RF oscillation generated by an electromagnetic shock wave in coupled transmission lines with anomalous and normal dispersion

The generation of rf oscillation when an electromagnetic shock runs in synchronism with a backward wave in coupled transmission lines with normal and anomalous dispersions and ferrite-related nonlinearity is considered. The oscillation damping can be significantly reduced if a large portion of the rf energy flux is directed to the anomalous-dispersion line, where rf losses are relatively low.     

Role of spin-flip transitions in the anomalous Hall effect of FePt alloy

We carry out ab?initio calculations which demonstrate the importance of the non-spin-conserving part of the spin-orbit interaction for the intrinsic anomalous Hall conductivity of ordered FePt alloys. The impact of this interaction is strongly reduced if Pt is replaced by the lighter isoelectronic element Pd. An analysis of the interband transitions responsible for the anomalous velocity reveals that spin-flip transitions occur not only at avoided band crossings near the Fermi level, but also between well-separated pairs of bands with similar dispersions. We also predict a strong anisotropy in the anomalous Hall conductivity of FePt caused entirely by low-frequency spin-flip transitions.     

Limit Theorems in the Stadium Billiard

We prove that the Birkhoff sums for ``almost every' relevant observable in the stadium billiard obey a non-standard limit law. More precisely, the usual central limit theorem holds for an observable if and only if its integral along a one-codimensional invariant set vanishes, otherwise a normalization is needed. As one of the two key steps in the argument, we obtain a limit theorem that holds in Young towers with exponential return time statistics in general, an abstract result that seems to be applicable to many other situations.     

Are the anomalons colored?

The local color symmetry of QCD is broken spontaneously to SU(2) × U(1) and it is assumed that only SU(2) × U(1) singlets are observable. This implies that in addition to the normal color singlet hadrons also long-lived, colored, integrally charged particles with large masses and cross sections are observable. The theory is applied to explain the anomalous nuclear effects found in heavy ion collisions by Judek et al.     

不同零色散点光子晶体光纤的超连续谱产生

本文实验研究了飞秒脉冲在不同零色散点光子晶体光纤中传输时产生超连续谱的现象。首先,我们通过非线性薛定谔方程理论计算了激光脉冲分别在正、负色散光子晶体光纤中传输时产生的超连续谱;计算结果表明在正色散光子晶体光纤产生的超连续谱远远大于在负色散中产生的超连续谱。其次,在实验上采用零色散点分别为800 nm、1 060 nm和2 000 nm的光子晶体光纤,将脉宽为130 fs,中心波长800 nm,脉冲重复频率为80 MHz的脉冲输入这些光纤中产生超连续谱并研究其特性,实验结果表明光子晶体光纤的零色散点越小,在其中产生的超连续谱越宽越平坦。同时产生的超连续谱也与激光脉冲的能量和中心波长相关。     

Apparent anomalous fading of thermoluminescence associated with competition with radiationless transitions

Anomalous fading of thermoluminescence (TL) is the effect of a fading which is significantly faster than what is warranted by the trapping parameters which are evaluated from the features of the TL peak in question. A previous work suggested that in certain cases, apparent anomalous fading may be a normal fading in disguise. The idea was that, at least in some cases, radiationless transitions into competing recombination centers may yield a very narrow peak which, while using either the curve fit technique or the different peak shape method will result in very high values of effective activation energy E and frequency factor s which, in turn, will yield an apparent life-time orders of magnitude higher than the real one. The question has been raised whether this anomaly is observable only when the peak shape methods are utilized and in particular, can the same effect occur when the broadly used initial-rise method is applied. It is demonstrated in this work that under similar circumstances of competition, very high effective values of E and s are evaluated which result in very high life-times when the activation energy is evaluated by the initial-rise method. Thus, the explanation of apparent anomalous fading as being a normal decay in disguise, is extended to cases in which the initial-rise method is utilized for the parameter evaluation.     

Optical bistability and temporal symmetry-breaking instability in nonlinear fiber resonators

In this work we analyze two different behaviors in a nonlinear passive fiber ring cavity with a synchronously pulsed pump iterating the infinite-dimensional Ikeda map. First, we show optical bistability with normal and anomalous dispersions. The obtained numerical results are compared with the cw pump case. Secondly, these cavities are subject to a temporal symmetry-breaking instability with anomalous dispersion. This instability is described and the range of parameters for its appearance is shown and discussed.     

Bell’s theory with no locality assumption

We prove versions of the Bell and the GHZ theorems that do not assume locality but only the effect after cause principle (EACP) according to which for any Lorentz observer the value of an observable cannot change because of an event that happens after the observable is measured. We show that the EACP is strictly weaker than locality. As a consequence of our results, locality cannot be considered as the common cause of the contradictions obtained in all versions of Bell’s theory. All versions of Bell’s theorem assume weak realism according to which the value of an observable is well defined whenever the measurement could be made and some measurement is made. As a consequence of our results, weak realism becomes the only hypothesis common to the contradictions obtained in all versions of Bell’s theory. Usually, one avoids these contradictions by assuming non-locality; this would not help in our case since we do not assume locality. This work indicates that it is weak realism, not locality, that needs to be negated to avoid contradictions in microscopic physics, at least if one refuses as false the de Broglie-Bohm hidden variable theory because of its essential violation of Lorentz invariance.     

Acceleration transforms and statistical kinetic models

For a restricted class of problems a mathematical model of microscopic degradation processes, statistical kinetics, is developed and linked throughacceleration transforms to the information which can be obtained from a system in which the only observable sign of degradation is sudden and catastrophic failure. The acceleration transforms were developed in accelerated life testing applications as a tool for extrapolating from the observable results of an accelerated life test to the dynamics of the underlying degradation processes. A particular concern of a physicist attempting to interpreted the results of an analysis based on acceleration transforms is determining the physical species involved in the degradation process. These species may be (a) relatively abundant or (b) relatively rare. The main results of this paper are a theorem showing that for an important subclass of statistical kinetic models, acceleration transforms cannot be used to distinguish between cases a and b, and an example showing that in some cases falling outside the restrictions of the theorem, cases a and b can be distinguished by their acceleration transforms.     

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.     

Self-action dynamics of ultrashort electromagnetic pulses

The self-action dynamics of three-dimensional wave packets whose width is on the order of the carrier frequency is studied under fairly general assumptions concerning the dispersion properties of the medium. The condition for the wave field collapse is determined. Self-action regimes in a dispersion-free medium and in media with predominance of anomalous or normal group velocity dispersions are numerically investigated. It is shown that, for extremely short pulses, nonlinearity leads not only to the self-compression of the wave field but also to a “turn-over” of the longitudinal profile. In a dispersionless medium, the formation of a shock front within the pulse leads to the nonlinear dissipation of linearly polarized radiation and to self-focusing stabilization. For circularly polarized radiation, the wave collapse is accompanied by the formation of an envelope shock wave.     

The inverse problem based on a full dispersive wave equation

The inverse problem for harmonic waves and wave packets was studied based on a full dispersive wave equation.First,a full dispersive wave equation which describes wave propagation in nondissipative microstructured linear solids is established based on the Mindlin theory,and the dispersion characteristics are discussed.Second,based on the full dispersive wave equation,an inverse problem for determining the four unknown coefficients of wave equation is posed in terms of the frequencies and corresponding wave numbers of four different harmonic waves,and the inverse problem is demonstrated with rigorous mathematical theory. Research proves that the coefficients of wave equation related to material properties can be uniquely determined in cases of normal and anomalous dispersions by measuring the frequencies and corresponding wave numbers of four different harmonic waves which propagate in a nondissipative microstructured linear solids.     

一种全频散波方程的反问题

基于一种全频散波方程研究了对于谐波和波包的反问题。首先根据Mindlin理论建立了描述无耗散微结构线性固体中波传播模型一一一种全频散波方程,并讨论了其频散特性。然后基于该全频散波方程,提出了利用四种不同谐波的频率和相应波数确定波方程四个未知系数的反问题,并用严格的数学理论论证了此反问题。研究证明,通过测量同一种无耗散微结构线性固体中传播的四种不同谐波的频率和相应波数,在正常频散和反常频散情况下可唯一地确定波方程的未知系数,即材料的未知参数。      

On the Generalized Ornstein–Ulenbeck Process

The model generalized Ornstein–Ulenbeck process is developed on the basis of the anomalous-diffusion nature of random walk. Asymptotics of the basic statistical characteristics of this process are found. It is shown that the asymptotics are governed by the classical or anomalous diffusion laws if the central limit theorem is fulfilled or violated, respectively.     

Biased diffusion in a piecewise linear random potential

We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second moments of the particle position as inverse Laplace transforms. By applying to these transforms the ordinary and the modified Tauberian theorem, we determine the short- and long-time behavior of the mean-square displacement of particles. Our results show that while at short times the biased diffusion is always ballistic, at long times it can be either normal or anomalous. We formulate the conditions for normal and anomalous behavior and derive the laws of biased diffusion in both these cases.     

Van der Waerden continuity theorem for semisimple lie groups

As was proved by van der Waerden in 1933, every finite-dimensional locally bounded representation of a semisimple compact Lie group is continuous. This is the famous “van der Waerden continuity theorem,” and it motivated a vast literature. In particular, relationships between the assertion of the theorem (and of the inverse, in a sense, to this theorem) and some properties of the Bohr compactifications of topological groups were established, which led to the introduction and the study of certain classes of the so-called van der Waerden groups and algebras. Until now, after more than 70 years have passed, the van der Waerden theorem appears in monographs and surveys in diverse forms; new proofs were found and then simplified in important special cases. In this paper, we prove that the statement of the van der Waerden theorem remains valid for all (not necessarily compact) real semisimple Lie groups, i.e., any given finite-dimensional representation of a real semisimple Lie group is continuous if and only if this representation is locally bounded. More subtle results are also obtained. The main theorem contains several conditions equivalent to the continuity condition for a finite-dimensional representation. In particular, it is proved that every finite-dimensional representation of a real semisimple Lie group is continuous if and only if the restriction of this representation to the “compact” part, to the Abelian part, or to the nilpotent part of the Iwasawa decomposition is locally bounded, and the original van der Waerden theorem is also somewhat refined. For instance, the following assertion holds: every finite-dimensional representation of a compact semisimple Lie group is continuous if and only if the restriction of this representation to some maximal torus is locally bounded. Dedicated to the memory of George Mackey (1916–2006) Partially supported by the Russian Foundation for Basic Research under grant no. 02-01-00574, by the Program of Supporting the Leading Scientific Schools under grant no. NSh 619.203.1, and by the INTAS grant.     

Detection of gravitational waves by electromagnetic radiation

A statistical theory of the ionization — recombination equilibrium of a non-degenerate plasma in a homogeneous magnetic field is given. It is shown that the magnetic field changes the reactive composition if the quanta of the oscillatory electron motion in the magnetic field — which corresponds classically to the electron gyration — are of the order of or larger than the thermal energy,?ω?kT. The ionization may be enhanced or depressed depending on whether the background gas of the plasma is diamagnetic or paramagnetic. Some low temperature experiments, where such an anomalous “magnetic ionization” might be observable, are discussed briefly.