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1.
D. E. Feldman 《JETP Letters》1999,70(2):135-140
The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r 1)m(r 2)〉∼|r 1r 2|− 0.62ε. The magnetic susceptibility diverges at low fields as χ∼H −1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.  相似文献   

2.
The excess 1/f noise in a random lattice with bond resistances r∼exp(−λx), where x is a random variable and λ≪1, is studied theoretically. It is shown that if the correlation function {δr 2}∼r r θ+2, then the relative spectral density of the noise in the system is expressed as C e∼λm exp(−λ(1−p c)), where p c is the percolation threshold and md (ν is the critical exponent of the correlation length and d is the dimensionality of the problem). It is hypothesized that the exponent m possesses a dual universality: It is independent of 1) the geometry of the lattice and 2) the θ-mechanism responsible for the generation of the local noise. Numerical modeling in a three-dimensional lattice gives m=52.3 for θ=1 and θ=0, in agreement with the hypothesis. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 614–618 (25 April 1996)  相似文献   

3.
4.
The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from \mathbbR2+1 ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d ρ 2 + g(ρ)2 dθ2, g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u tt  + u rr  + r −1 u r  = r −2 g(u)g′(u), λ(t) = t −1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0.  相似文献   

5.
M R M Witwit 《Pramana》1994,42(2):159-165
Eigenenergies are calculated for the potentialsV 1(r)=−(a/r)[1+(1+br)e−2br ] andV 2(r)=−(v/r)[1 −λr(1−Z −1)(1+λr)−1], using renormalized series technique. Accurate results produced here for various eigenstates agree with those available in the literature.  相似文献   

6.
A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ12 + ξ22 + ⋯ + ξN−12)1/2 only, where ξ12,…,ξN−1 are Jacobi relative coordinates which are functions of N-particle relative positions r12,r23,…,rN1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax2 + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.  相似文献   

7.
We investigate a one-dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ and τ+. Kipnis et al. (J. Statist. Phys., 27:65–74 (1982).) proved that this model satisfies Fourier’s law and that in the hydrodynamical scaling limit, when N → ∞, the stationary state has a linear energy density profile , u ∈[−1,1]. We derive the large deviation function S(θ(u)) for the probability of finding, in the stationary state, a profile θ(u) different from . The function S(θ) has striking similarities to, but also large differences from, the corresponding one of the symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational equation. Unlike the latter it is not convex and the Gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state. We also briefly discuss more general models and find the features common in these two and other models whose S(θ) is known.  相似文献   

8.
A new type of correlated wave function for the normal helium is proposed in the form:ψ(r1, r2)=Σc mφm withφ m=exp]−α(r 1+r 2)]/(br 12+a) m wherea, b, α are non-linear variational parameters. Optimizing these parameters by the Monte-Carlo technique, an energy eigen-value of −2.903645(a.u.) is obtained withonly three terms in the basis expansion alongwith satisfactory cusp condition, compared to the essentially exact non-relativistic value of −2.903724 as given by Freundet al (Phys. Rev. A29, 980 (1984)).  相似文献   

9.
Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θlab=165° and E lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σR(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σR(E,θ)=(1+Ue/E)−1, where U e is an atomic screening potential energy. The deduced average value, U e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998  相似文献   

10.
11.
We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral equation for the partition function G D(r,r′, N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r′ . The expression for G(r,r′, s) is found to be the sum of the commonly accepted Dirichlet result G D(r,r′, N) = G 0(r,r′, N) - G 0(r,r”, N) , where r” is the mirror image of r′ , and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall or contact theorem). A significant correction to the density profile (of magnitude 1/is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems are discussed.  相似文献   

12.
 We deal with the existence of positive radial solutions concentrating on spheres to a class of singularly perturbed elliptic problems like −ɛ2Δu+V(|x|)u=u p ,uH 1 (ℝ n ). Under suitable assumptions on the auxiliary potential M(r)=r n−1 V θ (r), θ(p+1)/(p−1)−1/2, we provide necessary and sufficient conditions for concentration as well as the bifurcation of non-radial solutions.  相似文献   

13.
IVS Rathore  B P Singh 《Pramana》1977,8(1):91-97
β-γ-γ directional correlation studies for the cascades (i)β-rays ofE max=0.12 MeV,γ-rays of 557 keV andγ-rays of 53 keV and (ii)β-rays ofE max=0.21 MeV,γ-rays of 444 keV andγ-rays of 53 keV have been made. The triple correlation functionsW(θ) were obtained to beW(θ)=1+(−0.153±0.031)P 2(cosθ)+(0.004±0.035)P 4(cosθ) forβ-rays ofE max 0.12 MeV→557→53 keV cascade andW(θ)=1+(0.163±0.042)P 2(cosθ)+(−0.035±0.058)P 4(cosθ) forβ rays ofE max=0.21 MeV→444 keV→53 keV cascade. Spins and parities of the 650, 537 and 93 keV levels of103Rh are deduced by triple angular correlation and the internal conversion coefficient studies. Multipolarities of the transitions are also determined.  相似文献   

14.
Bound states and critical behavior of the Yukawa potential   总被引:1,自引:0,他引:1  
We investigate the bound states of the Yukawa potential V (r)=−λexp(−αr)/r, using different algorithms: solving the Schr?dinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = αC, above which no bound state exists. We study the relation between αC and λ for various angular momentum quantum number l, and find in atomic units, αC(l) = λ[A 1 exp(−l/B 1) + A 2 exp(−l/B 2)], with A 1 = 1.020(18), B 1 = 0.443(14), A 2 = 0.170(17), and B 2 = 2.490(180).  相似文献   

15.
N. N. Achasov 《JETP Letters》1996,63(8):601-606
It is shown that BR b1(1 P)→e + e )≃3.3· 10−7 and BR c1(1 P)→e + e )≃10−8. This gives realistic possibilities for searching for the production of χ b1(1 P) and ξ c1(1 P) states in e + e collisions, even on the present-day colliders, to say nothing of b and c-τ factories. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 569–574 (25 April 1996)  相似文献   

16.
The correlation of the local density of states 〈ρɛ(r 1ɛ + ω(r 2)〉 in quasi-one-dimensional disordered wires in a magnetic field is calculated under the assumption that |r 1r 2| is much smaller than the localization length. This amounts to finding the zero mode of the transfer-matrix Hamiltonian for the supersymmetric σ model, which is done exactly by mapping to the three-dimensional Coulomb problem. Both the regimes of level repulsion and level attraction are obtained, depending on |r 1r 2|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional cases are dissimilar. The text was submitted by the authors in English.  相似文献   

17.
We exhibit a newansatz for the solution of the homogeneous three-dimensional time-dependent wave equation in spherical coordinates of the form Φ(r,t)=Y(θ, φ)(I(r)+G(g)), wheregct/r. FunctionG(g) has explicit solution in terms of three independent nonperiodic functionss ,t ,u (s andt are related to the associated Legendre functions of the first and second kinds).G(g) is nonperiodic and may be cast as a superposition of incoming and outgoing waves. To obtainG(g), we solved a nonhomogeneous associated Legendre equation (this solution, to our knowledge, is also new).G(g) may prove useful in many microscopic and macroscopic problems, representable by homogeneous wave equations.  相似文献   

18.
We have used the PBE/3z, B3LYP/6-31G, B3LYP/6-31G(d), and B3LYP/6-311G(d) methods to study the conformational mobility of 2,3-dihydro-3-O-(1,4-naphthoquinon-2-yl)-2-oxo-1,4-naphthoquinones (1–4). We have shown that more than 99% of these compounds exist as the major tautomeric form, while differences in the structure of the Q2H (2,3-dihydro-2-oxo-1,4-naphthoquinones) and Q1,4 (1,4-naphthoquinon-2-yl) moieties lead to qualitative differences in the internal rotation potentials of the ethyl substituents V(θEt−1) and V(θEt−2), and consequently each of compounds 1−4 exists as six different rotameric forms. For diquinone 3, we have calculated the dependences of the frequencies (ν) and intensities (A) of the normal vibrations on the torsional angles θEt−1 and θEt−2, and also on the changes in the geometry of the ether bond. We have found that the values of ν and A for the bands in the carbonyl region of the IR spectrum change little on going from one rotameric form to another, and also for the in-plane bends of the ether bond, and change considerably for the out-of-plane bends of the ether bond. However, for T ≤ 300 K, there is no qualitative change in the overall contour, and it can be interpreted based on a simple additive model. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 573–581, September–October, 2006.  相似文献   

19.
The coefficient R(ν) of reflection from the surface of 6H-SiC single crystals is studied in the case in which the long-wavelength optical vibrations of the lattice are coupled with the electron plasma. It is shown for the first time that the anisotropy of the properties of electrons and phonons in 6H-SiC gives rise to special features in the spectrum of the coupled vibrations and the transparency regions. It is found, in particular, that if the axis of the crystal lies in the polarization plane of the incident radiation (0<θ<90°), for 30 cm−1ν p<320 cm−1 the spectrum of R(ν) acquires three regions of transparency and opacity, and for ν p⩾320 cm−1 four such regions, which are absent in an isotropic medium. The width of these regions is found to depend on the electron concentration in the conduction band and on the angle θ. Zh. éksp. Teor. Fiz. 116, 646–654 (August 1999)  相似文献   

20.
Co x Pt1−x (x≥0.7) alloy nanowires are grown into self-synthesized anodic alumina templates by electrodeposition. Magnetic and magnetization properties of Co x Pt1−x alloy nanowires are measured as functions of wire length, temperature, and field orientation. X-ray diffraction shows that as-prepared CoPt nanowires are of fcc polycrystalline structure. A crossover of easy axis of magnetization is observed from parallel to perpendicular of the nanowire axis as a function of length. The coercivity (H c) and remanent squareness (SQ) of Co x Pt1−x nanowire arrays are derived from hysteresis loops measured at various angles (θ) between the field and wire axis. H c(θ) and SQ(θ) curves show bell-shaped or otherwise bell-shaped behavior corresponding to the easy axis of their magnetization.  相似文献   

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