共查询到20条相似文献,搜索用时 31 毫秒
1.
D.J. Gates 《Physica A》1975,81(1):47-71
The k-particle, infinite-volume distribution functions and modified Ursell correlation functions of a classical system of particles with the two-body potential are considered. The limiting values of the functions and in the limit γ → 0 are calculated, under fairly weak conditions on q and K, by a method involving functional differentiation. These limiting functions are used to describe the molecular structure of the various states of the system both in the range of the potential q(r) and in the rage of the potential γνK(γr). The direct correlation function c? (r, γ) is also considered and it is shown that for , , for all one-phase states, where β is the reciprocal temperature. Special cases of our results confirm those of other authors, including the well-known results of Ornstein and Zernike. 相似文献
2.
The deep inelastic structure function D(ω, q2) is calculated in the leading log approximation for . For larger ω up to ( the influence of reggeon cuts proves to slow down the growth of the structure function. A reggeon diagram technique is developed, and D is calculated up to a pre-exponent O(1), leading to D(ω, q2) ∝ q2 for . By assuming the reggeon diagrams when ω is still greater, one can expect to obtain a strong coupling behaviour: D(ω, q2) ∝ q2(ln ω)η (η <2). 相似文献
3.
John Lekner 《Physica A》1982,112(3):544-556
We derive comparison identities for waves satisfying the equation d2Ψ/dz2+q2(z)Ψ=0. One of these identities is used to show that to second order in the product (wavenumber component normal to interface) × (interface thickness), the reflection amplitude is given by , where l is a legnth determined by the deviation of the interface profile from a step, and q1, q2 are the normal components of the wave numbers in media 1 and 2 on either side of the interface. For the continuous interfaces discussed, l is about two-fifths of the 10–90 interface thickness. The corresponding formula for the transmission amplitude is . 相似文献
4.
Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γn associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γn=Γ(1)n+Γ(2)n+…where Γ(i)n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained. 相似文献
5.
Eugene Feenberg 《Annals of Physics》1973,81(1):154-164
A set of normalized linearly independent basis functions φ1, φ2, …, φj, … generates matrix representatives and of the Hamiltonian operator and the identity. An orthonormal basis , , …, , … generated by a Löwdin transformation is characterized by the distance in Hilbert space between and φj. The choice of positive definite minimizes these distances and maximizes the diagonal elements of . Again for positive definite and a finite basis, 1 ? j ? p, the analysis yields a general theorem on Trace (? p for all positive and negative integral values of n except n = ?1 and ? p for n = ?1).Sufficient conditions are determined which permit the application of the binomial theorem to the evaluation of the transform of . Approximate formulas for the energy eigenvalues through third order in nondiagonal matrix elements are presented in a compact form containing characteristic nonorthogonality corrections depending on the exterior or interior location of the matrix element in the perturbation formulas. 相似文献
6.
The temperature dependence of the field emission flicker noise spectral density functions has been investigated for potassium adsorbed on tungsten (112) planes by a probe hole technique. By integration of the spectral density functions the noise power for different frequency intervals Δ? is obtained. From the exponential temperature dependence of noise power “activation energies” qΔ? are determined. Plots of these energies versus coverage show a similar “oscillating” behaviour as recently found for or which indicates phase transitions of the adsorbed potassium submonolayers. The noise activation energies are discussed in terms of existing models and a comparison is made between the experimental q values and surface diffusion energies Ed as determined by conventional methods. 相似文献
7.
Consider an instantaneous severing interaction which at t = ts transforms is given N-soliton solution q0 into two new solutions, qL and qR, with discontinuous anitial conditions at t = ts such that qL(qR) is equal to q0 to the left (right) of the severing point xs and vanishes to the right (left) of xs. The soliton content of qL and qR is studied in the context of the cubic Schrödinger equation and the sine-Gordon equation by solving the direct scattering problem. It is shown that the motion constants Cn, n = 1, 2 …, are related by , Furthermore, if q0 contains N solitons and no contribution from the continuous spectrum, then qL(qR) contains NL(NR) solitons with 0 ? NL, NR ? N and NL + NR = N. The slicing puts a soliton into qL or qR, respectively as the slicing point xs is taken to the right or left of the soliton's “center” at t = ts. 相似文献
8.
In this paper we consider a product of n complex m×m matrices Ak (k=1,…,n) with singular values ∝(k)i ordered in decreasing magnitude. Using the spectral resolution for the operators , it is shown that This inequality is an extension of an inequality of von Neumann in the simple case that n=2. The necessary and sufficient condition for the equality sign to hold is established. Application of Hölder's inequality leads to further inequalities which can be useful in statistical mechanics. 相似文献
9.
B. Timmermann 《Reports on Mathematical Physics》1979,15(1):47-55
It is shown that under quite general assumptions on the operators A1,…,An (unbounded, symmetric) and on the domain on the realization of the algebra of polynomials , the strongest locally convex topology τst coincides with the uniform topology τ as well as with the strong operator topology τs. In the case n = 2 some conditions are given, under which these general assumptions are fulfilled. 相似文献
10.
The stress-optical coefficients and of RbCl and RbBr crystals have been measured at room temperature (26°C) over the wave length range 5750-2500 Å. 相似文献
11.
The linearized Fokker-Planck operator reads . The first term is rather simple, but the second one is very complicated. A much simpler - though exact - form of C(f0j, f1k) is proposed, for a special class of f1k occuring in diffusion theory. 相似文献
12.
13.
Yu. Oročko 《Reports on Mathematical Physics》1979,15(2):163-172
Let ,m? 1.Consider the operatorT0 = ?Δ+q with domain consisting of all bounded measurable functions , having bounded support, for which the distribution ?Δu+qu belongs to . The main result of the paper is essential self-adjointness of . The proof is independent of a method due to Kato who recently established the self-adjointness of a maximal Schrödinger operator corresponding to such potential. 相似文献
14.
The mobility μ of a very pure semiconductor at very low temperatures is investigated in terms of a model where electrons are scattered by charged impurities distributed uniformly in space, and the electron-electron interaction is taken into account by the Debye-Hueckel screening in the interaction potential. The equation for the current relaxation rate Γ, derived previously by the proper connected diagram expansion, incorporates the quasi-particle effect in a self-consistent manner. The solution of this equation at high carrier concentrations n yields the so-called Brooks-Herring formula. At lower concentrations, the solution deviates significantly from the latter. The solution is in general smaller than the standard expression for the rate based on the Boltzmann equation; and this is consistent with the existing conductivity data available. At the very low concentrations e.g. n = n3 = 1013cm?3 or lower for Ge, the mobility calculated is inversely proportional to the square-root of the impurity concentration ns, and has a -dependence (T: temperature). , where k is the dielectric constant. The conductivity data directly comparable with this formula are not available at present. However, the quasi-particle effect which led to this peculiar concentration-dependence should also show itself in the cyclotron resonance width; there, experiment and theory both show the -dependence for very pure semiconductors. 相似文献
15.
Exclusive decays such as G → ππ are studied in the framework ofperturbative QCD. We discuss the possibility of the constituent gluons' virtualness scaling as the glueball mass MG, which is a picture equivalent to a glueball containing a few slow-moving, heavy gluons. In this case, the decay rate exhibits a pinch singularity which enhances it by a factor of order (MG2/mq2)2 over the dimensional scaling expectation. This singularity is partially suppressed by Sudakov effects which reduce the enhancement factor to . 相似文献
16.
《Physics letters. A》2002,305(5):231-238
With the help of complexifying a five-parameter exponential-type potential model, we obtain a general complex version of the Pöschl–Teller II potential, , where qc=q0e2iαε, real V1>0, q0>0 and . It has been shown that this complex potential is P-pseudo-Hermitian and PT-symmetric, where the parity operator P acts on the position operator as . The discrete energy eigenvalues are shown to be real when while they are complex conjugate pairs if . 相似文献
17.
During the last few years many dynamical systems have been identified, that are completely integrable or even such to allow an explicit solution of the equations of motion. Some of these systems have the form of classical one-dimensional many-body problems with pair interactions; others are more general. All of them are related to Lie algebras, and in all known cases the property of integrability results from the presence of higher (hidden) symmetries. This review presents from a general and universal viewpoint the results obtained in this field during the last few years. Besides it contains some new results both of physical and mathematical interest.The main focus is on the one-dimensional models of n particles interacting pairwise via potentials V(q) = g2ν(q) of the following 5 types: . Here (q) is the Weierstrass function, so that the first 3 cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbor potential, gj2exp[-a(qj?qj+1)], is moreover considered. Various generalizations of these models, naturally suggested by their association with Lie algebras, are also treated. 相似文献
18.
W.K. Theumann 《Physica A》1975,83(1):85-120
The two-point correlation function ? (q, ξ) is calculated in the critical region of momentum space q in terms of a suitable correlation lenght ξ, by means of perturbation expansion to order 1/n, for an n-vector system with long-range interactions decaying as , for , where a is the spacing on a d-dimensional lattice, σ < d < 2σ and 0 < σ ? 2 ? ηSR. The calculations are done in zero field for T ? Tc. Explicit expansions for long-range propagators are developed for and for the neighborhood of σ ? 2 ? ηSR, in terms of which a universal, cut-off independent scaling function is obtained over the whole range of , and it is shown that the amplitude of the correlation-length dependence of the susceptibility becomes a universal parameter. Both the exponents and the coefficients of the expansion for fixed q as are calculated explicitly. The former are shown to require the validity of the operator-product expansion and explicit logarithmic correction terms are obtained for . For these and other dimensionalities, the coefficients are shown to be finite functions of d and σ. The correction to the Ornstein-Zernike form is given explicitly, with non-integer powers of x that have finite coefficients. 相似文献
19.
Jan T. łopuszański 《Reports on Mathematical Physics》1976,9(3):301-307
It is shown that for spinorial charges Q(L))α (α = 1, 2, L = 1, …, S) satisfying the commutation relations where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields. 相似文献
20.
The J = 2?1 microwave spectrum of six isotopic species of HSiF3 has been observed and assigned in excited states of five of the six fundamental vibrations. The assignment is based on relative intensities, double resonance experiments, and trial anharmonic force constant calculations. Analysis of the spectra leads to experimental values for five of the constants, all three l-doubling constants qt, one Fermi resonance constant φ233, and one zeta constant .The harmonic force field has been refined to all the available data on vibration wavenumbers, centrifugal distortion constants, and zeta constants. The cubic anharmonic force field has been refined to the data on and qt constants, using two models: a valence force model with two cubic force constants for SiH and SiF stretching, and a more sophisticated model. With the help of these calculations, the following equilibrium structure has been determined: , , ∠HSiF = 110.64(±3)°, 相似文献