Symmetry Properties and Reduction of the Generalized Nonlinear System of Two-Phase Liquid Equations

Abstract

We consider discontinuous flows of relativistic magnetic fluid with a general equation of state that is not supposed to be normal in the sense of Bethe and Weyl. The criteria of admissibility of the shock waves without a supposition of the relativistic version of the convexity condition are obtained. The results are used to analyze the cases of perpendicular and parallel shock waves.     

Gravitational anomaly and transport phenomena

Quantum anomalies give rise to new transport phenomena. In particular, a magnetic field can induce an anomalous current via the chiral magnetic effect and a vortex in the relativistic fluid can also induce a current via the chiral vortical effect. The related transport coefficients can be calculated via Kubo formulas. We evaluate the Kubo formula for the anomalous vortical conductivity at weak coupling and show that it receives contributions proportional to the gravitational anomaly coefficient. The gravitational anomaly gives rise to an anomalous vortical effect even for an uncharged fluid.     

相对论重离子碰撞的输运模型研究

美国的布鲁克海文国家实验室相对论重离子对撞机（RHIC）和欧洲核子中心的大型强子对撞机（LHC）的大量实验结果表明,在相对论重离子碰撞中已经产生了一种近似完美流体的强耦合部分子物质。基于一个多相粒子输运模型（AMPT）理论工具,对RHIC和LHC实验上的一些重要结果的开展了三个方面的理论研究工作（集体流、喷注淬火、手征磁效应）,研究结果揭示了初始的夸克胶子等离子体（QGP）能量密度涨落经过部分子输运演化产生末态粒子的各阶次的集体流、喷注和部分子物质的相互作用导致喷注的能量损失、末态相互作用严重影响手征磁效应的大小等物理过程作用机制。The experimental results from the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) show that a nearly perfect fluid (i.e. strong-coupling Quark Gluon Plasma) has been created in relativistic heavy-ion collisions. I introduce our theoretical results based on a multi-phase transport (AMPT) model. Several important topics such as collective flow, jet quenching, chiral magnetic effect, are addressed. The simulation results indicate that the initial fluctuations of energy density of the QGP lead to all orders of harmonic flows of final particles via parton cascade, the strong interactions between jet and the QGP make jet lose much energy, and the final state interactions play an important role to affect the initial chiral magnetic effect in relativistic heavy-ion collisions.     

Instabilities Driven by an Intense Beam in a Plasma-Filled Dielectric-Lined Waveguide Immersed in a Finite Axial Magnetic Field

A linear analysis is described on stabilities driven by an intense relativistic electron beam in an infinitely long, plasma-filled, and dielectric-lined circular waveguide immersed in a finite strength axial magnetic field. A dispersion equation is derived from the cold fluid theory and solved numerically. Beam-plasma instabilities due to interaction between beam modes and the Trivelpiece-Gould modes appear as well as the Cherenkov and the cyclotron Cherenkov instabilities. Parametric researches are carried out varying magnetic field strength, plasma density, and dielectric constant. Effects of a finite magnetic field and plasma filling are discussed in connection with the possibilities of using this system as a microwave radiation source.     

String behaviour of magnetic field lines and their rotation in neutron star’s interior

It is found from Maxwell’s equations that the magnetic field lines are good analogues of relativistic strings. The Lorentz force per unit length of magnetic tube is interpretable as Magnus force acting on each individual magnetic tube. It is shown that the superconducting current in pulsar’s interior causes local rotation of magnetic flux tubes carrying quantized flux. Such local rotation remains operative as long as the induced magnetic field of normal electron fluid is above the lower critical field but below the upper. The conservation of magnetic flux leads to a geometrical condition in the form of the Weingarten identity which ensures the existence of family of “magnetic world sheetrdquo;. Each “magnetic world sheet” is a magnetic flux conserving surface. In the process of collapse, a compact spacelike cross-section of a magnetic tube terminates into a trapped surface if the magnetic energy grows faster along the fluid flow lines than that along the magnetic field lines.     

Three-dimensional evolution of a relativistic current sheet: triggering of magnetic reconnection by the guide field

The linear and nonlinear evolution of a relativistic current sheet of pair (e(+/-)) plasmas is investigated by three-dimensional particle-in-cell simulations. In a Harris configuration, it is obtained that the magnetic energy is fast dissipated by the relativistic drift kink instability (RDKI). However, when a current-aligned magnetic field (the so-called "guide field") is introduced, the RDKI is stabilized by the magnetic tension force and it separates into two obliquely propagating modes, which we call the relativistic drift-kink-tearing instability. These two waves deform the current sheet so that they trigger relativistic magnetic reconnection at a crossover thinning point. Since relativistic reconnection produces a lot of nonthermal particles, the guide field is of critical importance to study the energetics of a relativistic current sheet.     

Magnetization of High Density Hadronic Fluid

In the present paper the magnetization of a high density relativistic fluid of elementary particles is studied. At very high densities, such as may be found in the interior of a neutron star, when the external magnetic field is gradually increased, the energy of the normal phase of the fluid remains practically constant before extremely high magnetic fields are reached. However, if pion condensation occurs, the energy decreases linearly while the magnetic field strength increases, so that a non vanishing magnetization, independent of the magnetic field, is present. The expression of the magnetization is derived by first considering and solving the Dirac equation of a fermion in interaction with a magnetic field and with a chiral sigma-pion pair. The solution provides the energies of single-particle states. The energy of the system is found by summing up contributions from all particles in the particle fluid. For nuclear densities above 2 to 3ρ ₀, where ρ ₀ is the equilibrium nuclear density, the resulting magnetic field turns out to be rather huge, of the order of 10¹⁷ Gauss.     

On Three Magnetic Relativistic Schr?dinger Operators and Imaginary-Time Path Integrals

Three magnetic relativistic Schr?dinger operators are considered corresponding to the classical relativistic Hamiltonian symbol with magnetic vector and electric scalar potentials. We discuss their difference in general and their coincidence in the case of constant magnetic fields, as well as whether they are covariant under gauge transformation. Then results are surveyed on path integral representations for their respective imaginary-time relativistic Schr?dinger equations, i.e. heat equations, by means of the probability path space measure coming from the Lévy process concerned.     

Self-Focusing and de-Focusing of Intense Left- and Right-Hand Polarized Laser Pulse in Hot Magnetized Plasma in the Presence of an External Non-Uniform Magnetized Field

In this paper, self-focusing of an intense circularly polarized laser beam in the presence of a non-uniform positive guide magnetic field with slope constant parameter δ in hot magnetized plasma, using Maxwell’s equations and relativistic fluid momentum equation is investigated. An envelope equation governing the spot-size of laser beam for both of left- and right-hand polarizations has been derived, and the effects of the plasma temperature and magnetic field on the electron density distribution of hot plasma with respect to variation of normalized laser spot-size has been studied. Numerical results show that self-focusing is better increased in the presence of an external non-uniform magnetic field. Moreover, in plasma density profile, self-focusing of the laser pulse improves in comparison with no non-uniform magnetic field. Also, with increasing slope of constant parameter of the non-uniform magnetic field, the self-focusing increases, and subsequently, the spot-size of laser pulse propagated through the hot magnetized plasma decreases.     

磁单极与磁洛伦兹力

概述了磁单极概念的历史发展,从洛伦兹变换出发,利用电磁场张量和四维力的协变性以及电荷相对论不变,直接证明了运动磁单极受磁洛伦兹力,建议了一个磁洛伦兹力的验证方案,并用磁洛伦兹力公式导出狄拉克电荷量子化条件．证明了磁洛伦兹力公式具有与库仑定律相同的精确度．     

Supersonic Shock Wave with Landau Quantization in a Relativistic Degenerate Plasma

A three-dimensional(3D)BurgersJ equation adopting perturbative methodology is derived to study the evolution of a shock wave with Landau quantized magnetic field in relativistic quantum plasma.The characteristics of a shock wave in such a plasma under the influence of magnetic quantization,relativistic parameter and degenerate electron density are studied with assistance of steady state solution.The magnetic field has a noteworthy control,especially on the shock wave's amplitude in the lower range of the electron density,whereas the amplitude in the higher range of the electron density reduces remarkably.The rate of increase of shock wave potential is much higher(lower)with a magnetic Held in the lower(higher)range of electron density.With the relativistic factor,the shock wave's amplitude increases significantly and the rate of increase is higher(lower)for lower(higher)electron density.The combined effect of the increase of relativistic factor and the magnetic field on the strength of the shock wave,results in the highest value of the wave potential in the lower range of the degenerate electron density.     

Spin-1/2 relativistic particle in a magnetic field in NC phase space

This work provides an accurate study of the spin-l/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle in a magnetic field in noncommutative space has similar behaviour to what happens in the Landau problem in commutative space even if an exact map does not exist. By solving the Dirac equation in NC phase space, we not only obtain the energy level of the spin-1/2 relativistic particle in a magnetic field in NC phase space but also explicitly offer some additional terms related to the momentum-momentum non-commutativity.     

Neutrino beam plasma instability

We derive relativistic fluid set of equations for neutrinos and electrons from relativistic Vlasov equations with Fermi weak interaction force. Using these fluid equations, we obtain a dispersion relation describing neutrino beam plasma instability, which is little different from normal dispersion relation of streaming instability. It contains new, nonelectromagnetic, neutrino-plasma (or electroweak) stable and unstable modes also. The growth of the instability is weak for the highly relativistic neutrino flux, but becomes stronger for weakly relativistic neutrino flux in the case of parameters appropriate to the early universe and supernova explosions. However, this mode is dominant only for the beam velocity greater than 0.25c and in the other limit electroweak unstable mode takes over.     

Calculation of nuclear magnetic shieldings XIV. Relativistic mass—velocity corrected perturbation Hamiltonians

A two-component relativistic SCF perturbation theory, based on the Douglas—Kroll—Hess (DKH) transformation, has been applied to the calculation of nuclear magnetic shielding tensors of hydrogen halides, HX (X = F, Cl, Br, I). Calculations were performed via the unrestricted coupled Hartree—Fock (CHF) scheme using gauge-including atomic orbitals (GIAOs) at four different levels. In the level I calculation, both the scalar relativistic (SR) and spin—orbit (SO) interactions were included in the zero-order Hamiltonian. However, the magnetic pertubation Hamiltonians were treated non-relativistically. The results of these calculations indicated a large interplay between the SR and SO interactions. The level I calculation was found to be insufficient to explain the full relativistic effect on the halogen atom shieldings. In order to reproduce the full relativistic effect, the mass-velocity effect on the magnetic perturbation Hamiltonians was introduced in the levels II—IV calculations. Inclusion of the mass-velocity effects into all of the perturbation Hamiltonians made in levels III and IV improved the results greatly. The cross term between the nuclear attraction potential and the magnetic vector potential was introduced approximately in level IV. The level III calculation agreed most closely with the four-component relativistic random phase approximation (RPA) calculation.     

Hilbert Expansion from the Boltzmann Equation to Relativistic Fluids

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellians. The Maxwellians are constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.     

A class of exact solutions of the cylindrically symmetric Marder’s metric of relativistic magneto-fluid in the Sen-Dunn theory of gravitation

A class of exact solutions is obtained by considering the cylindrically symmetric Marder’s metric for relativistic magneto-fluid or thermodynamical perfect fluid with infinite electric conductivity and constant magnetic permeablity in the Sen-Dunn theory of gravitation. The solutions do not reduce all the components of the Riemann curvature tensor R _hjik to zero. This implies that the cylindrical waves in the Sen-Dunn theory produce real curvature in space. Various physical consequences arising out of the solutions are discussed.     

Spin-1/2 relativistic particle in a magnetic field in NC phase space

This work provides an accurate study of the spin-1/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle in a magnetic field in noncommutative space has similar behaviour to what happens in the Landau problem in commutative space even if an exact map does not exist. By solving the Dirac equation in NC phase space, we not only obtain the energy level of the spin-1/2 relativistic particle in a magnetic field in NC phase space but also explicitly offer some additional terms related to the momentum-momentum non-commutativity.     

Estimation of the Influence of the Magnetic Component on the Transition Rate in a Linearly Polarized Laser Field

We theoretically improved the relativistic ADK formula for a linearly polarized laser field. We have taken into account the influence of the magnetic component of laser field on the transition rate, in near relativistic field intensity. It was shown that the magnetic component results in a decrease of the transition rate in comparison to the results obtained by the original relativistic expression. We gave considered noble and alkali atoms. The obtained results show that this influence is larger (more significant) for alkali atoms.     

拉曼型自由电子激光器中相对论电子运动稳定性的比较研究

拉曼型自由电子激光器作为一种兆瓦级高功率毫米波、太赫兹波辐射源, 其电子的运动稳定性对整体器件的性能至关重要.本文采用科尔莫戈罗夫熵方法, 以典型的麻省理工学院公布的实验数据为例, 比较研究拉曼型正向导引磁场和反向导引磁场两类自由电子激光器中相对论电子的运动稳定性. 结果表明:摇摆器绝热压缩磁场对电子运动的稳定性无实质性影响, 但对电子运动影响大; 电子束自身场在拉曼型正向导引磁场自由电子激光器中使电子运动稳定性变差, 而在拉曼型反向导引磁场自由电子激光器中则可改善电子运动稳定性. 关键词： 拉曼型自由电子激光器 相对论电子运动稳定性 科尔莫戈罗夫熵 电子束自身场