共查询到20条相似文献,搜索用时 31 毫秒
1.
M. Melgaard 《Few-Body Systems》2002,32(1-2):1-22
For a fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schr?dinger operator with a constant
magnetic field and an axisymmetrical electric potential V. Asymptotic expansions for the resolvent of the Hamiltonian H
m
= H
om
+ V are deduced as the spectral parameter tends to the lowest Landau threshold E
0. In particular it is shown that E
0 can be an eigenvalue of H
m
. Furthermore, asymptotic expansions of the scattering matrix associated with the pair (H
m
, H
om
) are derived as the energy parameter tends to E
0.
Received December 11, 2000; accepted in final form June 16, 2001 Published online June 10, 2002 相似文献
2.
D. Yafaev 《Communications in Mathematical Physics》1998,191(1):183-218
We consider the Schr?dinger operator with a long-range potential V(x) in the space . Our goal is to study spectral properties of the corresponding scattering matrix and a diagonal singularity of its kernel
(the scattering amplitude). It turns out that in contrast to the short-range case the Dirac-function singularity of at the diagonal disappears and the spectrum of the scattering matrix covers the whole unit circle. For an asymptotically homogeneous function
V(x) of order we show
that typically , where the module w and the phase ψ are asymptotically homogeneous functions, as , of orders and , respectively. Leading terms of asymptotics of w and ψ at are calculated. In the case ρ=1 our results generalize (in the limit ) the well-known formula of Gordon and Mott.
As a by-product of our considerations we show that the long-range
scattering fits into the theory of smooth perturbations. This gives an elementary proof of existence and completeness of wave
operators in the theory of long-range scattering. In this paper we concentrate on the case ρ>1/2 when the theory of pseudo-differential
operators can be extensively used.
Received: 29 January 1997 / Accepted: 6 May 1997 相似文献
3.
A scattering approach for correlated one-dimensional systems is developed. The perfect contact to charge reservoirs is encoded
in time-dependent boundary conditions. The conductance matrix for an arbitrary gated wire, respecting charge conservation,
is expressed through a dynamic scattering matrix. Two applications are developed. First, it is shown that the dc conductance
is equal to e
2/h for any model with conserved total left- and right-moving charges. Second, the ac conductance matrix is explicitly computated
for the Tomonaga-Luttinger model (TLL).
Received 31 August 1998 相似文献
4.
A. H. Taub 《Letters in Mathematical Physics》1987,13(3):201-210
Five-dimensional classical unified field theories may be described in terms of the geometry of a five-dimensional Lorentz space V
5.This space may be considered as a principal bundle over spacetime V
4with metric g
ij
and gauge group U(1). It has been shown that when V
4is asymptotically flat, the total energy momentum vector of V
5is nonspacelike, and that the gravitational mass of V
4has a lower bound. These results obtain when V
5is replaced by a Lorentzian space V
N
,a principal bundle over an asymptotically flat V
4with an Abelian group G as its gauge group. 相似文献
5.
Dong Zhengchao 《中国科学G辑(英文版)》2006,49(5):597-605
We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field
can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal
state, exhibiting a first-order phase transition; (2) the Zeeman magnetic field may make the zero-bias conductance peak split
into two peaks, and the energy difference between the two splitting peaks in the conductance spectrum is equal to 2h
0 (h
0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes
of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear
out the peaks, however, neither of them can influence the Zeeman effect. 相似文献
6.
The interplay between superconductivity (SC) and antiferromagnetism (AFM) is studied in strongly correlated systems of high
T
c
Cuprate superconductors. It is assumed that superconductivity arises due to BCS pairing mechanism in presence of AFM in Cu lattices of Cu-O planes. The total Hamiltonian of the system is mean field one
and has been solved exactly by writing the equations of motion for the single particle Green’s functions. Equations for the
appropriate single particle co-relation functions are derived and the order parameters corresponding to SC and AFM are determined.
It is assumed that the Fermi energy ∈
F
= 0 and the renormalized localized f energy level coincide with the Fermi level. All the quantities in the final equation for h and Δ are made dimensionless by dividing by 2t, where t is the hopping integral. The temperature dependent values of staggered magnetic field (h) and SC gap (Δ) were determined by solving self-consistent equations for h and Δ. The quasiparticle energy bands are function of AFM gap (h), SC gap (Δ) and hybridization (V). Then the dispersion of quasi-particles are studied at different temperatures by considering temperature dependent values
of h and Δ and varying other different model parameters.
相似文献
7.
András Vasy 《Communications in Mathematical Physics》1999,200(1):105-124
In this paper we show that generalized eigenfunctions of many-body Hamiltonians H with short-range two-body interactions have distributional asymptotics at non-threshold channels. The leading terms of the
asymptotics can be used to define a scattering matrix, and we show that this is the same (up to normalization) as that arising
from the standard wave-operator approach. We also prove the existence of local distributional asymptotics for locally approximate
generalized eigenfunctions in the more general setting of short range perturbations of a scattering metric, defined by Melrose
in [13].
Received: 29 October 1997 / Accepted: 19 June 1998 相似文献
8.
In this paper the quantum hyperbolic equation formulated in our earlier paper [Found. Phys. Lett.
10, 599 (1997)] is applied to the study of the propagation of the initial thermal state of the universe. It is shown that the
propagation depends on the barrier height. The Planck wall potential is introduced,V
P
= ħ/8tP
= 1.125 1018 GeV, wheret
P
is a Planck time. For the barrier heightV <V
P
, the master thermal equation isthe modified telegrapher’sequation, and for barrier heightV >V
P
the master equation is theKlein- Gordon equation. The solutions of both type equations for Cauchy boundary conditions are discussed. 相似文献
9.
A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV
(3) (k
1j1; —k
1j1;o
j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction
picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings
in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements
will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets
altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that
the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV
(3) (k
1j1;k
2j2;k
3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients. 相似文献
10.
Proton elastic scattering data from 197Au, 208Pb and 209Bi at energies near the Coulomb barrier are analyzed. The energy dependences of the real volume and imaginary surface-derivative potential depths VR and WSF of a local optical-model potential with fixed geometric parameters are found to be much more rapid than at higher energies. The strong energy dependence of VRnear the Coulomb barrier is explained in terms of the non-locality of the nucleon-nucleus interaction. 相似文献
11.
A.G. Moritz 《Molecular physics》2013,111(5):945-946
The rotation-ring-puckering problem of four-membered ring cyclobutane-type molecules with D 4h -D 2d conformations is formulated as a dynamical system in the eulerian angles and the polar coordinate ?. Classical and quantum-mechanical hamiltonians and their symmetry group O ++(3) × D ∞h are discussed. The kinetic energy matrix coefficients gmm are found to be irrational functions of the trigonometric polynomial 3 + cos 2? in the internal coordinate ?. It is shown that the energy matrix coefficients may all be expressed as Laurent coefficients by means of the hypergeometric function 2 F 1, the convergence being determined by the roots of the kinetic determinant. Selection rules and matrix elements for rotation-ring-puckering Raman transitions are given. 相似文献
12.
R. N. Kyutt 《Physics of the Solid State》1997,39(7):1052-1056
Double-and triple-crystal diffractometry have been used to study structural perfection of a ∼1 μm-thick Ga1−x
InxSb1−y
Asy epitaxial film (x=0.9, y=0.8) on GaSb. It is shown that scattering from samples of this system can be divided into coherent and diffuse. The arrangement
of reciprocal-lattice points of the film and substrate in the two-dimensional intensity distribution for asymmetrical reflections
argues for the absence of elastic-strain relaxation. No dislocation networks are formed, and the diffuse scattering is produced
by Coulomb-type defects. Localization of diffuse scattering in reciprocal space suggests that these defects reside in the
epitaxial film. The diffuse-scattering distribution in asymmetrical reflections is shown to be anomalous; namely, it extends
in a direction parallel to the surface and is split into two maxima. Schemes have been proposed and realized for measuring
integral distributions of diffracted intensity along the surface and perpendicular to it, and their potential for studying
diffuse scattering from defects is explored.
Fiz. Tverd. Tela (St. Petersburg) 39, 1188–1193 (July 1997) 相似文献
13.
We report on a strong damping of the localized surface plasmon polariton resonance of gold nanoparticles. The ultra-fast dephasing
time of localized surface plasmon polariton resonances in gold nanoparticles was systematically studied as a function of the
particle size at a fixed photon energy of h
ν=1.85 eV. Dephasing times ranging from T2expT_{2}^{\mathrm{exp}} = 5.5 fs to 15.0 fs were extracted and an influence of the reduced dimensions was detected. We have identified two dominant
damping mechanisms: the well-known surface scattering and, for the first time, band structure changes. We have quantified
the influence of these band structure changes on the optical properties by determining the essential damping parameter A to be A
exp=0.32 nm/fs. 相似文献
14.
S.-H. Dong 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,11(2):159-165
In terms of the modified Sturm-Liouville theorem, the Levinson theorem for the one-dimensional Klein-Gordon equation with
a symmetric potential V(x) is established. It is shown that the number N+ (N-) of bound states with even (odd) parity is related to the phase shift of the scattering states with the same parity at zero momentum as and The solution of the one-dimensional Klein-Gordon equation with the energy M or -M is called as a half bound state if it is finite but does not decay fast enough at infinity to be square integrable.
Received 22 December 1999 相似文献
15.
We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L
V
the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ
v
associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering
groups are Sunada pairs. 相似文献
16.
The inverse scattering problem at a fixed energy for a complex-valued potential is solved in the WKB approximation. The method is used to reconstruct the optical potential for elastic 16O + 16O scattering at E lab = 350 MeV. The stability of the solution against small changes in the scattering matrix is studied. 相似文献
17.
U. Kasper 《Annalen der Physik》1976,488(2):113-124
After an introduction to the formalism used throughout the paper there follows a concise presentation of the theory of fermion fields in one-tetrad gravitational theories. That presentation gives a hint to the construction of a bi-tetrad theory, the two tetrad fields being denoted by hAk and h?Ak. The tetrad field hAk. gives the Riemannian metric gkl while the tetrad field h?hAk is orthonormalized with respect to the flat metric akl. Specializing h?Ak in such a way that they have the form δAk in the preferred coordinates of Minkowski space and using a matter Lagrangian which contains these h?Ak only by the anholonomic components of the metric Christoffel symbols, we obtain a dynamical energy momentum tensor which is equal to the canonical one. Then we consider the relations of the bi-tetrad theory to other theories which are only covariant with respect to global Lorentz transformations from the beginning. As an example we formulate the main relations of the two-component neutrino theory. 相似文献
18.
Let ℤ+
d
+1= ℤ+×ℤ+, let H
0 be the discrete Laplacian on the Hilbert space l
2(ℤ+
d
+1) with a Dirichlet boundary condition, and let V be a potential supported on the boundary ∂ℤ+
d
+1. We introduce the notions of surface states and surface spectrum of the operator H=H
0+V and explore their properties. Our main result is that if the potential V is random and if the disorder is either large or small enough, then in dimension two H has no surface spectrum on σ(H
0) with probability one. To prove this result we combine Aizenman–Molchanov theory with techniques of scattering theory.
Received: 18 September 2000 / Accepted: 21 November 2000 相似文献
19.
Using the high energy resolution of the Mössbauer effect, the elastic and inelastic scattering of gamma-rays from single crystals of HF-doped IceI
h has been distinguished. The crystals were studied in the region of 100 K, since measurements by previous workers have suggested the possibility of an order-disorder transition at this temperature. Marked anomalies in the scattered intensity were observed between 106 and 125 K, and these were shown to depend on the thermal history of the crystals. 相似文献
20.