in English.     

Signatures of chiral dynamics in the nucleon to Delta transition⋆

Utilizing the methods of chiral effective field theory we present an analysis of the electromagnetic NΔ-transition current in the framework of the non-relativistic “small scale expansion” (SSE) to leading-one-loop order. We discuss the momentum dependence of the magnetic dipole, electric quadrupole and Coulomb quadrupole transition form factors up to a momentum transfer of Q² < 0.3GeV^2. Particular emphasis is put on the identification of the role of chiral dynamics in this transition. Our analysis indicates that there is indeed non-trivial momentum dependence in the two quadrupole form factors at small Q² < 0.15GeV^2 arising from long-distance pion physics, leading, for example, to negative radii in the (real part of the) quadrupole transition form factors. We compare our results with the EMR(Q²) and CMR(Q²) multipole ratios from pion-electroproduction experiments and find a remarkable agreement up to four-momentum transfer of Q² ≈ 0.3GeV^2. Finally, we discuss the chiral extrapolation of the three transition form factors at Q² = 0, identifying rapid changes in the (real part of the) quark mass dependence of the quadrupole transition moments for pion masses below 200MeV, which arise again from long-distance pion dynamics. Our findings indicate that dipole extrapolation methods currently used in lattice QCD analyses of baryon form factors are not applicable for the chiral extrapolation of NΔ quadrupole transition form factors.     

Finite-size-scaling analyses of the chiral ordert in the Josephson-junction ladder with half a flux quantum per plaquette

Chiral order of the Josephson-junction ladder with half a flux quantum per plaquette is studied by means of the exact diagonalization method. We consider an extreme quantum limit where each superconductor grain (order parameter) is represented by S=1/2 spin. So far, the semi-classical case, where each spin reduces to a plane rotator, has been considered extensively. We found that in the case of S=1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except in a region, where attractive intrachain and, to our surprise, repulsive interchain interactions both exist. On the contrary, for considerably wide range of parameters, the superconductor (XY) order is kept critical. The present results are regarded as a demonstration of the critical phase accompanying chiral-symmetry breaking predicted for frustrated XXZ chain field-theoretically. Received 20 February 2000     

Field-induced winding of chiral polymers

We propose a microscopic model of a chiral polymer chain with permanent transverse dipoles interacting with an external electric field. Its behaviour has been investigated by computer simulation in the limit of weak chirality. Large-scale (tertiary) helical winding induced along the field direction has been found above a threshold field E_c, and the helix parameters have been calculated as functions of the field strength. Below E_c there is no coherent helical structure of the chain conformation. We find a characteristic scaling of the threshold and the winding radius a with the chain bending modulus , and . Received: 15 November 1997 / Accepted: 16 February 1998     

Neutron-deuteron scattering in chiral effective field theory

We perform a complete analysis of nd scattering at next-to-next-to-leading order (NNLO) in chiral effective field theory (EFT) and compare our predictions for selected observables with the ones based on conventional nuclear forces.Received: 1 November 2002, Published online: 15 July 2003PACS: 21.30.Cb Nuclear forces in vacuum - 21.45.+v Few-body systems     

Gluon condensates,chiral symmetry breaking and pion wave-function

We consider here chiral symmetry breaking in quantum chromodynamics arising from gluon condensates in vacuum. Through coherent states of gluons simulating a mean field type of approximation, we show that the off-shell gluon condensates of vacuum generate a mass-like contribution for the quarks, giving rise to chiral symmetry breaking. We next note that spontaneous breaking of global chiral symmetry links the four component quark field operator to the pion wave function. This in turn yields many hadronic properties in the light quark sector in agreement with experiments, leading to the conclusion that low energy hadron properties are primarily driven by the vacuum structure of quantum chromodynamics.     

Spontaneous violation of chiral symmetry in QCD vacuum is the origin of baryon masses and determines baryon magnetic moments and their other static properties

A short review is presented of the spontaneous violation of chiral symmetry in QCD vacuum. It is demonstrated that this phenomenon is the origin of baryon masses in QCD. The value of nucleon mass is calculated, as well as the masses of hyperons and some baryonic resonances, and expressed mainly through the values of quark condensates—, q = u, d, s,—the vacuum expectation values (v.e.v.) of quark field. The concept of v.e.v. induced by external fields is introduced. It is demonstrated that such v.e.v. induced by static electromagnetic field results in quark condensate magnetic susceptibility, which plays the main role in determination of baryon magnetic moments. The magnetic moments of proton, neutron, and hyperons are calculated. The results of calculation of baryon octet β-decay constants are also presented. The text was submitted by the author in English.     

Radiative noise in circuits with inductance

Using the general idea of the fluctuation–dissipation theorem we study a new contribution to the voltage fluctuations which is associated with the presence of radiation resistance. We consider the particular case of a solenoid immersed in a cavity with equilibrium radiation at temperature T. We prove that these new fluctuations are generated by the random magnetic field present in the cavity. These magnetic voltage fluctuations are shown to be experimentally distinguishable from the voltage fluctuations associated with the well known Nyquist noise. Accordingly we suggest feasible experiments to measure this magnetic noise. All the calculations are made within the context of Stochastic Electrodynamics, a theory in which the vacuum zero-point field is taken as a real electromagnetic field. We also study the average energy of an RLC circuit in thermodynamic equilibrium with the radiation.     

Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory

We discuss lattice simulations of the ground state of dilute neutron matter at next-to-leading order in chiral effective field theory. In a previous paper the coefficients of the next-to-leading-order lattice action were determined by matching nucleon-nucleon scattering data for momenta up to the pion mass. Here the same lattice action is used to simulate the ground state of up to 12 neutrons in a periodic cube using Monte Carlo simulations. We explore the density range from 2% to 8% of normal nuclear density and analyze the ground-state energy as an expansion about the unitarity limit with corrections due to finite scattering length, effective range, and P -wave interactions.