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1.
Approximate expressions for the NMR spin relaxation rate constant in the rotating frame of reference R 1ρ are derived for two-site chemical exchange by consideration of the evolution of the average density operator using the stochastic Liouville equation. R 1ρ is obtained as a linearized approximation to the largest (least negative) eigenvalue of the matrix describing the evolution of the average density operator in the long-term limit. The expressions obtained are more accurate than existing expressions when exchange is not fast and the populations of the exchanging sites are close to equal. The new expressions for R 1ρ facilitate the interpretation of chemical exchange phenomena in proteins and other biological macromolecules. 相似文献
2.
A new and simple method to expand the anharmonic vibrational wave functions with respect to the harmonic oscillator wave functions is proposed. The coefficients of the expansion are given as matrix elements of the S function of the contact transformation in the perturbation theory and the explicit expressions of these coefficients are given within the approximation to the second order in λ. As an example of the expansion, the wave functions of water molecules were calculated and applied to the calculation of infrared band intensities and average values of dipole moments in several states. 相似文献
3.
O. Nachtmann 《The European Physical Journal C - Particles and Fields》2003,26(4):579-596
We relate the structure functions of deep inelastic lepton-nucleon scattering to current-current correlation functions in
a Euclidean field theory depending on a parameter r. The r-dependent Hamiltonian of the theory is P
0
-(1-r)P
3
, with P0 the usual Hamiltonian and P3 the third component of the momentum operator. We show that a small in the structure functions corresponds to the small r limit of the effective theory. We argue that for there is a critical regime of the theory where simple scaling relations should hold. We show that in this framework Regge
behaviour of the structure functions obtained with the hard pomeron ansatz corresponds to a scaling behaviour of the matrix
elements in the effective theory where the intercept of the hard pomeron appears as a critical index. Explicit expressions
for various analytic continuations of the structure functions and matrix elements are given as well as path integral representations
for the matrix elements in the effective theory. Our aim is to provide a framework for truly non-perturbative calculations
of the structure functions at small for arbitrary Q2.
Received: 16 July 2002 / Published online: 9 December 2002
RID="a"
ID="a" e-mail: O.Nachtmann@thphys.uni-heidelberg.de 相似文献
4.
Traditionally, the moment method has been used in kinetic theory to calculate transport coefficients. Its application to the
solution of more complicated problems runs into enormous difficulties associated with calculating the matrix elements of the
collision operator. The corresponding formulas for large values of the indices are either lacking or are very cumbersome.
In this paper relations between matrix elements are derived from very general principles, and these can be employed as simple
recurrence relations for calculating all the nonlinear and linear anisotropic matrix elements from assigned linear isotropic
matrix elements. Efficient programs which implement this algorithm are developed. The possibility of calculating the distribution
function out to 8–10 thermal velocities is demonstrated. The results obtained open up prospects for solving many topical problems
in kinetic theory.
Zh. Tekh. Fiz. 69, 6–9 (September 1999) 相似文献
5.
L. Stanton 《Molecular physics》2013,111(4):655-662
A study has been carried out on the relationship between formal scattering theory and the density matrix formalism. The density operator is developed in terms of the scattering operator S and the observable square modulus matrix elements of S are shown to be equivalent to elements of the density matrix. The Møller wave operators are similarly treated and subsequently used in obtaining the density matrix expression for the transition matrix. Finally, using the latter, it is shown that the hierarchy of approximations to the density matrix yields equivalent results to those obtained from the Born series. 相似文献
6.
V. S. Gerdjikov 《Letters in Mathematical Physics》1982,6(5):315-324
The main steps of constructing the spectral theory of the integro-differential operator A generating a class of exactly soluble nonlinear evolution equations (NLEE) related to the linear matrix first-order problem L, are outlined. Compact expressions for the diagonal of the resolvent of operator L through A are obtained. 相似文献
7.
S. M. Dunaevskii 《Physics of the Solid State》1999,41(12):2000-2003
Analytic expressions for the dispersion curves E(k) of RMnO3 (R=La, Pr, Nd, Sm, and other RE elements) have been obtained in the tight-binding approximation for the main types of magnetic
ordering on the Mn sublattice. The first calculation of E(k) taking into account the oxygen subsystem and mutual ordering of the manganese and RE sublattices is reported. The results
obtained permit a qualitative interpretation of some features observed in the behavior of the rare-earth manganites.
Fiz. Tverd. Tela (St. Petersburg) 41, 2179–2182 (December 1999) 相似文献
8.
G. V. Golubkov A. Z. Devdariani 《Russian Journal of Physical Chemistry B, Focus on Physics》2011,5(6):892-906
An analysis of the modern theory of associative ionization (AI) is performed, and ways of its further development are discussed.
The threshold behavior of the cross section of endothermic AI reactions is considered and it is shown that, in the quantum
case, its dependence on the above-threshold energy E is strictly linear, i.e., significantly different from the E
3/2 law ensuing from the semiclassical theory. This has a simple explanation, since the matrix elements of the scattering operator
are finite at E = 0 due to the tunneling effect. The possibility of describing the dynamics of an elementary AI event within the framework
of the diffusion approximation is substantiated, and the conditions of applicability of the theory of “quantum chaos” to treating
the spectrum of highly excited Rydberg molecules are examined. The quantum properties of the exothermic processes of AI and
Penning ionization in the case of the states of the interacting atoms being autoionizing are discussed in detail. A comparison
with the semiclassical theory is presented. 相似文献
9.
N. Iorgov S. Pakuliak V. Shadura Y. Tykhyy G. von Gehlen 《Journal of statistical physics》2010,139(5):743-768
We derive spin operator matrix elements between general eigenstates of the superintegrable ℤ
N
-symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed
by Baxter. For each pair of spaces (Onsager sectors) of the irreducible representations of the Onsager algebra, we calculate
the spin matrix elements between the eigenstates of the Hamiltonian of the quantum chain in factorized form, up to an overall
scalar factor. This factor is known for the ground state Onsager sectors. For the matrix elements between the ground states
of these sectors we perform the thermodynamic limit and obtain the formula for the order parameters. For the Ising quantum
chain in a transverse field (N=2 case) the factorized form for the matrix elements coincides with the corresponding expressions obtained recently by the
Separation of Variables method. 相似文献
10.
R. R. Nigmatullin A. A. Khamzin I. I. Popov 《Journal of Experimental and Theoretical Physics》2012,114(2):314-323
We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting
Fermi-gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable
approximation allows obtaining the so-called far-distance equations. These equations connecting the quantum states of a Fermi
particle with variables of the local field operator contain all necessary information related to the calculation of the desired
correlation functions and basic thermodynamic parameters of the many-body system. The basic expressions for the mean energy
and heat capacity for the electron gas at low temperatures in the high-density limit were obtained. All expressions are given
in the units of r
s
, where r
s
determines the ratio of a mean distance between electrons to the Bohr radius a
0. In these expressions, we calculate terms of the respective order r
s
and r
s
2. It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition
with respect to the parameter r
s
. 相似文献
11.
《Waves in Random and Complex Media》2013,23(4):321-337
Abstract We present a new asymptotic theory for scalar and vector wave scattering from rough surfaces which federates an extended Kirchhoff approximation (EKA), such as the integral equation method (IEM), with the first and second order small slope approximations (SSA). The new development stems from the fact that any improvement of the ‘high frequency’ Kirchhoff or tangent plane approximation (KA) must come through surface curvature and higher order derivatives. Hence, this condition requires that the second order kernel be quadratic in its lowest order with respect to its Fourier variable or formally the gradient operator. A second important constraint which must be met is that both the Kirchhoff approximation (KA) and the first order small perturbation method (SPM-1 or Bragg) be dynamically reached, depending on the surface conditions. We derive herein this new kernel from a formal inclusion of the derivative operator in the difference between the polarization coefficients of KA and SPM-1. This new kernel is as simple as the expressions for both Kirchhoff and SPM-1 coefficients. This formal difference has the same curvature order as SSA-1 + SSA-2. It is acknowledged that even though the second order small perturbation method (SPM-2) is not enforced, as opposed to the SSA, our model should reproduce a reasonable approximation of the SPM-2 function at least up to the curvature or quadratic order. We provide three different versions of this new asymptotic theory under the local, non-local, and weighted curvature approximations. Each of these three models is demonstrated to be tilt invariant through first order in the tilting vector. 相似文献
12.
Waterman's surface-integral expressions for the T-matrix elements are derived on the basis of the quantum-mechanical potential scattering approach in electromagnetic scattering problem. We use general definition of the elements of the T-matrix as the matrix elements of the dyadic transition operator and Lippman–Schwinger volume integral equation for the dyadic transition operator. The interrelations of the Q- and Waterman's T-matrix with the transition operator are shown. 相似文献
13.
W. Witschel 《Molecular physics》2013,111(2):419-424
A simple derivation of off-diagonal operator equivalents and their matrix elements is given in the framework of Schwinger's coupled boson representation of angular momentum theory. The operator equivalents are up to a factor identical with those recently given by Atkins and Seymour, but they are derived differently without making use of properties of spherical harmonics, symmetrization, 3j coefficients and the Wigner-Eckart theorem. 相似文献
14.
Spin-other-orbit interaction in highly excited configurations with p and g electrons in outer shells
The matrix of the operator of the spin-other-orbit interaction energy is constructed for npn’g and np
5
n’g configurations. The matrix elements of this operator are calculated in the single-configuration approximation with wave functions
in the LSJM representation and in the representation of uncoupled angular momenta using the known general formulas. The spin-other-orbit
interaction is represented by three direct and three exchange radial Marvin spin interaction integrals. 相似文献
15.
V. A. Ignatchenko D. S. Polukhin 《Journal of Experimental and Theoretical Physics》2017,125(1):91-103
Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter ε(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value ε and rms fluctuation Δε of the coupling parameter between waves from the homogeneous case (ε ≠ 0, Δε = 0) to the extremely randomized case (ε = 0, Δε ≠ 0) at various correlation wavenumbers of inhomogeneities k c. For the limiting case of infinite correlation radius (k c = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k c value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k c, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k c/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k c values), because it describes both the shape and width of peaks much better than the standard approximation. 相似文献
16.
K. B. Korotchenko 《Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques》2010,4(4):599-602
A new type of combinational channeling radiation induced by subbarrier (interband) transitions for the transverse motion of
relativistic electrons (positrons) is studied. It is known as diffracted channeling radiation (DCR). The formula describing
the DCR angular distribution in the case of axial channeling is obtained by taking into account the band structure of energy
levels for the transverse motion of electrons (positrons). It is shown that, in the two-wave approximation of the wave function
A(r) of virtual photons, the DCR matrix elements in the dipole approximation for axial and plane channeling coincide formally
(with the dimension of the problem taken into account). However, the formulas for DCR angular distributions in the cases of
axial and plane channeling differ considerably. 相似文献
17.
The finite-element approach to lattice field theory is both highly accurate (relative errors 1/N
2, whereN is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this Letter, we construct matrix elements for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian isH=p
2/2+q
2k
/2k. Construction of such matrix elements does not require solving the implicit equations of motion. Low-order approximations turn out to be quite accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator groundstate gives a result for thek=2 anharmonic oscillator groundstate energy accurate to better than 1% while a two-state approximation reduces the error to less than 0.1%. Accurate wavefunctions are also extracted. Analogous results may be obtained in the continuum, but there the computation is more difficult, and not generalizable to field theories in more dimensions. 相似文献
18.
19.
We propose and apply a combination of an ab initio
(band-structure) calculation with a many-body treatment including
screening effects.
We start from a linearized muffin-tin orbital (LMTO) calculation to
determine the Bloch functions for the Hartree one-particle
Hamiltonian, from which we calculate the static susceptibility
and dielectric function within the standard random
phase approximation (RPA). From the Bloch functions
we obtain maximally localized Wannier
functions, using a method proposed by Marzari and Vanderbilt.
Within this Wannier basis all relevant one-particle and unscreened and
screened Coulomb
matrix elements are calculated. This yields a
multi-band Hamiltonian in second quantization with ab initio parameters, for
which screening has been taken into account within the simplest standard
approximation. Then, established
methods of many-body theory are used.
We apply this concept to a simple metal, namely lithium (Li). Here the
maximally localized Wannier functions turn out to be of the sp3-orbital
kind. Furthermore, only the on-site contributions of the screened Coulomb
matrix elements are relevant, and a generalized, four-band Hubbard
model is justified. The screened
on-site Coulomb matrix elements are considerably smaller than the band width
because of which it is sufficient to calculate the selfenergy in
weak-coupling approximation. We compare results obtained within the screened
Hartree-Fock approximation (HFA) and within the second-order perturbation
theory (SOPT) in the Coulomb matrix elements for
Li and find that many-body effects are small but not negligible even for
this simple metal. 相似文献
20.
V Ramamurthy 《Pramana》1978,11(3):233-243
The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron, instead of approximating
it by a sphere, by making use of simple coordinate axes transformations and lattice symmetry in the case of f.c.c. and b.c.c.
structures. It is shown that there are several alternative ways of expressing the interference factor,S(q) and the different expressions given by Sharan and others and Bross and Bohn are just two of these equivalent expressions.
By comparing these expressions in the symmetry directions with those obtained under spherical approximation their apparent
differences are discussed. 相似文献