Problem of the Landau Poles in Quantum Field Theory: from N. N. Bogolyubov to the Present Day

Russian Physics Journal - A review of problems associated with the unphysical Landau pole in propagators of quantum particles is given. Approaches to eliminating this pole within the framework of...     

Stability Diagrams of a Bose-Einstein Condensate in Excited Bloch Bands

Landau and dynamical instabilities o/a Bose-Einstein condensate （BEC） in the excited bands of a one-dimensional optical lattice are investigated by the Gross Pitaevskii theory. Our results show that there always exists Landau instability for a BEC in the whole region of excited bands. We also map out the dangerous zones of the dynamical instability. The experimental implications of the stability diagram are discussed.     

Renormalization flow of QED

We investigate textbook QED in the framework of the exact renormalization group. In the strong-coupling region, we study the influence of fluctuation-induced photonic and fermionic self-interactions on the nonperturbative running of the gauge coupling. Our findings confirm the triviality hypothesis of complete charge screening if the ultraviolet cutoff is sent to infinity. Though the Landau pole does not belong to the physical coupling domain owing to spontaneous chiral-symmetry-breaking (chiSB), the theory predicts a scale of maximal UV extension of the same order as the Landau pole scale. In addition, we verify that the chiSB phase of the theory which is characterized by a light fermion and a Goldstone boson also has a trivial Yukawa coupling.     

Triviality of Quantum Electrodynamics Revisited

Quantum electrodynamics is often considered to be a trivial theory.This is based on a number of evidences,both numerical and analytical.One of the strong indications for triviality of QED is the existence of the Landau pole for the running coupling.We show that by treating QED as the leading order approximation of an effective field theory and including the next-to-leading order corrections,the Landau pole is removed.We also analyze the cutoff dependence of the bare coupling at two-loop order and conclude that the conjecture,that for reasons of self-consistency,QED needs to be trivial is a mere artefact of the leading order approximation to the corresponding effective field theory.     

Instability of Bose-Einstein condensates moving in optical lattices

We investigate the Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at a finite temperature. Using a 1D tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence reveals the microscopic mechanism of the Landau instability.     

Avoidance of a Landau pole by flat contributions in QED

We consider massless Quantum Electrodynamics in the momentum scheme and carry forward an approach based on Dyson–Schwinger equations to approximate both the β$\beta$-function and the renormalized photon self-energy (Yeats, 2011). Starting from the Callan–Symanzik equation, we derive a renormalization group (RG) recursion identity which implies a non-linear ODE for the anomalous dimension and extract a sufficient but not necessary criterion for the existence of a Landau pole. This criterion implies a necessary condition for QED to have no such pole. Solving the differential equation exactly for a toy model case, we integrate the corresponding RG equation for the running coupling and find that even though the β$\beta$-function entails a Landau pole it exhibits a flat contribution capable of decreasing its growth, in other cases possibly to the extent that such a pole is avoided altogether. Finally, by applying the recursion identity, we compute the photon propagator and investigate the effect of flat contributions on both spacelike and timelike photons.     

Dynamical gauge bosons from fundamental fermions

In a class of four-dimensional, non-linear fermionic lagrangians, a classical gauge symmetry induces dynamical gauge fields at the quantum level. The construction requires flavour (or families) as well as the “unification” of all gauge couplings at the common Landau pole mass.     

Geodesic mode instability driven by the electron current in tokamak plasmas

Effect of the parallel electron current on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current modeled by shifted Maxwell distribution may overcome the phase velocity threshold and ion Landau damping thus resulting in the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity Rqω. The instability occurs due to its cross term of the current with the ion diamagnetic drift. Possible applications to tokamak experiments are discussed.     

Instabilities in nuclear matter and finite nuclei

Spinodal instability in nuclear matter and finite nuclei is investigated. This instability occurs in the low-density region of the phase diagram. The thermodynamical and dynamical analysis is based on Landau theory of Fermi liquids. It is shown that asymmetric nuclear matter can be characterized by a unique spinodal region, defined by the instability against isoscalar-like fluctuation, as in symmetric nuclear matter. Everywhere in this density region the system is stable against isovector-like fluctuations related to the species separation tendency. Nevertheless, this instability in asymmetric nuclear matter induces isospin distillation leading to a more symmetric liquid phase and a more neutron-rich gas phase.     

Vlasov-Poisson方程半拉格朗日守恒算法

利用三阶迎风插值多项式结合限制子方法,构造Vlasov-Poisson方程的半拉格朗日守恒型格式,可保持Vlasov-Poisson方程解的正性.计算朗道阻尼,双束不稳定性等典型问题,并与样条插值方法、UGKS方法进行比较,模拟结果表明半拉格朗日守恒性格式在Vlasov-Poisson方程求解中具有较高分辨率.     

Numerical coupling of Landau damping and Raman amplification

In this paper, we present a numerical model for laser-plasma interaction involving Raman instability and Landau damping. This model exhibits three main difficulties. The first one is the coupling of PDE’s posed both in Fourier space and in physical space. The second one is a three-waves resonance condition that has to be verified. The third one is the boundary conditions. We overcome these difficulties using, respectively a splitting scheme, a numerical dispersion relation and absorbing boundary conditions. We present some comparison between several phenomena that are involved and the influence of the Raman amplification and the Landau damping.     

Study of the gluon propagator in the axial gauge

It is shown that a non-linear integral equation for the gluon propagator in the axial gauge (Baker et al.) can be simplified considerably. A comparison is made with an approximate equation for the gluon propagator in the Landau gauge (Mandelstam). Both equations have polynomial kernels where the argument is the divisor of the internal and external momenta. A solution which behaves as a double pole for low momenta remains consistent.     

Point impurities remove degeneracy of the Landau levels in a two-dimensional electron gas

The density of states of a two-dimensional electron gas in a magnetic field has been studied taking into account the scattering on point impurities. It is demonstrated that allowance for the electron-impurity interaction completely removes degeneracy of the Landau levels even for a small volume density of these point defects. The density of states is calculated in a self-consistent approximation taking into account all diagrams without intersections of the impurity lines. The electron density of states ρ is determined by the contribution from a cut of the one-particle Green’s function rather than from a pole. In a wide range of the electron energies ω (measured from each Landau level), the value of ρ(ω) is inversely proportional to the energy |ω| and proportional to the impurity concentration. The obtained results are applicable to various two-dimensional electron systems such as inversion layers, heterostructures, and electrons on the surface of liquid helium.     

Pulsating hydrodynamic instability and thermal coupling in an extended Landau/Levich model of liquid-propellant combustion: I. Inviscid analysis

Hydrodynamic (Landau) instability in combustion is typically associated with the onset of wrinkling of a flame surface, corresponding to the formation of steady cellular structures as the stability threshold is crossed. In the context of liquid-propellant combustion, such instability has recently been shown to occur for critical values of the pressure sensitivity of the burning rate and the disturbance wavenumber, significantly generalizing previous classical results for this problem that assumed a constant normal burning rate. Additionally, however, a pulsating form of hydrodynamic instability has been shown to occur as well, corresponding to the onset of temporal oscillations in the location of the liquid/gas interface. In the present work, we consider the realistic influence of a non-zero temperature sensitivity in the local burning rate on both types of stability thresholds. It is found that for sufficiently small values of this parameter, there exists a stable range of pressure sensitivities for steady, planar burning such that the classical cellular form of hydrodynamic instability and the more recent pulsating form of hydrodynamic instability can each occur as the corresponding stability threshold is crossed. For larger thermal sensitivities, however, the pulsating stability boundary evolves into a C-shaped curve in the (disturbance-wavenumber, pressure-sensitivity) plane, indicating loss of stability to pulsating perturbations for all sufficiently large disturbance wavelengths. It is thus concluded, based on characteristic parameter values, that an equally likely form of hydrodynamic instability in liquid-propellant combustion is of a non-steady, long-wave nature, distinct from the steady, cellular form originally predicted by Landau.     

On nonlinear model equations for the response of premixed flames to acoustic like accelerations

The response of a dynamical flame model to imposed acoustic accelerations is studied analytically and numerically. Through linear stability analyses, two analytical approximations for the primary and the parametric stability boundaries are found. The approximation for the primary instability boundary is accurate for any periodic accelerations, in the limit of large acoustic frequencies. The critical acoustic amplitude u _a for Landau–Darrieus instability suppression is identified and found to depend only on the density contrast and the shape of the periodic acoustic stimuli. The proposed model evolution equation is next integrated numerically with various imposed acoustic accelerations; the primary and parametric flame responses are identified. It is shown analytically and numerically that in the presence of a fully developed, yet weakened by acoustics, Landau–Darrieus (or primary) instability the wrinkle amplitude and the mean flame speed oscillate at the same frequency as the acoustic stimuli; the threshold for suppression of primary instability by acoustic forcing is determined exactly. Increasing the acoustic amplitude allows the flame to respond parametrically to the acoustics. This response is characterised by troughs and crests interchanging their roles while the mean flame speed again oscillates with the same frequency as the acoustic stimuli and at twice that of wrinkle amplitude oscillations.     

Instabilities of a tangential discontinuity

A critical analysis of Landau and Lifshitz’s data concerning the instability of a tangential discontinuity in a compressible liquid is given. The simplest case when the liquid flow velocity alone experiences a discontinuity is considered. The influence of a high transverse gravitational field on the stability of a tangential discontinuity is investigated.     

Triplet exciton and ferromagnetic instability of a two-dimensional electron gas in a large magnetic field with filling factor v=2

We have investigated the phase diagram of a two-dimensional electron gas in a large magnetic field as a function of the difference between the cyclotron and the spin resonance splittings. For suitable values of this difference we find that when the two spin states of the lowest Landau level are fully occupied the paramagnetic ground state suffers a triplet exciton (spin-density-wave) instability. However our analysis shows that in the simplest case such an instability is preempted by a paramagnetic to ferromagnetic phase transition. The occurence of this transition and some of its consequences have been studied.     

Velocity of weakly turbulent flames of finite thickness

The velocity increase of a weakly turbulent flame of finite thickness is investigated using analytical theory developed in previous papers. The obtained velocity increase depends on the flow parameters: on the turbulent intensity, on the turbulent spectrum and on the characteristic length scale. It also depends on the thermal and chemical properties of the burning matter: thermal expansion, the Markstein number and the temperature dependence of transport coefficients. It is shown that the influence of the finite flame thickness is especially strong close to the resonance point, when the wavelength of the turbulent harmonic is equal to the cut off wavelength of the Darrieus–Landau instability. The velocity increase is almost independent of the Prandtl number. On the contrary, the Markstein number is one of the most important parameters controlling the velocity increase. The relative role of the external turbulence and the Darrieus–Landau instability for the velocity increase is studied for different parameters of the flow and the burning matter. The velocity increase for turbulent flames in methane and propane fuel mixtures is calculated for different values of the equivalence ratio. The present theoretical results are compared with previous experiments on turbulent flames. In order to perform the comparison, the theoretical results of the present paper are extrapolated to the case of a strongly corrugated flame front using the ideas of self-similar flame dynamics. The obtained theoretical results are in a reasonable agreement with the experimental data, taking into account the uncertainties of both the theory and the experiments. It is shown that in many experiments on turbulent flames the Darrieus–Landau instability is more important for the flame velocity than the external turbulence.     

On the Kelvin-Helmholtz instability in superfluids

The Kelvin-Helmholtz instability in superfluids is discussed on the basis of the first experimental observation of such an instability at the interface between superfluid ³He-A and superfluid ³He-B (R. Blaauwgeers, V. B. Eltsov, G. Eska et al., cond-mat/0111343). We discuss why the Kelvin-Helmholtz criterion, the Landau critical velocity for nucleation of ripplons, and the free-energy consideration all give different values for the instability threshold.