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1.
In order to clarify physical consequences due to the presence of a set of auxiliary functions k (q,t) in quantum mechanics with a non-negative phase-space distribution function, the simplest quantum-mechanical problems are solved. It is shown that k (q,t) influence upon the results of a problem. Therefore it is supposed that k (q, t) reflect some physical reality (subquantum situation), interacting with a mechanical system. In particular the subquantum situation determines the minimum coordinate and momentum uncertainties ((q)2 and (p)2) as well as the coordinate distribution of a fixed system and the momentum distribution of a free system. These results provide the opportunity to formulate the notion of a stationary homogeneous isotropic subquantum situation. Supposing thatq andp are small an attempt is made to develop an approximate method of solutions (quasi-orthodox approximation). Energy spectrum of an electron in a hydrogen atom is found in the second order of this approximation.On leave of absence from Peoples' Friendship University, Chair of Theoretical Physics, 3, Ordjonikidze Street, B-302, Moscow, U.S.S.R.  相似文献   

2.
Under the condition of nearly equilibrium concentration of vacancies, time dependence of the amount of isothermal transformation given byy=R/R f was investigated whereR f is the total structural change of resistivity on completion of the whole process andR is the measured resistivity change. The investigation was done on the 21·8 at.% (40·3wt.%) Zn alloy under the condition of relatively low supersaturation of a few degrees centigrade below the metastable R solvus line. The total transformation involves four kinetic stages: the first two stages correspond probably to diffusion-controlled growth of the R particles from the supersaturated solid solution and to the ripening of these particles till their conversion to the cubic phase takes place. The last two kinetic stages account analogously for the particles growth and ripening. Both R and phases were identified by the transmission electron microscopy. When separating the individual stages, the approximation byy=1–exp [–(mt) n] of the amount of transformationy was used. The approximation allowed to get the starting values of both the time and the change of the structural part of the electrical resistance for individual stages and also to derive the parametersm i, ni which had to be redetermined for the individual separated stages. These data made it possible to synthetize the experimental curves ofR andy vs. time for the total transformation.It is a pleasure to thank Doc. Dr. V.Syneek CSc. for stimulating the author's interest in this problem and for providing helpful discussions. I also would like to express my thanks to Ing. P.Bartuka CSc. for the transmission electron microscopic study carried out to identify the particular phases. The author is indebted to Ing.V. íma for the preparation of the investigated alloy and to Mrs. A.Mendlová and Mr. P.Vyhlídka for technical assistance.  相似文献   

3.
We consider a variant of the problem of directed polymers on a disordered lattice, in which the disorder is geometrical in nature. In particular, we allow a finite probability for each bond to be absent from the lattice. We show, through the use of numerical and scaling arguments on both Euclidean and hierarchical lattices, that the model has two distinct scaling behaviors, depending upon whether the concentration of bonds on the lattice is at or above the directed percolation threshold. We are particularly interested in the exponents and, defined by ft and xt , describing the free-energy and transverse fluctuations, respectively. Above the percolation threshold, the scaling behavior is governed by the standard random energy exponents (=1/3 and =2/3 in 1+1 dimensions). At the percolation threshold, we predict (and verify numerically in 1+1 dimensions) the exponents=1/2 and =v/v, where v and v are the directed percolation exponents. In addition, we predict the absence of a free phase in any dimension at the percolation threshold.  相似文献   

4.
It is rigorously proven that the spectrum of the tight-binding Fibonacci Hamiltonian,H mn= m, n+1+ m, n–1+ m, n [(n+1)]–[n]) where =(5–1)/2 and [·] means integer part, is a Cantor set of zero Lebesgue measure for all real nonzero, and the spectral measures are purely singular continuous. This follows from a recent result by Kotani, coupled with the vanishing of the Lyapunov exponent in the spectrum.On leave from the Central Research Institute for Physics, Budapest, Hungary.  相似文献   

5.
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   

6.
We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (2/dq2){F([1/1(q)]), with F= –.  相似文献   

7.
Equilibrium size distributions for finite system containingM monomers in a volumeV undergoing coagulation (polymerization)/fragmentation, are determined for coagulation rateK ij and fragmentation rateF ij , corresponding to the processA i +A j A i+j (hereA k denotes a cluster containingk monomeric units). It is shown that microscopic detailed balance impliesF ij /K ij =a i a j /a i+j , where anda k are arbitrary. The mean and most probable size distributionc k = –1 a k e –k coincide in the thermodynamic limitM, V, =M/V fixed. If , 2<<3, then the theory predicts a (solgel) phase transition at a well defined value ofq = –1, with critical exponents = and = –2. The gel fraction exponent assumes its classical value unity, probably due to the neglect of spatial fluctuations. Finally it is indicated how the theory can in principle be extended to account for isomerism and cyclization.  相似文献   

8.
Let be a von Neumann algebra with a cyclic and separating vector . Let =i[H, ·] be the spatial derivation implemented by a selfadjoint operatorH, such thatH=0. Let be the modular operator associated with the pair (, ). We prove the equivalence of the following three conditions:1)H is essential selfadjoint onD(), andH commutes strongly with .2) The restriction ofH toD() is essential selfadjoint onD(1/2) equipped with the inner product(|)#=(|)+(1/2|1/2), , D(1/2).3) exp (itH) exp (–itH)= for anyt.We show by an example, that the first part of 1),H is essential selfadjoint onD(), does not imply 3). This disproves a conjecture due to Bratteli and Robinson [3].Part of this work was done while O.B. was a member of Zentrum für interdisziplinäre Forschung der Universität Bielefeld  相似文献   

9.
We report new limits on right-handed currents, based on precise measurements of the endpoint of the e+ spectrum from + decay. Highly polarized + from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding logitudinal field, or a 70-gauss spin-precessing transverse field. Decay e+ emitted within 200 mrad of the beam direction were momentum-analyzed to ±0.2%. For the spin-held data, decay via (V-A) currents requires the e+ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90%-confidence limits P />0.9959 and M(WR)>380 GeV, where WR is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit P />0.9918.We are indebted to the entire TRIUMF management and staff for their splendid support of this experiment. In its early stages we benefited from discussion with J. Brewer, R. Cahn, K. Crowe, and W. Wenzel. Rapid commissioning of the polarimeter was made possible by the superb efforts of the LBL support staff. This research was supported in part by the U.S. Department of Energy, Division of Basic Energy Sciences, Office of Energy Research under contracts W-7405-ENG-48 and AC02-ER02289.  相似文献   

10.
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  相似文献   

11.
The57Fe-Mössbauer spectroscopy has been used in order to study the quadrupole splitting EQ at the Fe-site and its dependence on temperature in Fe85–XCrXB15 and Fe80–XMoXB20 amorphous alloys. In all investigated compositions the local symmetry was lower than cubic with room temperature values of EQ in the range of 0.4–0.5 mm/s. In all cases relatively broad distributions of EQ and therefore of the EFG have been obtained. The EFG of the investigated compounds changes reversibly with temperature up to about 650 K according to the relation EQ (T)=EQ (O)·(1-BTV3/2) as in the case of crystalline noncubic metals. Assuming that the same dependence of B on the Debye temperature as in crystalline non-cubic metals holds for amorphous alloys, values of have been obtained in good agreement with those determined from the temperature dependence of the Mössbauer f-factor.  相似文献   

12.
The k theory is compared with the multilinear theory of scalar fields 1, 2, ..., k having the same mass as that of . In particular, it is shown that Feynman integrals encountered in the 3 theory are not necessarily present also in the 1 2 3 theory, but they are if they correspond to planar Feynman graphs having no tadpole part. Furthermore, a necessary and sufficient condition for the presence of a 3 Feynman integral in the 1 2 2 theory is found. Those considerations are applications of graph theory, especially of the coloring problem of graphs, to Feynman graphs.  相似文献   

13.
We consider the effect of a high-frequency pumping cost on the escape rate of a classical underdamped Brownian particle out of a deep potential well. The energy dependence of the oscillation frequency(E) is assumed to be weak on the scale of thermal energy,E(0)T(0)T/V0 (0)[E(0) is the derivative of(E) atE= 0,V 0 is the barrier height,V 0 T]. The quadratic-in- contribution to the decay rate is calculated in two different regimes: (1) for the case of resonance of the pumping frequency with the nth harmonic of the internal motion at an energye, when = n(e); (2) for a rollout region of the basic resonance near the bottom of the potential well, when ¦-(0)¦ and is the damping coefficient. In the latter case the absorption spectrum and the enhancement of the decay rate are calculated as functions of two reduced parameters, the anharmonicity of the potential,v E (0)T/, and the resonance mismatch, [(0)]/. It is shown that the effect of the pumping increases with diminishing ¦v¦ and at small v is proportional tov –1. In this regime, the dependence on is stepwise: the pumping contribution is large for v > 0 and small for v < 0. In the frame of our theory, the decay rate is invariant against the simultaneous alternation of the signs of andv. The spectrum of the energy absorption has the standard Lorentzian shape in the absence of anharmonicity,v=0, and with increasing of ¦v¦ shifts and widens retaining its bell-shape form.  相似文献   

14.
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.  相似文献   

15.
The reaction p K0+ was measured in the photon energy range from threshold up to 2.6 GeV with the SAPHIR detector at the electron stretcher facility, ELSA, in Bonn. Results are presented on the reaction cross-section and the polarization of the + as a function of the kaon production angle in the centre-of-mass system, cosc.m.K, and the photon energy. The cross-section is lower and varies less with photon energy and kaon production angle than that of p K+0. The + is polarized predominantly at cosc.m.K 0. The data presented here are more precise than previous ones obtained with SAPHIR and extend the photon energy range to higher values. They are compared to isobar model calculations.  相似文献   

16.
The Raman scattering spectra of isostructural Bi2O3 and Bi1.8Tm0.2O3 in the course of heating have been investigated. It is shown that the sequences of structural changes with increase in temperature differ: and * , respectively. In the hightemperature region, the structure takes the form of a disordered cube irrespective of the previous history of specimens.  相似文献   

17.
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   

18.
We investigate the band-gap structure of some second-order differential operators associated with the propagation of waves in periodic two-component media. Particularly, the operator associated with the Maxwell equations with position-dependent dielectric constant (x),xR 3, is considered. The medium is assumed to consist of two components: the background, where (x) = b , and the embedded component composed of periodically positioned disjoint cubes, where (x) = a . We show that the spectrum of the relevant operator has gaps provided some reasonable conditions are imposed on the parameters of the medium. Particularly, we show that one can open up at least one gap in the spectrum at any preassigned point provided that the size of cubesL, the distancel=L betwen them, and the contrast = b / a are chosen in such a way thatL –2, and quantities -1-3/2 and 2 are small enough. If these conditions are satisfied, the spectrum is located in a vicinity of widthw(3/2)-1 of the set {2 L -2 k 2:kZ3}. This means, in particular, that any finite number of gaps between the elements of this discrete set can be opened simultaneously, and the corresponding bands of the spectrum can be made arbitrarily narrow. The method developed shows that if the embedded component consists of periodically positioned balls or other domains which cannot pack the space without overlapping, one should expect pseudogaps rather than real gaps in the spectrum.  相似文献   

19.
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   

20.
We present a model for a one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring of lengthL with a single defect, across which they move with probability 0 p 1. This model is equivalent to a two-dimensional, six-vertex model in an extreme anisotropic limit with a defect line interpolating between open and periodic boundary conditions. We solve this model with a Bethe ansatz generalized to this kind of boundary condition. We discuss in detail the steady state and derive exact expressions for the currentj, the density profilen(x), and the two-point density correlation function. In the thermodynamic limitL the phase diagram shows three phases, a low-density phase, a coexistence phase, and a high-density phase related to the low-density phase by a particle-hole symmetry. In the low-density phase the density profile decays exponentially with the distance from the boundary to its bulk value on a length scale . On the phase transition line diverges and the currentj approaches its critical valuej c = p as a power law,j c – j –1/2. In the coexistence phase the width of the interface between the high-density region and the low-density region is proportional toL 1/2 if the density f 1/2 and=0 independent ofL if = 1/2. The (connected) two-point correlation function turns out to be of a scaling form with a space-dependent amplitude n(x1, x2) =A(x2)A Ke–r/ withr = x 2x 1 and a critical exponent = 0.  相似文献   

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