共查询到20条相似文献,搜索用时 31 毫秒
1.
Oluwole Adetunji 《Communications in Mathematical Physics》1976,48(3):199-205
This paper contains a few simple remarks on a paper by S. Schlieder and E. Seiler. For the special class of local fields treated by these authors we arrive at the same necessary condition for the existence of the Wilson-Zimmermann expansion (considered both as an operator expansion and as an expansion in bilinear forms) of the product ofn real scalar fields under the assumption that the singularities occurring asx
j
x
j+1;j=1, 2, ...,n–1, do not influence each other as long as these limits are simultaneously taken.This paper is part of a thesis presented to the University of Manitoba in partial fulfillment of the degree of Doctor of Philosophy. 相似文献
2.
A stochastic derivation of the Sivashinsky equation for the self-turbulent motion of a free particle
Kh. Namsrai 《Foundations of Physics》1980,10(9-10):731-742
Within the framework of the Kershaw approach and of a hypothesis on spatial stochasticity, the relativistic equations of Lehr and Park, Guerra and Ruggiero, and Vigier for stochastic Nelson mechanics are obtained. In our model there is another set of equations of the hydrodynamical type for the drift velocityv i(x j,t) and stochastic velocityu i(x j,t) of a particle. Taking into account quadratic terms in l, the universal length, we obtain from these equations the Sivashinsky equations forv i(x j,t) in the caseu i →0. In the limit l →0, these equations acquire the Newtonian form. 相似文献
3.
Steven Zelditch 《Communications in Mathematical Physics》1983,90(1):1-26
We determine the behavior in time of singularities of solutions to some Schrödinger equations onR n . We assume the Hamiltonians are of the formH 0+V, where \(H_0 = 1/2\Delta + 1/2 \sum\limits_{k = 1}^n { \omega _k^2 x_k^2 } \) , and whereV is bounded and smooth with decaying derivatives. When all ω k =0, the kernelk(t,x,y) of exp (?itH) is smooth inx for every fixed (t,y). When all ω1 are equal but non-zero, the initial singularity “reconstructs” at times \(t = \frac{{m\pi }}{{\omega _1 }}\) and positionsx=(?1) m y, just as ifV=0;k is otherwise regular. In the general case, the singular support is shown to be contained in the union of the hyperplanes \(\{ x|x_{js} = ( - 1)^l js_{y_{js} } \} \) , when ω j t/π=l j forj=j 1,...,j r . 相似文献
4.
《Journal of Physics and Chemistry of Solids》2001,62(9-10):1819-1825
The anomalous Pr antiferromagnetic order with high Néel temperature TN(Pr) are reported throughout the whole Pr1+xBa2−xCu3O7−y or 1212-type Cu(Ba2−xPrx)PrCu2O7−y system (−0.2<x<1; −0.4<y<1), where three distinct crystal structures were observed: orthorhombic 1212-chain O(I) (space group Pmmm), tetragonal T (P4/mmm), and orthorhombic O(II) (Cmmm). Systematic variation of TN(Pr) in this system as well as in other 1212 and 2212 cuprates MnA2PrCu2O7 (n=1, 2, M=Hg, Tl, Pb/Cu, Bi, Nb, Cu; A=Sr, Ba, Ba/Pr) was discussed through the correlation of TN(Pr) with Pr–O bond length. The importance of quasi-two-dimensional Pr–O–Pr superexchange magnetic coupling through strong wave function overlap between the overextended Pr-4f orbital with eight O-2pπ orbitals in the adjacent CuO2 bi-layer is discussed. No superconductivity was observed in the present study. 相似文献
5.
Omer Nur Magnus Willander Muhammad Q. Israr Fawzy G. El Desouky Mohamed A. Salem Ali B. Abou Hamad Inas K. Battisha 《Physica B: Condensed Matter》2012,407(14):2697-2704
Nano-composite Ba1−xSr(x)TiO3 (BST), where x=0.01–0.50 and doped with different concentrations of iron Ba(1−x−y)Sr(x)TiFe (y)O3 (BSTF), where x=0.01 and y=0.01–0.05 powders were prepared by sol–gel method. 相似文献
6.
JOSE PITARCH-RUIZ JOSE SANCHEZ-MARIN ALFREDO SANCHEZ DE MERAS DANIEL MAYNAU 《Molecular physics》2013,111(3):483-494
The vertical electronic spectrum of formaldehyde has been studied by means of (SC)2-MR-SDCI and CCLR methods. Two basis sets of atomic natural orbitals (ANOs) complemented with a one-centre series of Rydberg orbitals were used. The first was taken from the CASPT2 study by Merchán, M., and Roos, B. O., 1995, Theoret. Chim. Acta, 92, 221, and may be described as C,O[4s3pld]/H[2slp] with a lslpld Rydberg series centred in the charge centroid of the 2B2 state of the cation. The second was a larger basis set that may be described as C,O[6s5p3d2f]/H[4s3p2d] + 3s3p3d in the same centre. The (SC)2 dressing may be applied efficiently to an MR-SDCI method and comparison with the dressed CAS-SDCI is satisfactory, in spite of the remarkable reduction in the CI space dimension. The consistency of the (SC)2-MR-SDCI results was tested also against the CCLR and CASPT2 results using the same basis sets and against the CCLR results using Dunning's aug- and daug-cc-pVQZ basis sets. The 3A1(π → π *) state is correctly placed as the second excited triplet while the highly multi-configurational nature of the 1A1(π → π *) state is confirmed as well as its greatly mixed valence-Rydberg nature. This state is predicted as lying under the 10 eV level, on top of the (ny → 3d) Rydberg states that are predicted in the 8.9–9.5eV region. The 5 1B2(ny → 4s) Rydberg state and the 1B2(σy → π*) also are predicted in this region. The triplet states also were calculated with the (SC)2-MR-SDCI method. The vertical ordering of the 2 1A1(ny → 3py) and 2 1B2(ny → 3pz) states is discussed, as well as that of the 1B1(σ → π*) and the Rydberg 1B1(ny → 3dxy) states. This work shows the highly reliable values that may be reached applying the dressing method along with a large basis set. Such a procedure is made possible using an MR-SDCI selection of spaces instead of the CAS-SDCI that was used up to now in most (SC)2 dressing applications. 相似文献
7.
8.
Ai-Bing Yu 《Particle & Particle Systems Characterization》1994,11(4):291-298
An investigation was carried out of the transformation between the number, length, surface and volume size distributions expressed by Johnson's SB distribution function – the bounded log-normal distribution function. As is well known, if any of the number, length, surface and volume distributions is log-normal, all the others will also be log-normal. Theoretical analysis suggests that the SB function may have a similar property. This was confirmed by a computer-aided numerical simulation, in which emphasis was given to the transformation between successive order size distributions, i.e. ?i(x) → ?i + 1(x) or ?i(x) → ?i ? 1(x). The numerical results can be applied to the particle size distribution transformation because this transformation can generally be made step by step, for example, ?i → ?i?1 (x) → ?i ? 2(x) → … → ?j(x) for ?i(x) → ?j(x) ( i > j). 相似文献
9.
If for a relativistic field theory the expectation values of the commutator (Ω|[A (x),A(y)]|Ω) vanish in space-like direction like exp {? const|(x-y 2|α/2#x007D; with α>1 for sufficiently many vectors Ω, it follows thatA(x) is a local field. Or more precisely: For a hermitean, scalar, tempered fieldA(x) the locality axiom can be replaced by the following conditions 1. For any natural numbern there exist a) a configurationX(n): $$X_1 ,...,X_{n - 1} X_1^i = \cdot \cdot \cdot = X_{n - 1}^i = 0i = 0,3$$ with \(\left[ {\sum\limits_{i = 1}^{n - 2} {\lambda _i } (X_i^1 - X_{i + 1}^1 )} \right]^2 + \left[ {\sum\limits_{i = 1}^{n - 2} {\lambda _i } (X_i^2 - X_{i + 1}^2 )} \right]^2 > 0\) for all λ i ≧0i=1,...,n?2, \(\sum\limits_{i = 1}^{n - 2} {\lambda _i > 0} \) , b) neighbourhoods of theX i 's:U i (X i )?R 4 i=1,...,n?1 (in the euclidean topology ofR 4) and c) a real number α>1 such that for all points (x):x 1, ...,x n?1:x i ∈U i (X r ) there are positive constantsC (n){(x)},h (n){(x)} with: $$\left| {\left\langle {\left[ {A(x_1 )...A(x_{n - 1} ),A(x_n )} \right]} \right\rangle } \right|< C^{(n)} \left\{ {(x)} \right\}\exp \left\{ { - h^{(n)} \left\{ {(x)} \right\}r^\alpha } \right\}forx_n = \left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ r \\ \end{array} } \right),r > 1.$$ 2. For any natural numbern there exist a) a configurationY(n): $$Y_2 ,Y_3 ,...,Y_n Y_3^i = \cdot \cdot \cdot = Y_n^i = 0i = 0,3$$ with \(\left[ {\sum\limits_{i = 3}^{n - 1} {\mu _i (Y_i^1 - Y_{i{\text{ + 1}}}^{\text{1}} } )} \right]^2 + \left[ {\sum\limits_{i = 3}^{n - 1} {\mu _i (Y_i^2 - Y_{i{\text{ + 1}}}^{\text{2}} } )} \right]^2 > 0\) for all μ i ≧0,i=3, ...,n?1, \(\sum\limits_{i = 3}^{n - 1} {\mu _i > 0} \) , b) neighbourhoods of theY i 's:V i(Y i )?R 4 i=2, ...,n (in the euclidean topology ofR 4) and c) a real number β>1 such that for all points (y):y 2, ...,y n y i ∈V i (Y i there are positive constantsC (n){(y)},h (n){(y)} and a real number γ(n){(y)∈a closed subset ofR?{0}?{1} with: γ(n){(y)}\y 2,y 3, ...,y n totally space-like in the order 2, 3, ...,n and $$\left| {\left\langle {\left[ {A(x_1 ),A(x_2 )} \right]A(y_3 )...A(y_n )} \right\rangle } \right|< C_{(n)} \left\{ {(y)} \right\}\exp \left\{ { - h_{(n)} \left\{ {(y)} \right\}r^\beta } \right\}$$ for \(x_1 = \gamma _{(n)} \left\{ {(y)} \right\}r\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 1 \\ \end{array} } \right),x_2 = y_2 - [1 - \gamma _{(n)} \{ (y)\} ]r\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 1 \\ \end{array} } \right)\) and for sufficiently large values ofr. 相似文献
10.
Makoto Matsumoto 《Reports on Mathematical Physics》1979,15(3):375-386
We consider the length of a vector in a Finsler space with the fundamental function L(x,y). The length of a vector X is usually defined as the value L(x,X) of L. On the other hand, we have an essential tensor gij(x,y), called the fundamental tensor, and the concept of relative length |Xy| of X may be introduced by |X|yy = gij(x,y)XiXj with re spect to a supporting element y. The question arises whether is L(x,X) the minimum of |X|y or not? If there exists a supporting element y satisfying |X|y < L(x,X), then a curve x(t) in the Finsler space will be measured shorter than the usual length, by integrating |dx/dt|y with the field of such supporting element y(t) along the curve. 相似文献
11.
We prove that the one-site distribution of Gibbs states (for any finite spin setS) on the Bethe lattice is given by the points satisfying the equation π=T 2π, whereT=h·A·?, with?(x)=x (q?1/q,h(x)=(x∥x∥ q ) q ,A=(a(r, s)∶r, s∈S), and $$a(r,s) = \exp (K[r,s] + (1/q)[N,r + s])$$ We also show that forA a symmetric, irreducible operator the nonlinear evolution on probability vectorsx(n+1)=Ax(n) p ∥Ax(n) p ∥1 withp>0 has limit pointsξ of period?2. We show thatA positive definite implies limit points are fixed points that satisfy the equationAξ p=λξ. The main tool is the construction of a Liapunov functional by means of convex analysis techniques. 相似文献
12.
Kenji Yajima 《Communications in Mathematical Physics》1980,75(2):153-178
Scattering theory for time dependent HamiltonianH(t)=?(1/2) Δ+ΣV j (x?q j (t)) is discussed. The existence, asymptotic orthogonality and the asymptotic completeness of the multi-channel wave operators are obtained under the conditions that the potentials are short range: |V j (x)|≦C j (1+|x|)?2?ε, roughly spoken; and the trajectoriesq j (t) are straight lines at remote past and far future, and |q j (t)?q k (t)| → ∞ ast → ± ∞ (j≠k). 相似文献
13.
K. Pohlmeyer 《Communications in Mathematical Physics》1968,7(1):80-92
For a hermitean, scalar, tempered fieldA(x) the locality axiom can be replaced by the following condition: For any two natural numbersn andj with 1≦j<n and for any configurationX(n, j):X 1, ...,X j?1,X j ,X j+1,X j+2, ...X n that is totally space-like in both orders: 1, ...,j?1,j, j+1,j+2, ...,n and 1, ...,j?,j+1,j,j + 2, ...,n there exist constants α(n,j)>2,C(X(n, j))>0,h(X(n, j))>0 such that with \(x_k = X_k \sqrt { - x^2 } \) : $$\begin{gathered} |\langle A(x_1 ) \ldots A(x_{j - 1} )[A(x_j ), A(x_{j + 1} )] A(x_{j + 2} ) \ldots A(x_n )\rangle |< \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,< C(X(n, j)) exp\{ - h(X(n, j))\sqrt { - x^2 } ^{\alpha (n, j)} \} \hfill \\ \end{gathered} $$ for ?x 2>1. 相似文献
14.
H.A Tolhoek 《Physica A》1977,86(2):278-302
In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions GMR(x) and GMA(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions GMR(x) and GMA(x) approach the Green's functions ΔR(x) and ΔA(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of GMA(x) and GMA(x) is the same as of ΔR(x) and ΔA(x) - and also the same as for DR(x) and DA(x) for t→ ± ∞, where DR and DA are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. 相似文献
15.
An exact solution to the Schrödinger equation for the ground state of two-dimensional Pauli electrons in a nonuniform transverse magnetic field H is presented for two cases. In the first case, the field H depends on a single variable, H = H(y), while in the second case, the field is axially symmetric, H = H(ρ), ρ2=x 2+y 2. The electron density distributions n = n(y) and n = n(ρ) that correspond to a completely filled lower level are found. For quasiuniform fields of fixed sign, the functions n(y) and n(ρ) are locally related to the magnetic field: n(y) = H(y)/?0 and n(ρ) = H(ρ)/?0, where ?0 = hc/|e| is a magnetic flux quantum. Magnetic fields are considered that are periodic, singular, and bounded in the plane xy. Finite electron objects in a nonuniform magnetic field are analyzed. 相似文献
16.
Generating relations involving two variable laguerre polynomials Ln(x, y) are derived. The process involves the construction of a three-dimensional Lie algebra isomorphic to special linear algebra sl(2) with the help of Weisner's method by giving suitable interpretations to the index n of the polynomials Ln(x, y). 相似文献
17.
Electron paramagnetic resonance (EPR) studies of V O2+ ions in L-asparagine monohydrate single crystals are reported at room temperature. It is found that the V O2+ ion takes up an interstitial site. The angular variations of the EPR spectra in three mutually perpendicular planes are used to determine the principal g and A values and their direction cosines. The values of g and A parameters are: gx=1.9011, gy=2.1008, gz=1.9891 and Ax=100, Ay=78, Az=126 (×10−4) cm−1. The optical absorption spectrum of V O2+ ions in L-asparagine monohydrate is also studied at room temperature. The band positions are calculated using the energy expressions and compared with the observed band positions to confirm the transitions. The best-fit values of the crystal field (Dq) and tetragonal (Ds and Dt) parameters are evaluated from the observed band positions. 相似文献
18.
For a q × q matrix x = (x i, j ) we let ${J(x)=(x_{i,j}^{-1})}For a q × q matrix x = (x
i, j
) we let J(x)=(xi,j-1){J(x)=(x_{i,j}^{-1})} be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x)=(xi,j)-1{I(x)=(x_{i,j})^{-1}} denote the matrix inverse, and we define K=I°J{K=I\circ J} to be the birational map obtained from the composition of these two involutions. We consider the iterates Kn=K°?°K{K^n=K\circ\cdots\circ K} and determine the degree complexity of K, which is the exponential rate of degree growth d(K)=limn?¥( deg(Kn) )1/n{\delta(K)=\lim_{n\to\infty}\left( deg(K^n) \right)^{1/n}} of the degrees of the iterates. Earlier studies of this map were restricted to cyclic matrices, in which case K may be represented by a simpler map. Here we show that for general matrices the value of δ(K) is equal to the value conjectured by Anglès d’Auriac, Maillard and Viallet. 相似文献
19.
Freeman J. Dyson 《Communications in Mathematical Physics》1969,12(2):91-107
Existence of a phase-transition is proved for an infinite linear chain of spins μ j =±1, with an interaction energy $$H = - \sum J(i - j)\mu _i \mu _j ,$$ whereJ(n) is positive and monotone decreasing, and the sums ΣJ(n) and Σ (log logn) [n 3 J(n)]?1 both converge. In particular, as conjectured byKac andThompson, a transition exists forJ(n)=n ?α when 1 < α < 2. A possible extension of these results to Heisenberg ferromagnets is discussed. 相似文献
20.
For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ j N =1 (x j ? 〈x〉) is computed exactly and shown to satisfy a central limit theorem asN → ∞. For the circular random matrix ensemble the p.d.f.’s for the statistics ½Σ j N =1 (θ j ?π) and ? Σ j N =1 log 2 |sinθ j/2| are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem asN → ∞. 相似文献