Velocity-dependent KAM islands

We revisit the non-dissipative time-dependent annular billiard and we consider the chaotic dynamics in two planes of conjugate variables in order to describe the behavior of the growth, or saturation, of the mean velocity of an ensemble of particles. We observed that the changes in the 4-d phase space occur without changing any parameter. They occur depending on where the initial conditions start. The emerging KAM islands interfere in the behavior of the particle dynamics especially in the Fermi acceleration mechanism. We show that Fermi acceleration can be suppressed, without dissipation, even considering the non-dissipative energy context.     

Kinetic Equation for Quantum Fermi Gases and the Analytic Solution of Boundary Value Problems

We construct a kinetic equation describing the behavior of quantum Fermi gases with the molecule collision frequency proportional to the molecule velocity. We obtain an analytic solution of the generalized Smoluchowski problem with the temperature gradient and the mass flow velocity specified away from the surface. We find exact formulas for jumps of the gas temperature, concentration, and chemical potential. Analysis of limit cases demonstrates a transition of the quantum Fermi gas to the classical or degenerate gas.     

Temperature Green’s functions in Fermi systems: The superconducting phase transition

We consider the model of an equilibrium Fermi system of arbitrary-spin particles with the density-densitytype interaction. Based on the microscopic Hamiltonian in the formalism of temperature Green’s functions, we find critical modes and construct an effective action describing a neighborhood of the phase transition point. A renormalization group analysis of the obtained model leads to the standard critical behavior indices for spin-1/2 fermions but shows that in the system of higher-spin fermions, a first-order phase transition occurs whose temperature exceeds the standard estimates for the temperature of a second-order phase transition.     

Envelope Solitary Waves and Periodic Waves in the AB Equations

This article deals with the envelope solitary waves and periodic waves in the AB equations that serve as model equations describing marginally unstable baroclinic wave packets in geophysical fluids and also ultra‐short pulses in nonlinear optics. An envelope solitary wave has a width proportional to its velocity and inversely proportional to its amplitude. The velocity of the envelope solitary wave is partially dependent on its amplitude in the sense that the amplitude determines the upper or lower limit of the velocity. When two envelope solitary waves collide, they survive the collision and retain their identities except for a shift in the positions of both the envelopes and the carrier waves. The periodic wave solutions in sine wave form may be stable or unstable depending upon the wave parameters. When the sine wave is destabilized by small perturbations, its long‐time evolution shows a Fermi–Pasta–Ulam‐type oscillation.     

Marginal Fermi Liquid Behaviour in the d = 2 Hubbard Model with Cut-Off

We consider the half-filled Hubbard model with a cut-off forbidding momenta close to the angles of the square shaped Fermi surface. By renormalization group methods we find a convergent expansion for the Schwinger function up to exponentially small temperatures. We prove that the system is not a Fermi liquid, but on the contrary it behaves like a Marginal Fermi liquid, a behaviour observed in the normal phase of high T_c superconductors.     

Fermi Coordinates, Simultaneity, and Expanding Space in Robertson�CWalker Cosmologies

Explicit Fermi coordinates are given for geodesic observers comoving with the Hubble flow in expanding Robertson–Walker space–times, along with exact expressions for the metric tensors in Fermi coordinates. For the case of non-inflationary cosmologies, it is shown that Fermi coordinate charts are global, and space–time is foliated by space slices of constant Fermi (proper) time that have finite extent. A universal upper bound for the proper radius of any leaf of the foliation, i.e., for the proper radius of the spatial universe at any fixed time of the geodesic observer, is given. A general expression is derived for the geometrically defined Fermi relative velocity of a test particle (e.g., a galaxy cluster) comoving with the Hubble flow away from the observer. Least upper bounds of superluminal recessional Fermi velocities are given for space–times whose scale factors follow power laws, including matter-dominated and radiation-dominated cosmologies. Exact expressions for the proper radius of any leaf of the foliation for this same class of space–times are given. It is shown that the radii increase linearly with proper time of the observer moving with the Hubble flow. These results are applied to particular cosmological models.     

Superconductive states in the two-dimensional repulsive Hubbard model

The investigation of the two-dimensional repulsive Hubbard model is continued for the case in which the Fermi level is close to one of the saddle Van Hove points of the quasiparticle energy function. The Bethe-Salpeter equation for the two-particle scattering amplitude and the system of Dyson-Gor'kov equations for normal and anomalous Green functions are considered. The closeness of the Van Hove point to the Fermi level makes the investigation substantially simpler. A new method of evaluating the kernel of the equations, i.e., the oneloop polarization diagram, is suggested. It is shown that a nontrivial Cooper pairing (the superposition of the pairings with odd angular momenta) appears in the model if and only if the Fermi level is close to one of the Van Hove points. The temperature of the superconductive phase transition is maximal for some special mutual location of the Fermi level and the Van Hove point. Two different superconductive solutions (modes) are found which are antisymmetric functions in the momentum representation. These modes coexist in close vicinity of the doping parameter value corresponding to the intersection of the Van Hove point and the Fermi level. The values of the energy gap for these modes are, generally speaking, different (the two different gap values are observed in some experiments). Bibliography: 18 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 199, 1992, pp. 147–176. Translated by V. N. Popov.     

夹层圆柱壳在移动内压作用下的临界速度研究

基于夹层壳理论和三维弹性动力学理论,研究了无限长夹层圆柱壳在移动内压作用下的临界速度．首先,基于夹层壳理论,考虑夹芯的压缩和剪切变形以及面板的剪切变形,研究了轴对称简谐波在无限长夹层圆柱壳中的传播问题;其次,基于三维弹性动力学理论,将位移变量用Legendre正交多项式系表示,同时引入位置相关函数,将求解导波问题化为简单的特征值问题．利用这两种方法得到了最低模态的频散曲线,最小相速便是内压移动的临界速度．最后,用算例和数值模拟来验证方法的有效性．结果表明,两种理论得到临界速度吻合得较好;当波数较小时,两种理论得到的频散曲线吻合得很好,当k→∞时,夹层壳理论和弹性动力学理论得到的极限相速分别趋于面板和夹芯的剪切波波速．波数较小时,两种理论分析夹层圆柱壳的导波问题是有效的．数值模拟预测的临界速度与理论分析的结果吻合得很好．     

一类Fermi气体光晶格非线性机制的轨线研究

研究了一类Fermi气体光晶格轨线的非线性扰动模型.首先求得了Fermi气体光晶格在无扰动情形下模型轨线的精确解.然后引入一组广义泛函分析同伦映射,构造一组迭代系统,得到了Fermi气体光晶格非线性扰动模型轨线的任意次渐近解.最后讨论了一个微扰系统.该文在方法上可较方便地得到轨线的渐近表示式.     

Anomalous Behavior in an Effective Model of Graphene with Coulomb Interactions

We analyze by exact Renormalization Group (RG) methods the infrared properties of an effective model of graphene, in which two-dimensional (2D) massless Dirac fermions propagating with a velocity smaller than the speed of light interact with a 3D quantum electromagnetic field. The fermionic correlation functions are written as series in the running coupling constants, with finite coefficients that admit explicit bounds at all orders. The implementation of Ward Identities in the RG scheme implies that the effective charges tend to a line of fixed points. At small momenta, the quasi-particle weight tends to zero and the effective Fermi velocity tends to a finite value. These limits are approached with a power law behavior characterized by non-universal critical exponents.     

Boundary Problems for a Quantum Fermi Gas

We derive a relaxation kinetic equation describing the behavior of Fermi gases. We consider the Kramers problem for the isothermal slipping in a half-space and obtain an analytic solution of the problem and the explicit form of the distribution function for particles moving toward the wall. We analyze the dependence of the equation itself and the slipping velocity on the parameter, the ratio between the chemical potential and the product of the Boltzmann constant and the absolute temperature.     

Free convection effects on the oscillatory flow of an incompressible viscous fluid past an infinite,vertical plate with variable suction

An analysis of a two-dimensional flow of an incompressible, viscous fluid past an infinite, vertical porous plate has been carried out under the following conditions: (i) the suction velocity normal to the plate varies periodically with time (ii) the free stream velocity oscillates in time about a constant mean (iii) the temperature difference between the constant plate temperature and the free stream temperature, causing the free convection currents in the boundary layer. Approximate solutions for the transient velocity, the transient temperature, the amplitude and the phase of the skin-friction and the rate of heat transfer are derived. The fluctuating parts of the velocity profiles, the transient velocity, the transient temperature are shown on graphs whereas the numerical values of the amplitude and the phase of the skin-friction and the rate of heat transfer are entered in tables. The results are discussed in a quantitative way.     

Modelling of an Homogeneous Equilibrium Mixture Model (HEM)

We present here a model for two phase flows which is simpler than the 6-equations models (with two densities, two velocities, two temperatures) but more accurate than the standard mixture models with 4 equations (with two densities, one velocity and one temperature). We are interested in the case when the two-phases have been interacting long enough for the drag force to be small but still not negligible. The so-called Homogeneous Equilibrium Mixture Model (HEM) that we present is dealing with both mixture and relative quantities, allowing in particular to follow both a mixture velocity and a relative velocity. This relative velocity is not tracked by a conservation law but by a closure law (drift relation), whose expression is related to the drag force terms of the two-phase flow. After the derivation of the model, a stability analysis and numerical experiments are presented.     

Homogenization and Hydrodynamic Limit for Fermi‐Dirac Statistics Coupled to a Poisson Equation

This paper deals with the diffusion approximation of a Boltzmann‐Poisson system modeling Fermi‐Dirac statistics in the presence of an extra external oscillating electrostatic potential. Here we extend the analysis done in [19] to the case of a nonlinear collision operator. In addition to the averaging lemma and control from entropy dissipation used in [19], here we use two‐scale Young measures and renormalization techniques to prove the convergence. This result rigorously justifies the formal analysis of [3]. © 2015 Wiley Periodicals, Inc.     

Nonlinear vibration and stability analysis of the curved microtube conveying fluid as a model of the micro coriolis flowmeters based on strain gradient theory

Micro coriolis flowmeters are extensively used in fluidic micro circuits and are of great interest to many researchers. Straight and curved coriolis flowmeters are common types of coriolis flowmeters. Therefore in the present work, the out-of- plane vibration and stability of curved micro tubes are investigated to study the dynamic behavior of curved coriolis flowmeters. The Hamilton principle is applied to derive a novel governing equation based on strain gradient theory for the curved micro tube conveying fluid. Lagrangian nonlinear strain is adopted to take into account the geometric nonlinearity and analyze hardening behavior as a result of the cubic nonlinear terms. Linear stability analysis is carried out to investigate the possibility of linear instabilities. Afterwards, the first nonlinear out-of-plane natural frequency is plotted versus fluid velocity to determine the influence of nonlinear terms and hardening behavior on stability of the system. The influence of the length scale parameter is studied by comparison of the results for classical, coupled stress and strain gradient theory. Finally the phase difference between two points at upstream and downstream is plotted versus fluid velocity. Linear relation between the phase difference and fluid velocity is noticed, thus the curved coriolis flowmeter can be calibrated to measure flow rate by measuring the phase difference between two points.     

Fermi Liquid Behavior in the 2D Hubbard Model at Low Temperatures

We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations. Communicated by Vincent Rivasseau Submitted: January 4, 2006 Accepted: January 31, 2006     

Adiabatic charge transport and the Kubo formula for Landau‐type Hamiltonians

The adiabatic charge transport is investigated in a two‐dimensional Landau model perturbed by a bounded potential at zero temperature. We show that if the Fermi level lies in a spectral gap, then in the adiabatic limit the accumulated excess Hall charge is given by the linear response Kubo‐?treda formula. The proof relies on the expansion of Nenciu, some generalized phase space estimates, and a bound on the speed of propagation. © 2004 Wiley Periodicals, Inc.     

Coexistence of superconductivity and antiferromagnetism in heavy-fermion intermetallides

Using the two-time retarded Green’s function, we study the conditions for realizing the phase of the superconductivity and antiferromagnetism coexistence in the framework of the effective Hamiltonian for the periodic Anderson model. Such a phase was experimentally observed in rare-earth intermetallides with heavy fermions under an external pressure. In the chosen model, the Cooper instability is induced in the presence of long-range antiferromagnetic ordering as a result of the combined effect of a superexchange interaction in the subsystem of localized electrons and the hybridization between two groups of electrons. Applying an external pressure induces an increase in the energy of the localized level accompanied by an abrupt destruction of the long-range antiferromagnetic ordering in a certain region of the phase diagram. The superconductivity order parameter has a maximum value at the destruction point. We show that the decrease in the antiferromagnetic-sublattice magnetization with increasing pressure leads to a significant increase in the masses of Fermi quasiparticles, and the sign of the current carriers reverses at the critical point. The obtained results qualitatively agree well with the experimental data for the heavy-fermion intermetallide CeRhIn ₅ .     

Turbulent Energy Spectrum via an Interaction Potential

For a large system of identical particles interacting by means of a potential, we find that a strong large scale flow velocity can induce motions in the inertial range via the potential coupling. This forcing lies in special bundles in the Fourier space, which are formed by pairs of particles. These bundles are not present in the Boltzmann, Euler and Navier–Stokes equations, because they are destroyed by the Bogoliubov–Born–Green–Kirkwood–Yvon formalism. However, measurements of the flow can detect certain bulk effects shared across these bundles, such as the power scaling of the kinetic energy. We estimate the scaling effects produced by two types of potentials: the Thomas–Fermi interatomic potential (as well as its variations, such as the Ziegler–Biersack–Littmark potential), and the electrostatic potential. In the near-viscous inertial range, our estimates yield the inverse five-thirds power decay of the kinetic energy for both the Thomas–Fermi and electrostatic potentials. The electrostatic potential is also predicted to produce the inverse cubic power scaling of the kinetic energy at large inertial scales. Standard laboratory experiments confirm the scaling estimates for both the Thomas–Fermi and electrostatic potentials at near-viscous scales. Surprisingly, the observed kinetic energy spectrum in the Earth atmosphere at large scales behaves as if induced by the electrostatic potential. Given that the Earth atmosphere is not electrostatically neutral, we cautiously suggest a hypothesis that the atmospheric kinetic energy spectra in the inertial range are indeed driven by the large scale flow via the electrostatic potential coupling.