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1.
We propose modified Faddeev-Merkuriev integral equations for solving the 2→2, 3 quantum three-body Coulomb scattering problem.
We show that the solution of these equations can be obtained using a discrete Hilbert-space basis and that the error in the
scattering amplitudes due to truncating the basis can be made arbitrarily small. The Coulomb Green’s function is also confined
to the two-body sector of the three-body configuration space by this truncation and can be constructed in the leading order
using convolution integrals of two-body Green’s functions. To evaluate the convolution integral, we propose an integration
contour that is applicable for all energies including bound-state energies and scattering energies below and above the three-body
breakup threshold. 相似文献
2.
In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate
Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew’s triple and induced Dirac
structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this
framework provides a means of deriving discrete Lagrange–Dirac and nonholonomic Hamiltonian systems. In particular, this yields
nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange–d’Alembert–Pontryagin and Hamilton–d’Alembert
variational principles, which provide an alternative derivation of the same set of integration algorithms. The paper provides
a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of discrete Dirac mechanics,
as well as a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators. 相似文献
3.
A. V. Shanin 《Journal of Mathematical Sciences》2008,148(5):769-783
The problems of diffraction by a slit or a strip having ideal boundary conditions, and some other problems, can be reduced
to the problem of wave propagation on a multisheet surface by applying the method of reflections. Further simplifications
of the problem can be achieved by applying an embedding formula. As a result, the solution of the problem with a plane wave
incidence becomes expressed in terms of the edge Green’s functions, i.e., in terms of the fields generated by dipole sources
localized at branchpoints of the surface.
The present paper is devoted to finding the edge Green’s functions. For this problem, two sets of differential equations,
namely, the coordinate and spectral equations, are used. The properties of solutions of these equations are studied. Bibliography:
9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 233–256. 相似文献
4.
V. A. Moskalenko 《Theoretical and Mathematical Physics》1997,110(2):243-255
We investigate the system of conductivity electrons and f-localized electrons described by the periodic Anderson model. Single-site
hybridization of the state of two constituent subsystems of electrons is treated as a perturbation. We develop a new diagram
technique based on the use of multiparticle one-site irreducible Green’s functions for the f-electrons and the standard Wick
theorem for the subsystem of conductivity electrons. We derive the Dyson equations for the one-particle Green’s functions
and find the relation between these functions. These results are exact and can be used as a starting point for self-consistent
approximations. In the Hubbard-I approximation, we analyze the spectrum of one-particle perturbations.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 308–322, February, 1997. 相似文献
5.
6.
In this paper, we investigate Green’s functions for various stationary problems with nonlocal boundary conditions. We express
the Green’s function per Green’s function for a problem with classical boundary conditions. This property is illustrated by
various examples. Properties of Green’s functions with nonlocal boundary conditions are compared with those for classical
problems.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-73/09. 相似文献
7.
N. M. Plakida 《Theoretical and Mathematical Physics》2008,154(1):108-122
Based on the method of the equations of motion for two-time Green’s functions, we derive superconductivity equations for different
types of interactions related to the scattering of electrons on phonons and spin fluctuations or caused by strong Coulomb
correlations in the Hubbard model. We derive an exact Dyson equation for the matrix Green’s function with the self-energy
operator in the form of the multiparticle Green’s function. Calculating the self-energy operator in the approximation of noncrossing
diagrams leads to a closed system of equations corresponding to the Migdal-Eliashberg strong-coupling theory. We propose a
theory of high-temperature superconductivity due to kinematic interaction in the Hubbard model. We show that two pairing channels
occur in systems with a strong Coulomb correlation: one due to the antiferromagnetic exchange in interband hopping and the
other due to the coupling to spin and charge fluctuations in hopping within one Hubbard band.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 129–146, January, 2008. 相似文献
8.
V. A. Moskalenko P. Entel D. F. Digor L. A. Dohotaru R. Citro 《Theoretical and Mathematical Physics》2008,155(3):914-935
We propose a diagram theory around the atomic limit for the single-impurity Anderson model in which the strongly correlated
impurity electrons hybridize with free (uncorrelated) conduction electrons. Using this diagram approach, we prove a linked-cluster
theorem for the vacuum diagrams and derive Dyson-type equations for localized and conduction electrons and the corresponding
equations for mixed propagators. The system of equations can be closed by summing an infinite series of ladder diagrams containing
irreducible Green’s functions. The result allows discussing resonances associated with quantum transitions at the impurity
site.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 474–497, June, 2008. 相似文献
9.
N. M. Plakida 《Theoretical and Mathematical Physics》2011,168(3):1303-1317
Based on constructing the equations of motion for the two-time Green’s functions, we discuss calculating the dynamical spin
susceptibility and correlation functions in the Heisenberg model. Using a Mori-type projection, we derive an exact Dyson equation
with the self-energy operator in the form of a multiparticle Green’s function. Calculating the self-energy operator in the
mode-coupling approximation in the ferromagnetic phase, we reproduce the results of the temperature diagram technique, including
the correct formula for low-temperature magnetization. We also consider calculating the spin fluctuation spectrum in the paramagnetic
phase in the framework of the method of equations of motion for the relaxation function. 相似文献
10.
L. A. Alexeyeva G. K. Zakir’yanova 《Computational Mathematics and Mathematical Physics》2011,51(7):1194-1207
The method of boundary integral equations is developed as applied to initial-boundary value problems for strictly hyperbolic
systems of second-order equations characteristic of anisotropic media dynamics. Based on the theory of distributions (generalized
functions), solutions are constructed in the space of generalized functions followed by passing to integral representations
and classical solutions. Solutions are considered in the class of singular functions with discontinuous derivatives, which
are typical of physical problems describing shock waves. The uniqueness of the solutions to the initial-boundary value problems
is proved under certain smoothness conditions imposed on the boundary functions. The Green’s matrix of the system and new
fundamental matrices based on it are used to derive integral analogues of the Gauss, Kirchhoff, and Green formulas for solutions
and solving singular boundary integral equations. 相似文献
11.
Yuri A. Melnikov 《Central European Journal of Mathematics》2010,8(1):53-72
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value
problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous
isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected
region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range
of effective applicability for the Green’s function version of the boundary integral equation method making the latter usable
for equations with piecewise-constant coefficients. 相似文献
12.
M. O. Katanaev 《Theoretical and Mathematical Physics》2006,148(3):1264-1294
The phase space of general relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and
conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial form.
We propose a new expression for the generating functional for the Green’s functions. We show that the Dirac bracket defines
a degenerate Poisson structure on a manifold and the second-class constraints are the Casimir functions with respect to this
structure. As an application of the new variables, we consider the Friedmann universe.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 3, pp. 459–494, September, 2006. 相似文献
13.
K. V. Stepanyantz 《Theoretical and Mathematical Physics》2006,146(3):321-334
For the massless N=1 supersymmetric electrodynamics regularized by higher derivatives, we partially sum the Feynman diagrams
that define the divergent part of the two-point Green’s function and cannot be found from Schwinger—Dyson equations and Ward
identities. The result can be written as a special identity for Green’s functions.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 385–401, March, 2006. 相似文献
14.
Vladislav V. Kravchenko Marco P. Ramirez T. 《Advances in Applied Clifford Algebras》2011,21(3):547-559
Considering one of the fundamental notions of Bers’ theory of pseudoanalytic functions the generating pair via an intertwining
relation we introduce its generalization for biquaternionic equations corresponding to different first-order systems of mathematical
physics with variable coefficients. We show that the knowledge of a generating set of solutions of a system allows one to
obtain its different form analogous to the complex equation describing pseudoanalytic functions of the second kind and opens
the way for new results and applications of pseudoanalytic function theory. As one of the examples the Maxwell system for
an inhomogeneous medium is considered, and as one of the consequences of the introduced approach we find a relation between
the time-dependent one-dimensional Maxwell system and hyperbolic pseudoanalytic functions and obtain an infinite system of
solutions of the Maxwell system. Other considered examples are the system describing force-free magnetic fields and the Dirac
system from relativistic quantum mechanics. 相似文献
15.
Seyidali S. Akhiev 《Acta Appl Math》2007,95(2):73-93
A linear, completely nonhomogeneous, generally nonlocal, multipoint problem is investigated for a second-order ordinary integro-differential
equation with generally nonsmooth coefficients, satisfying some general conditions like p-integrability and boundedness. A system of three integro-algebraic equations named the adjoint system is introduced for the
solution. The solvability conditions are found by the solutions of the homogeneous adjoint system in an “alternative theorem”.
A version of a Green’s functional is introduced as a special solution of the adjoint system. For the problem with a nontrivial
kernel also a notion of a generalized Green’s functional is introduced by a projection operator defined on the space of solutions.
It is also shown that the classical Green and Cauchy type functions are special forms of the Green’s functional.
The author passed away in 2006 prior to publication of the article. 相似文献
16.
Using the diagram technique in the atomic representation in the generalized chaotic phase approximation, we solve the problem
of calculating the dynamical magnetic susceptibility of the periodic Anderson model in the strong electron correlation regime.
We express the dynamical magnetic susceptibility in terms of four Matsubara Green’s functions describing partial contributions,
which are calculated based on exact solutions of integral equations. 相似文献
17.
In this paper, we investigate a third-order linear differential equation with three additional conditions. We find a solution
to this problem and give a formula and an existence condition for Green’s function. We compare two Green’s functions for two
such problems with different additional conditions: nonlocal and classical boundary conditions. Formula applications are shown
by examples. 相似文献
18.
Yu. A. Tserkovnikov 《Theoretical and Mathematical Physics》2008,154(1):165-174
We use the mode-coupling approximation to derive a closed system of equations for the Green’s functions for the transverse
and longitudinal spin components taking the sum rules related to the finiteness of the spin into account exactly.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 197–207, January, 2008. 相似文献
19.
20.
We obtain a one-parameter family of (q, p)-representations of quantum mechanics; the Wigner distribution function and the distribution function we previously derived are particular cases in this family. We find the solutions o the evolution equations or the microscopic classical and quantum distribution functions in the form of integrals over paths in a phase space. We show that when varying canonical variables in the Green’s function of the quantum Liouville equation, we must use the total increment o the action functional in its path-integral representation, whereas in the Green’s function of the classical Liouville equation, the linear part o the increment is sufficient. A correspondence between the classical and quantum schemes holds only under a certain choice of the value of the distribution family parameter. This value corresponds to the distribution unction previously found.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 3, pp. 401–416, June, 2005. 相似文献