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1.
A short review of theoretical and experimental studies concerning the photoexcited florescence and Raman scattering of light for a substance in a space containing small material bodies is presented. Calculations of the radiativetransition probability for atoms (molecules) in the vicinity of bodies with a size much smaller than the light wavelength are performed. The probabilities of the singlephoton and doublephoton transitions are shown to increase by factors of 9 and 81 in the vicinity of a nanosize sphere with dielectric constant ||\ 1. The probability of a radiative transition in the vicinity of the vertex of a conic needle bearing up against a plane (both with || 1) increases by factors of (/R in)2 and (/R in)4 for singlephoton and doublephoton transitions, respectively (R in is the curvature radius for the needle vertex). This theoretical result is suggested as an explanation of the effect of increasing the radiation process intensity in the experiments carried out in the studies cited below.  相似文献   

2.
Let be aC -manifold and s and u be two Hölder foliations, transverse, and with uniformlyC leaves. If a functionf is uniformlyC along the leaves of the two foliations, then it isC on . The proof is elementary.  相似文献   

3.
We discuss the simple, randomly driven systemdx/dt = –x –x3 +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)n, whereR is the internal Reynolds number ()1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp 2/2 +m 2 x 2/2 +vx 4 +x 6/2, we evaluate the path integral on a lattice by assuming that thex 6 term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.  相似文献   

4.
A one-parameter family of piecewise-linear discontinuous maps, which bifurcates from a periodic state of periodm, (m=2, 3,...) to an intermittent chaos, is studied as a new model for the onset of turbulence via intermittency. The onset of chaos of this model is due to the excitation of an infinite number of unstable periodic orbits and hence differs from Pomeau-Manneville's mechanism, which is a collapse of a pair of stable and unstable periodic orbits. The invariant density, the time-correlation function, and the power spectrum are analytically calculated for an infinite sequence of values of the bifurcation parameter which accumulate to the onset point c from the chaos side - c > 0. The power spectrum near=0 is found to consist of a large number of Lorentzian lines with two dominant peaks. The highest peak lies around frequency=2/m with the power-law envelope l/¦-(2/m)¦4. The second-highest peak lies around o = 0 with the envelope l/¦¦2. The width of each line decreases as, and the separation between lines decreases as/lg3–1. It is also shown that the Liapunov exponent takes the form-/m and the mean lifetime of the periodic state in the intermittent chaos is given bym –1(ln –1+1).  相似文献   

5.
We show that the two-dimensional isotropic ferromagnetic rotator model exhibits a first order phase transition if the interaction decays asr with 2<<4.Work supported by Fonds National Suisse de la Recherche Scientifique.  相似文献   

6.
Hardening in modulated structure is evaluated using the periodic approximation. The critical shear stress increment due to the periodic structure is calculated in the constant line energy approximation. The results are applicable to any periodic structure (concentration waves must be neither homophase nor symmetric) exerting on the dislocation local glide forces with an amplitude smaller than ( denotes the line energy of corresponding straight dislocation directed along the concentration variations with the wave vector). In the zero approximation, the critical forceb is then simply the glide force on the straight dislocation averaged along its length in its most hardened position.  相似文献   

7.
We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 108 collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)2 and x(t)4, and examine the behavior ofq 2 (t)=x(t)4/3x(t)22. We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM. On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.  相似文献   

8.
The projection latticesP(1),P(2) of two von Neumann subalgebras 1, 2 of the von Neumann algebra are defined to be logically independent if A B0 for any 0AP(1), 0BP(2). After motivating this notion in independence, it is shown thatP(1),P(2) are logically independent if 1 is a subfactor in a finite factor andP(1),P(2 commute. Also, logical independence is related to the statistical independence conditions called C*-independence W*-independence, and strict locality. Logical independence ofP(1,P(2 turns out to be equivalent to the C*-independence of (1,2) for mutually commuting 1,2 and it is shown that if (1,2) is a pair of (not necessarily commuting) von Neumann subalgebras, thenP(1,P(2 are logically independent in the following cases: is a finite-dimensional full-matrix algebra and 1,2 are C*-independent; (1,2) is a W*-independent pair; 1,2 have the property of strict locality.  相似文献   

9.
The Feigenbaum phenomenon is studied by analyzing an extended renormalization group map . This map acts on functions that are jointly analytic in a position variable (t) and in the parameter () that controls the period doubling phenomenon. A fixed point * for this map is found. The usual renormalization group doubling operatorN acts on this function * simply by multiplication of with the universal Feigenbaum ratio *= 4.669201..., i.e., (N *(,t)= *( * ,t). Therefore, the one-parameter family of functions, * , * (t)=( *(,t), is invariant underN. In particular, the function 0 * is the Feigenbaum fixed point ofN, while * represents the unstable manifold ofN. It is proven that this unstable manifold crosses the manifold of functions with superstable period two transversally.  相似文献   

10.
We present the full set of evolution equations for the spatially homogeneous cosmologies of type VIh filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is found that only when the group parameter satisfies h > –1 a self-similar solution exists. In particular we show that for h > – there exists a self-similar equilibrium point provided that whereas for h < – the state parameter belongs to the interval (1, . This family of new exact self-similar solutions belongs to the subclass n = 0 having non-zero vorticity. In both cases the equilibrium points have a six-dimensional stable manifold and may act as future attractors at least for the models satisfying n = 0. Also we give the exact form of the self-similar metrics in terms of the state and group parameter. As an illustrative example we provide the explicit form of the corresponding self-similar radiation model ( = ), parametrised by the group parameter h. Finally we show that there are no tilted self-similar models of type III and irrotational models of type VIh.  相似文献   

11.
Dark resonances in the 154Sm -system 4f 66s 2(7 F 0) 4f 66s6p(9 F 1 0) 4f 6 s 2(7 F 1) are observed alongside the velocity selective optical pumping. The shape of the resulting spectra strongly depended on the buffer gas (He, Ar) pressure due to velocity-changing collisions (VCC): the sign of the effect could be reversed from the dark to the bright resonance. The observed spectra are interpreted within the framework of the hard-sphere collision model. The role of VCC in the formation of the dark state in the -system is discussed.  相似文献   

12.
We show the existence of a constant (0, ) such that if n is the extinction time for a supercritical contact process on [1, n] d starting from full occupancy, then {log(E[ n])}/n d tend to as n tends to infinity.  相似文献   

13.
The generally covariant Lagrangian densityG = + 2K matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form kl i = kl i for the coefficients kl i of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of , gik, and the coefficients kl i . Then the kl i are determined by the Palatini equations. From these equations and from the symmetry kl i = lk i for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / becomes dependent on the Dirac current, essentially with a coupling factor Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10–81erg cm3  相似文献   

14.
We consider a class of scalar field lattice models with action 1/2()+V(), V small. After n block renormalization group transformations, new formulas are obtained for the finite lattice generating and correlation functions. For some infrared asymptotic-free models in the thermodynamic and n limits, the formulas for correlation functions are especially simple, isolate the correct dominant long-distance behavior, and can be used to control the subdominant contributions.  相似文献   

15.
A gas of two Boson systems coexisting inR 3, and interacting only mutually, is analyzed. The interaction is quadratic, so that the dynamical problem may be solved completely and exactly.The initial state is taken to be the mutually uncorrelated Gibbs states: (1) (2) = . We find the time evolved state, and its projections onto the separate species and the subvolumes.The principle consequences of this model are discussed. In particular we examine the possible occurrence of harmonic oscillations between the species.On Study Leave at the Department of Physics and Astronomy, The University of Rochester.This research was partially supported by the National Science Foundation under Contract No. 5-28501.  相似文献   

16.
Successive band-splitting transitions occur in the one-dimensional map xi+1=g(xi),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2n) bands to 2Nbands is given by=(2)1/N (n=0, 1,2,...). The time-correlation function i=xix0/(x0)2,xi xi–xi is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, i–[(10–42)/17] i,0-[(102-8)/51]i,1 + [(7 + 42)/17](–1)ie–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for i has been obtained by deriving an analytic form of i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)1/N, the damping constant of i fori N is given by N=2(N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.  相似文献   

17.
The central limit theorem of Cushen and Hudson is reformulated on the algebra of the CCR. Namely, for a gauge invariant state , the weighted convolutions n of the central limit tend to the quasi-free reduction Q of pointwise. It is proved that if the initial relative entropy S(, Q ) is finite, then S( n , Q ) goes to 0 and so n Q 0. No restriction on the dimension of the test function space is made.  相似文献   

18.
We are dealing with the Dirac Hamiltonian H = H0 + V with no magnetic field and radially symmetric electrostatic potential V = V(r), preferably the Coulomb potential. While the observable H is precisely predictable, its components H0 (relativistic mass) and V (potential energy) are not. However they both possess precisely predictable approximations H0 and V which approximate accurately if the particle is not near its nucleus. On the other hand, near 0, H0 and V are practically unpredictable, perhaps in agreement with the fact, that a neutrino also should be in the game. [We have not yet studied the corresponding observables for the ( 12-dimensional) problem of electro-weak interaction.] Mathematically we are focusing on the spectral theory of the unbounded self-adjoint operators H0 and V . We can prove that V is unitarily equivalent to V(r) again, by a unitary map given as Wiener-Hopf-type singular integral operator in the standard separation of variables for radially symmetric Dirac Hamiltonians. [This is, as far as the continuous spectrum is concerned.] Very similar unitary equivalence holds for H 0 and H 0. We are tempted to regard this as a form of renormalization.  相似文献   

19.
We consider the one-dimensional planar rotator and classical Heisenberg models with a ferromagnetic Kac potential J (r)=J(yr), J with compact support. Below the Lebowitz-Penrose critical temperature the limit (mean-field) theory exhibits a phase transition with a continuum of equilibrium states, indexed by the magnetization vectors m s, s any unit vector and m the Curie–Weiss spontaneous magnetization. We prove a large-deviation principle for the associated Gibbs measures. Then we study the system in the limit 0 below the above critical temperature. We prove that the norm of the empirical spin average in blocks of order –1 converges to m , uniformly in intervals of order p , for any p 1. We also give a lower bound to the scale on which the change of phase occurs, by showing that the empirical spin average is approximately constant on intervals having length of order -1-with (0,1) small enough.  相似文献   

20.
We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx 1+2. The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.  相似文献   

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