Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: _k (-gg ^0k )=0 and _ik ⁰ _0g ^ik - _ik ^k _0g ⁰ⁱ =0. In aT-orthogonal metricgs ²=g ₀₀ dt ² -g dx dx these conditions take a simple form: ₀(detg )=0 and (₀ g )(₀ g )=0.     

Anomalous diffusion in a random velocity field

We construct diffusions in random velocity fields which present anomalous superdiffusive behavior. The mean square displacement can be made to have any power lawt for 1<2. Higher moments and characteristic functions are also investigated.     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.     

Cosmological Dynamics of the Tachyon with an Inverse Power-Law Potential

We investigate tachyon dynamics with an inverse power-law potential V () ^–. We find global attractors of the dynamics leading to a dust behavior for > 2 and to an accellerating universe for 0 < 2. We study linear cosmological perturbations and we show that metric fluctuations are constant on large scales in both cases. In the presence of an additional perfect fluid, the tachyon with this potential behaves as dust or dark energy.     

Renormalization of the fine structure constant at high energies

Continuing the discussion in [1], the renormalization of the fine-structure constant in the high-energy range, where a logarithmic increase in the constant is observed, is considered. It is shown that within the framework of the quantum electrodynamics of bilocal fields, when the energy increases the logarithmic "form" ln² of the constant changes into a power drop 1/². Hence, problems with the "Moscow zero" do not arise in this theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–12, January, 1996.     

The Sine-Gordon field theory model at α2=8π, the non-superrenormalizable theory

We study the Sine-Gordon field theory at ²=8. We prove that the theory is renormalizable but not superrenormalizable and we show how the perturbative renormalization procedure works in this case where the interaction is not polynomial. To go beyond the perturbative results we investigate the -functional equation for this theory and discuss in what sense at ²=8 the theory is lacking the asymptotic freedom and how it is asymptotic free for ²<8 in a appropriate region of the coupling constants.     

Light absorption by free semiconductor carriers in the presence of a laser wave

Within the framework of the conditions ; » ^–1 ( ^–1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency _o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < _o, including the jump () for ( – _o + ) ₀T as well as peaks in the function () at the points _s=s (s=1, 2, 3,...). The value (₁) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й СДВИГА ПЬЕЗОЭЛЕКТРИЧЕСКИХ СТЕРЖНЕЙ

n - , - .     

Solution of coupled differential equations of soliton theory

We present the complete set of solutions of the coupled differential equations of the form ()²=(), ² =(). Equations of this form appear in several physical situations.     

Some exact solutions to the sine-Gordon equations

We present some new exact (solitary and traveling) solutions to the sine-Gordon equationsc ²u_xx–u_tt = sinu andcu _xt+ u_tt = sinu, and the dissipative sine-Gordon equationc ²u_xx–u_tt–u_t=₁ sinu+ ₂ sin(2u). Here,, ₁, and ₂ are the coupling constants, real numbers;c is theintrinsic speed of the propagating wave determined by the system; and is the damping factor. The physical implication is briefly discussed.     

Disentangling q-Exponentials: A General Approach

We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson q-exponential of the sum of two non-q-commuting operators as an (in general) infinite product of q-exponential operators involving repeated q-commutators of increasing order, E_q(A+B) = E_q0(A)E_q1 (B) _i=2 E_qi. By systematically transforming the q-exponentials into exponentials of series and using the conventional Baker–Campbell–Hausdorff formula, we prove that one can make any choice for the bases ^qi, i=0, 1, 2, ..., of the q-exponentials in the infinite product. An explicit calculation of the operators C _i in the successive factors, carried out up to sixth order, also shows that the simplest q-Zassenhaus formula is obtained for ₀ = ₁ =1, and ₂ = 2, and ₃ = 3. This confirms and reinforces a result of Sridhar and Jagannathan, on the basis of fourth-order calculations.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Das Anhaften von Exzitonen an Störstellen des Kristallgitters

Zusammenfassung Es wird der Proze des Anhaftens von Exzitonen an Vakanzen und F-Zentren in den Ionenkristallen studiert. Die Bewegung der Exzitonen im Felde der Vakanz und des F-Zentrums wird in adiabatischer Annäherung untersucht. Mit Hilfe der klassischen Methoden werden die Wirkungsquerschnitte des Anhaftens des Exzitons an den Vakanzen und F-Zentren bestimmt und diskutiert.

---

F- . F- . F- .

     

Bunching phenomena during electron injection into the betatron II. Theory of starting conditions

A theory of the azimuthal bunching of electrons injected into the betatron is presented and compared with the experiments described in [1]. The bunching is treated as a small perturbation of the stationary beam.The stationary injected beam is replaced by the corresponding equilibrium beam of the same perveance so that the angular velocity spread of the injected electrons is proportional to the square root of the injection perveance.Self-consistent wave solutions for the perturbation of the stationary solution are then found. Equations giving the amplification of small density or energy disturbances along the beam are derived. These disturbances are assumed to be introduced by density or velocity modulation of the injected beam. The condition for the spontaneous occurrence of bunching is deduced by assuming that the disturbances do not vanish even when there is no modulation of the injected beam. The resulting expressions for the threshold perveance and the rise-time of the disturbance are in reasonably good agreement with the experiments. Such agreement may be considered as further verification of the statement made in [1] that the amplification of the disturbances is caused by the negative mass instability mechanism.

---

, .

, . , [1]. . . , , . . , ., . , , . . , , [1].

     

Radiative and nonradiative transitions to an unstable state

In this paper an expression is obtained, which enables us to treat radiative and nonradiative transitions in complex molecular systems, when the final state is unstable. Expressions are give for the matrix elements E/v and E|d/dR|v , where the stable state is described by a solution with a Morse potential, and the unstable state by a solution with a Hulthen potential. The possibility of the concrete realization of such transitions is discussed in the example of excimers.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 70–75, October, 1974.     

The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

---

. . . , , .

---

---

The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

---

In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.     

Multifractal Power Law Distributions: Negative and Critical Dimensions and Other “Anomalies,” Explained by a Simple Example

Divergence of high moments and dimension of the carrier is the subtitle of Mandelbrot's 1974 seed paper on random multifractals. The key words divergence and dimension met very different fates. Dimension expanded into a multifractal formalism based on an exponent and a function f(). An excellent exposition in Halsey et al. 1986 helped this formalism flourish. But it does not allow divergent high moments and the related inequalities f()<0 and <0. As a result, those possibilities did not flourish. Now their time has come for diverse reasons. The broad 1974 definitions of and f allow <0 and f()<0, but the original presentation demanded to be both developed and simplified. This paper shows that both multifractal anomalies occur in a very simple example, which has been crafted for this purpose. This example predicts the power law distribution. It generalizes and f() beyond their usual roles of being a Hölder exponent and a Hausdorff dimension. The effect is to allow either f or both f and to be negative, and the apparent anomalies are made into sources of new important information. In addition, this paper substantially clarifies the subtle way in which randomness manifests itself in multifractals.     

A model of Piron's preparation-question structures in Ludwig's selection structures

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of preparation-question structure (with four basic axioms and without axioms C, P, A), in terms of Ludwig's selection structure; in the latter structure the primitive notion of individual sample of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of question in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as performable together questions; moreover, results such as = or ()= can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.     

Phase transformations in Cu-Sn alloys containing Ni,Al, Ge,and In

After quenching from 700C and aging, Cu-Sn alloys containing Ni and Al were found to have a precipitation of-solid solution, with a DO₃ type of ordering, of metastable ,, and phases. It was established that the phase has an 4 type of ordering while the phase has the Cu₃Ti type. Observations revealed that Cu-Sn-Al alloys contained two phases, and, with an identical structure but with different ratios of electron concentration per atom.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 34–37, April, 1981.