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1.
Let (, , ) be a measure space with normalized measure,f: a nonsingular transformation. We prove: there exists anf-invariant normalized measure which is absolutely continuous with respect to if and only if there exist >0, and , 0<<1, such that (E)< implies (f –k(E))< for allk0.  相似文献   

2.
The spectrum of the mass operator on the soliton sectors of the anisotropic (|ø|4)2—and the (ø4)2—quantum field models in the two phase region is analyzed. It is proven that, for small enough >0, the mass gapm s() on the soliton sector is positive, andm s()=0(–1). This involves estimatingm s() from below by a quantity () analogous to the surface tension in the statistical mechanics of two dimensional, classical spin systems and then estimating () by methods of Euclidean field theory. In principle, our methods apply to any two dimensional quantum field model with a spontaneously broken, internal symmetry group.A Sloan Foundation Fellow; Research supported in part by the U.S. National Science Foundation under Grant No. MPS 75-11864.Supported in part by the National Science Foundation under Grant No. PHY 76-17191  相似文献   

3.
Fractional noise     
Fractional noiseN(t),t 0, is a stochastic process for every , and is defined as the fractional derivative or fractional integral of white noise. For = 1 we recover Brownian motion and for = 1/2 we findf –1-noise. For 1/2 1, a superposition of fractional noise is related to the fractional diffusion equation.  相似文献   

4.
The Newtonian equations of motion, and Newton's law of gravitation can be obtained by a limit of Einstein's equations. For a sufficiently small constant the existence of a set of solutions (0) of Einstein's equations of a stationary, axisymmetric star is proven. This existence is proven in weighted Sobolev spaces with the implicit function theorem. Since the value of the causality constant depends only on the units used to measure the velocity, the existence of a solution for any small is physically interesting.  相似文献   

5.
We study ergodic Jacobi matrices onl 2(Z), and prove a general theorem relating their a.c. spectrum to the spectra of periodic Jacobi matrices, that are obtained by cutting finite pieces from the ergodic potential and then repeating them. We apply this theorem to the almost Mathieu operator: (H , , u)(n)=u(n+1)+u(n–1)+ cos(2n+)u(n), and prove the existence of a.c. spectrum for sufficiently small , all irrational 's, and a.e. . Moreover, for 0<2 and (Lebesgue) a.e. pair , , we prove the explicit equality of measures: |ac|=||=4 –2.Work partially supported by the US-Israel BSF  相似文献   

6.
We investigate simple model systems in contact with an infinite heat bath. The former consists of a finite number of particles in a bounded region of d,d=1,2. The heat baths are infinite particle systems which can penetrate and interact with the system via elastic collisions. Outside the particles move freely and have a Gibbs probability measure prior to entering. We show that starting from almost any initial configuration, the system approaches, ast , the appropriate Gibbs distribution. The combined system plus bath is Bernoulli.Partially supported by NSF Grants PHY 8201708 and DMR 81-14726-02.  相似文献   

7.
We study the almost Mathieu operator: (H , , u)(n)=u(n+1)+u(n-1)+ cos (2n+)u(n), onl 2 (Z), and show that for all ,, and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely |4–2|. In particular, for ||=2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and ||=2) we show that the Hausdorff dimension of the spectrum is smaller than or equal to 1/2.Work partially supported by the GIF  相似文献   

8.
Positron lifetime spectra were re-measured for a series of synthetic zeolites using a large time window of observation. Magnetic quenching experiments were also performed for the zeolites, and it has been confirmed that both the 4 and the 3 components are due to o-Ps. The annihilation rate of the third component, 3, showed a good correlation with the size of the largest voids, which is similar to the correlation reported for other compounds. However the annihilation rate of the longest-lived component, 4, showed a poor correlation with the void size. The 3 component has thus been assigned to o-Ps in the regular voids of the zeolites, and the 4 component to that escaped to inter-particle open spaces.  相似文献   

9.
Absorption and fluorescence spectra of 2-aminoxanthone in solutions of different types at 77–350 K were studied. The existence of three bands (1 max = 417 nm, 1 = 14 ns; 2 max = 528 nm, 2 = 13 ns; and 3 max = 565 nm, 3 = 6 ns) in fluorescence of 2-aminoxanthone solutions has been established. It was shown that the first short-wave band was determined by deactivation of singlet excitation of an aminoxanthone molecule. The band with 3 max = 565 nm (depending on the concentration) is connected with excimer-type aggregates, which are formed by aminoxanthone molecules grouped with the help of dipole molecules of solvent or by weak hydrogen bonds between aminoxanthone molecules. The emission in band 2 max = 528 nm is caused by reversible changes in the 2-aminoxanthone molecule and probably is connected with an intramolecular proton transfer.  相似文献   

10.
The contact process onZ has one phase transition; let c be the critical value at which the transition occurs. Let N be the extinction time of the contact process on {0,...,N}. Durrett and Liu (1988), Durrett and Schonmann (1988), and Durrett, Schonmann, and Tanaka (1989) have respectively proved that the subcritical, supercritical, and critical phases can be characterized using a large finite system (instead ofZ) in the following way. There are constants 1() and 2() such that if < c , lim N N /logN = 1/1(); if > c , lim N log N /N = 2(); if = c , lim N N /N= and lim N N /N 4=0 in probability. In this paper we consider the asymmetric contact process onZ when it has two distinct critical values c1< c2. The arguments of Durrett and Liu and of Durrett and Schonmann hold for < c1 and > c2. We show that for [ c1< c2), lim N N /N=-1/, (where i is an edge speed) and for = c2, lim N log N /logN=2 in probability.  相似文献   

11.
The fluctuations in limit cycles of second-order bifurcation (transition from a stable to an unstable focus) are investigated near the bifurcation point c, being an external control parameter. Two different methods are applied: a time- and space-dependent Fokker-Planck equation obtained from an 1/2-expansion of the master equation ( being the volume) and a time- and space-dependent Langevin equation. Both methods give the same results. It is shown that the dependence of the radial correlation on 2 = | – c| and the time-behaviour of the phase correlation (ensemble dephasing) are determined by the dimensionality of space.  相似文献   

12.
The collision term of the Fokker-Planck-type magnetized kinetic equation is approximated for an electron-ion plasma in a strong external uniform magnetic field. The collision term is evaluated explicitly in the case of unmagnetized Maxwellian ions for 1<= e / pi 2<. It is shown that the dominant effects are determined by the parameter ln (/) which replaces the Coulomb logarithm ln in the components of the diffusion coeficientD.  相似文献   

13.
We studye()=inf spec(-+V) and examine whene()<0 for all 0. We prove thatc 2e()d 2 for suitableV and all small ||.Research partially funded under NSF grant number DMS-9101716.  相似文献   

14.
The C -extended oscillator algebra is generated by {1, a, a , N, T}, where T is the generator of the cyclic group C of order . It can be realized as a generalized deformed oscillator algebra (GDOA). Its unirreps can thus be easily exhibited using the representation theory of GDOAs and their carrier spaces show a Z-grading structure. Within its infinite-dimensional Fock space representation, this algebra provides a bosonization of parasupersymmetric quantum mechanics of order p = – 1.  相似文献   

15.
We demonstrate photographic techniques to record and visualize infrared (=10 m) and visible (=458 nm) wavetrains. The fields are mapped in the form of wavefronts. The method is applied to fields excited in the neighborhood of small scattering objects. Especially we record guided modes and surface plasmons such that the phase of scattering, the velocity of propagation and the decay length can be read directly from the photographs.  相似文献   

16.
The Julia setB for the mappingz (z–)2 is considered, where is a complex parameter. For 2 a new upper bound for the Hausdorff dimension is given, and the monic polynomials orthogonal with respect to the equilibrium measure onB are introduced. A method for calculating all of the polynomials is provided, and certain identities which obtain among coefficients of the three-term recurrence relations are given. A unifying theme is the relationship betweenB and -chains ± (± (± ...), which is explored for –1/42 and for with ||1/4, with the aid of the Böttcher equation. ThenB is shown to be a Hölder continuous curve for ||<1/4.Supported by NSF Grant MCS-8104862Supported by NSF Grant MCS-8002731  相似文献   

17.
We prove that for any diophantine rotation angle and a.e. phase the almost Mathieu operator (H()) n = n–1 + n+1 +cos(2(+n)) n has pure point spectrum with exponentially decaying eigenfunctions for 15. We also prove the existence of some pure point spectrum for any 5.4.  相似文献   

18.
The luminescence response of the leaves of higher plants exposed to laser radiation with different energy and time parameters has been investigated at a wavelength of 685 nm. The plants were irradiated by laser radiation at 1060, 632, and 530 nm. Radiation at = 632 nm was used as the control. It is shown that radiation at = 1060 nm suppresses photosynthesis, whereas that at = 530 nm stimulates it.  相似文献   

19.
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   

20.
The classical non-linear Schrödinger equation associated with a symmetric Lie algebra =km is known to possess a class of conserved quantities which from a realization of the algebrak []. The construction is now extended to provide a realization of the Kac-Moody algebrak[, –1] (with central extension). One can then define auxiliary quantities to obtain the full algebra [, –1]. This leads to the formal linearization of the system.  相似文献   

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