首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 46 毫秒
1.
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   

2.
We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in l so there are 2l Lyaponov exponents 1...l0 l+1...2l =–1. Our results include the fact that if 1=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049  相似文献   

3.
No Heading The uncertainty in the measured fluorescence decay lifetimes of 30 nm particles of YAG:Cc was used to evaluate the predictions of a novel form of the Heisenberg uncertainty principle suggested by de Sabbata and Sivaram, T t h/k. The worst-case uncertainty in temperature of 4.5 °K (as derived from the relationship between temperature and lifetime) and the measured uncertainty in decay lifetime, 0.45 ns, yielded an internal estimate of T t = 2.0 × 10–9 °K s, which is 263 times larger than /k = 7.6 × 10–12 °K s. An external estimate of T t = 4.5 × 1011 °K s (which is = 6 times /k) is derived from the independently measured uncertainty in the temperature of the sample and the experimentally determined uncertainty in lifetime. These results could be low by a factor of 5.6 if signal averaging must be taken into account. If valid, the findings are consistent with the predictions of this version of the uncertainty principle and they imply the existence of a type of thermal quantum limit.  相似文献   

4.
For the Ising model with nearest neighbour interaction it is shown that the spin correlations A B - A B decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).  相似文献   

5.
The ultraslow motion of defects in high purity hexagonal H2O ice has been studied by proton dipolarT 1D measurements in the strong collision limit, using the Jeener technique. The obtained NMR correlation times agree rather well with both the Schottky H2O diffusion timest s=r 2/6D and the deuteron correlation times in D2O ice, suggesting that Schottky rather than interstitial diffusion dominates spin-lattice relaxation in both H2O and D2O ice.On leave of absence from University of Ljubljana, Institute J. Stefan.  相似文献   

6.
Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT R is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h 2 are found to behave—lnFlnh 2(T R T)–1 for temperaturesT approachingT R from below. The linear relaxation rate of the order parameter is found to be proportional to –2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference aboveT R , shows a metastable regime belowT R with a spinodal limit of metastability c , beyond which oscillatory growth starts. The critical behavior of c is found to be ln c –(T R T)–1+O(ln (T R T)).  相似文献   

7.
We calculate, using numerical methods, the Lyapunov exponent (E) and the density of states (E) at energy E of a one-dimensional non-Hermitian Schrödinger equation with off-diagonal disorder. For the particular case we consider, both (E) and (E) depend only on the modulus of E. We find a pronounced maximum of (|E|) at energy E=2/ , which seems to be linked to the fixed point structure of an associated random map. We show how the density of states (E) can be expanded in powers of E. We find (|E|)=(1/ 2)+(4/3 3) |E|2+. This expansion, which seems to be asymptotic, can be carried out to an arbitrarily high order.  相似文献   

8.
We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.  相似文献   

9.
Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization |M|, susceptibility) and percolation cluster properties relating to the physical clusters, namely the Fortuin-Kasteleyn clusters (percolation probability P , percolation susceptibility p, cluster size distributionn l) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, P being identical to |M| in the thermodynamic limit, while finite-size corrections differ. In contrast, p differs from even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes to, but not to p. NearT c the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics.  相似文献   

10.
Hölder continuity of sample paths of the stochastic process t (f)=( t f) (f Y(R d–1)) in Euclidean field theory is proved under some assumptions on correlation functions. These assumptions are fulfilled inP()2 and in theories in which the GHS inequality holds. The continuity index is determined by the condition d(p)|p 0|2<, whered(p) is the Fourier transform of the two-point function.On leave of absence from Institute of Theoretical Physics, University of Wrocaw, Wrocaw, Poland  相似文献   

11.
Two solutions 5(x, x s) and 6(x, x s) related to the irregular singular point atx=+ of the radial wave equation in Schwarzschild's space-time are studied as functions of the independent variablex and the parameterx s. Analytic continuations of 5 and 6 are derived and their relation to the flat-space case solutions is established. Explicit expressions for 3(x, x s) and 4(x, x s) (the solutions about the regular singular point atx=x s) are given. From these expressions and the analytic continuations of 5 and 6 the coefficients relating linearly 5 and 6 with i (i=1, 2, 3, 4) are calculated.  相似文献   

12.
Three definitions of logical independence of two von Neumann latticesP1,P2 of two sub-von Neumann algebras 1, 2 of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P1, 0 B P2. Propositions relating logical independence ofP1,P2 toC *-independence,W * independence, and strict locality of 1, 2 are presented.  相似文献   

13.
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   

14.
The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m 2 h Finally, variation with respect tog yields the energy-momentum tensor.  相似文献   

15.
The tensor of reflected and refracted light was first introduced into the principal axes and then the latter were transformed into thep ands direction of the electric field strength. The amplitude coefficient of thep-components of refracted light has different forms depending on which complex unit vector is unit with respect to the square or the absolute value. The energy coefficient has the same value in both cases.
, p s . p- , . .
  相似文献   

16.
LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , N , N the modular operators to (, ), (N, ), resp (N , ). Assume now -it N it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups it , N ir , N is ,t, r, s generate a unitary representation of the group S1(2, )/Z 2 of positive energy.Another result is related to two half-sided modular inclusions (1 , ) and (2 , ). Under proper conditions the three modular groups it , 1 ir , 2 is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.  相似文献   

17.
LetA be a quasi-manual with finite operations. Associate to each E = {e 1 ,..., en} A the set E of modal formulas: (e 1 ··· en), ei (e 1 ··· ei–1 ei+1 ··· en), i=1,..., n. Set A = {E|E A}. We show that supports ofA are in one-to-one correspondence with certain Kripke models of A where the supports are given by {x |A x is true}.On leave from the Department of Mathematics, Pontificia Universidade Catolica, Rio de Janeiro, Brazil.  相似文献   

18.
The exponent d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<23/4. Monte Carlo simulations are done to suggest 2=0.61 and 30.29.  相似文献   

19.
Using the CNDO/S method, we have performed quantumchemical calculations of the ground and excited electronic states of porphin molecules (symmetry D 2h ) and a number of porphin isomers: porphycene (C2h ), hemiporphycene, corphycene (C2v ), isoporphycene, and three nonsynthesized structural isomers of the porphin skeleton by its bridge groups —(CH) meso —. The results of the calculations are compared with the corresponding data for the freebase porphin molecule (H2P). Near the boundary between the occupied and vacant orbitals the isomers form rows of singleelectron levels with similar energy characteristics. For the MOs of these isomers, the H2P MOs closest in distribution on the comparable atomic centers are given. The weak (Q) and strong (B) transitions in the visible and near UV regions point to the porphyrin type of spectra of all the isomers. The calculation data on the excited electronic states of N, g, and ntype H2P near and above the B states are given; the presence of such states in other isomers is shown. The calculation does not point to a difference in the position of the first singlet transitions in the first five isomers. The calculation data on the lower singlettriplet transitions are also reported.  相似文献   

20.
We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L *( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号