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1.
Four classes of solutions are found to the equations R=–2; ; and g ;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations Rij=0 in a vacuum for the metric . The metric ds2 assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.  相似文献   

2.
Let t be an analytic solution of the Schrödinger equation with the initial condition . Let t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then t (x) t (x)1 ( t (x)), where t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.  相似文献   

3.
The sticking process dt + n, which constitutes the most severe limit to the number of fusions which a muon can catalyze, is reviewed. Many attempts were made to determine by calculations and measurements the probability for initial sticking s 0 (immediately after dt fusion) and for final sticking s (after the came to rest). Previous results based on neutron disappearance rates and on the observation of -X-rays were controversial and also in some disagreement with theory. New data are reported from PSI on direct observation of final sticking, using a setup with the St. Petersburg ionization chamber. These data mark a significant improvement in reliability and may clarify questions concerning previous discrepancies. The new results is s(0.56±0.04)%, lower than the theory prediction s=(0.65±0.03)%, at medium density.  相似文献   

4.
A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, 3 + (for d), 4 , and 2m 2m+2 (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.  相似文献   

5.
6.
Different models of luminescence centres are discussed on the basis of measurements of the composition of ZnS monocrystal photo-luminescence in different polarizations and temperature dependence of the degree of polarization. Those of the models submitted by Birman, which assume the polarization to be due to the different force of the oscillators for transitions withEc andEc, or models assuming luminescence polarization to be due to the orientation of the luminescence centres, agree with the results of experiments, i.e. the temperature independence of the degree of polarization and the conformable spectral composition of both polarizations. It is also shown that measurements made up to now of the degree of polarization must be taken as orientational as a consequence of the depolarizing influence of the diffused rays of luminescence on its value.
ZnS: Cu
ZnS , . , . . , , , E E, , . , , - .
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7.
Letw = {w(x)xZd} be a positive random field with i.i.d. distribution. Given its realization, letX t be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w–1(Xt). The processX={X t:t0} combined withw on a common probability space is an example of random walk in random environment. We consider the quantities t =(d/dt) E (X t 2M –1 t and t(w) = (d/dt)Ew(X t 2 – M 1t). Here Ew. is expectation overX at fixedw and E = Ew (dw) is the expectation over bothX andw. We prove the following long-time tail results: (1) limt td/2t= V2Md/2–3(d/2)d/2 and (2) limt td/4 st(w)= Zs weakly in path space, with {Zs:s>0} the Gaussian process with EZs=0 and EZrZs= V2Md/2–4(d)d/2 (r + s)–d/2. HereM and V2 are the mean and variance of w(0) under . The main surprise is that fixingw changes the power of the long-time tail fromd/2 tod/4. Since , with 0 the stationary measure for the environment process, our result (1) exhibits a long-time tail in an equilibrium autocorrelation function.  相似文献   

8.
We use a quite concrete and simple realization of sl q (2, ) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the noncommutative scheme 1 II 1* as the counterpart of the standard 1 = Sl(2, )/B.  相似文献   

9.
The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:() c as c and ()( c)–1 as c, where () and () are the spread probability and the susceptibility of the infection respectively, and c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.  相似文献   

10.
It is shown that by solving the linear integral Agranovi-Marenko equation for potentials-scattering one can obtain: 1) in the simplest case, when the scattering matrixS has one redundant pole in the upper half-plane of the impulse, the Bargmann potentials; 2) if theS-matrix hasn redundant poles — the equations, which Petras derived fors-scattering using an adapted and simplified Bargmann method; 3) if theS-matrix is discontinuous on a certain interval — the non-relativistic Noyes-Wong equation and 4) further relations — for combinations of isolated poles and discontinuities of theS-matrix on intervals. The former equations can be obtained from the latter as specific cases. In the discussion, the relation between the value of the residuum of theS-matrix in the redundant poles and the number of bound states is shown and the solution of the inverse problem for a band spectrum is sketched.
, - s-, : 1) , S — . 2) , S-n — , , s-. 3) S- — . 4) — S- . . S- .
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11.
The dynamics of ann-component vector spin glass with infinite range interactions are investigated near and above the Gabay-Toulouse (GT) line. The local transverse susceptibility T for 0 varies along the whole GT lineT c1 (H) as v , with a field and temperature independent critical exponentv=1/2. The longitudinal susceptibility L () remains analytic for all (T, H)T c1 (H), except for a cross-over fromv=1 tov=1/2 forH0 at the freezing temperatureT=T f . The dynamic susceptibilities T () and L () are already coupled above the GT line via self-energy terms. BelowT c1 (H), this coupling is strongly enhanced by other mechanisms.  相似文献   

12.
A general relation between the moments of the functionsf,g, andh, in the integral equationh(x)=f(y)g(x–y) dy, is derived. This enables any moment of the unknown functionf to be calculated from the moments of the functionsg andh. In particular, if certain assumptions are fulfilled, the moments of the components of the doublet can be calculated with advantage from the moments of the total profile. The statistical significance of the moment characteristics is also emphasized.
f, g, h h(x)=f(y)g(x–) dy, f g h. , . .
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13.
It was shown in a previous communication that the nonlinear Schrödinger equation exhibits a spectrum of eigenfunctions of the form = k,A k (coshkx) –k and = k B k (coshkx) –k–1sinhkx, and the corresponding eigenvalues of the energy are related to a band structure with a characteristic energy gap as a significant feature. In the present paper, it is shown that a further spectrum exists exhibiting the general structure = k=0 A k(cosh kx)–k–1/2and = k=0 Bk(cosh kx)–k–3/2sinhkx and yielding also a band structure. An extension of the solution spectrum to a nonlinear Klein-Gordon equation and a nonlinear Dirac equation does not imply essential difficulties, and the corresponding characteristic band structure has to be related to a mass spectrum.  相似文献   

14.
From the eigenvalue equationH \ n () =E n ()\ n () withH H 0 +V one can derive an autonomous system of first order differential equations for the eigenvaluesE n () and the matrix elementsV mn () where is the independent variable. To solve the dynamical system we need the initial valuesE n ( = 0) and \ n ( = 0). Thus one finds the motion of the energy levelsE n (). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH =H 0 +V 1 + 2 V 2 and give an application to a supersymmetric Hamiltonian.  相似文献   

15.
An analytic gravitational fieldZ (Z y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds 2 =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c 2–10–29 gm/cm3.  相似文献   

16.
A geometrical gravitational theory based on the connection ={ } + ln + lng ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter 2. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to –2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter 2 is experimentally determined by applying the solutions to the solar system.  相似文献   

17.
High-accuracy Monte Carlo simulations of the time-dependent excitation probabilityG s (t) and steady-state emission anisotropyr M /r 0M for one-component three-dimensional systems were performed. It was found that the values ofr M /r 0M obtained for the averaged orientation factor only slightly overrate those obtained for the real values of the orientation factor ik 2 . This result is essentially different from that previously reported. Simulation results were compared with the probability coursesG s (t) andR(t) obtained within the frameworks of diagrammatic and two-particle Huber models, respectively. The results turned out to be in good agreement withR(t) but deviated visibly fromG s (t) at long times and/or high concentrations. Emission anisotropy measurements on glycerolic solutions of Na-fluorescein and rhodamine 6G were carried out at different excitation wavelengths. Very good agreement between the experimental data and the theory was found, with ex0-0 for concentrations not exceeding 3.5·10–2 and 7.5·10–3 M in the case of Na-fluorescein and rhodamine 6G, respectively. Up to these concentrations, the solutions investigated can be treated as one-component systems. The discrepancies observed at higher concentrations are caused by the presence of dimers. It was found that for ex <0-0 (Stokes excitation) the experimental emission anisotropies are lower than predicted by the theory. However, upon anti-Stokes excitation (ex>0-0), they lie higher than the respective theoretical values. Such a dispersive character of the energy migration can be explained qualitatively by the presence of fluorescent centers with 0-0 transitions differing from the mean at 0-0.  相似文献   

18.
    
, B. A. .  相似文献   

19.
Let {X t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew –1(X t), where {w(x):xd} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E 0 (qd) is completely monotonic int (E 0 denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 0 cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|2, whereD is the diffusion constant.  相似文献   

20.
We study the change of an quasienergy spectrum upon variation of the weight of a perturbation in the Floquet operatorF=F 0e–iV . Employing ideas from level dynamics and random matrix-theory we show that the distribution of nearest-neighbor spacings can display effectively irreversible behavior. Small deviations from equilibrium relax in a certain collision time which scales with the numberN of levels as collN –3/2.  相似文献   

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