共查询到20条相似文献,搜索用时 15 毫秒
1.
We present an approach to solve Bethe-Salpeter (BS) equations
exactly without any approximation if the kernel of the BS
equations exactly is instantaneous, and take positronium as an
example to illustrate the general features of the exact solutions.
The key step for the approach is from the BS equations to derive a
set of coupled and well-determined integration equations in linear
eigenvalue for the components of the BS wave functions
equivalently, which may be solvable numerically under a controlled
accuracy, even though there is no analytic solution. For
positronium, the exact solutions precisely present corrections to
those of the corresponding Schrödinger equation in order v1
(v is the relative velocity) for eigenfunctions, in order v2
for eigenvalues, and the mixing between S and D components in
JPC=1-- states etc., quantitatively. Moreover, we also point out that there is a
questionable step in some existent derivations for the
instantaneous BS equations if one is pursuing the exact solutions.
Finally, we emphasize that one should take the O(v) corrections
emerging in the exact solutions into account accordingly if one is
interested in the relativistic corrections for relevant problems
to the bound states. 相似文献
2.
Bound-State Soliton Solutions of the Nonlinear Schr?dinger Equation and Their Asymmetric Decompositions
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We study the asymmetric decompositions of bound-state(BS) soliton solutions to the nonlinear Schr?dinger equation. Assuming that the BS solitons are split into multiple solitons with different displacements, we obtain more accurate decompositions compared to the symmetric decompositions. Through graphical techniques, the asymmetric decompositions are shown to overlap very well with the real trajectories of the BS soliton solutions. 相似文献
3.
With the aid of the classical Lie group method and nonclassical Lie group method, we derive the classical Lie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS) equation. Using the symmetries, we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation. Varieties of exact solutions of the BS equation are obtained by solving the reduced equations. 相似文献
4.
5.
CHANG Chao-Hsi CHEN Jiao-Kai WANG Guo-Li 《理论物理通讯》2006,46(3):467-480
We have precisely derived a "rigorous instantaneous formulation" for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter (BS) equation (i.e. the kernel of the equation is instantaneous "occasionally"). The obtained rigorous instantaneous formulation, in fact, is expressed as an operator sandwiched by two "reduced BS wave functions" properly, while the reduced BS wave functions appearing in the formulation are the rigorous solutions of the instantaneous BS equation, and they may relate to Schroedinger wave functions straightforwardly. We also show that the rigorous instantaneous formulation is gauge-invariant with respect to the Uem(1) transformation precisely, if the concerned transitions are radiative. Some applications of the formulation are outlined. 相似文献
6.
YANZhen-Ya 《理论物理通讯》2002,37(3):269-276
We have found two types of important exact solutions,compacton solutions,which are solitary waves with the property that after colliding with their own kind,they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction,in the (1 1)D,(1 2)D and even (1 3)D models,and dromion solutions (exponentially decaying solutions in all direction) in many (1 2)D and (1 3)D models.In this paper,symmetry reductions in (1 2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m,n) equation)ut b(u^m)xxy 4b(u^n δx^-1uy)x=0,which is a generalized model of (1 2)D break soliton equation ut buxxy 4buuy 4buxδx^-1uy=0,by using the extended direct reduction method.As a result,six types of symmetry reductions are obtained.Starting from the reduction equations and some simple transformations,we obtain the solitary wavke solutions of BS(1,n) equations,compacton solutions of BS(m,m-1) equations and the compacton-like solution of the potential form (called PBS(3,2)) ωxt b(ux^m)xxy 4b(ωx^nωy)x=0.In addition,we show that the variable ∫^x uy dx admits dromion solutions rather than the field u itself in BS(1,n) equation. 相似文献
7.
V. A. Karmanov 《Few-Body Systems》2014,55(5-7):545-554
Recently developed methods allowing to find the solutions of the Bethe–Salpeter equations in Minkowski space, both for the bound and scattering states, are reviewed. For the bound states, one obtains the bound state mass and the corresponding BS amplitude. For the scattering states, the phase shifts (complex above the meson creation threshold) and the half-off-shell BS amplitude are found. Using these solutions, the elastic and transition electromagnetic form factors are calculated. 相似文献
8.
The Bethe–Salpeter (BS) equation for the imaginary part of the scattering amplitude is examined in the ladder approximation of scalar quantum electrodynamics (QED). Asymptotic solutions of the BS equation derived for the imaginary part of the scattering amplitude are shown to exhibit the Regge amplitude behavior for small momentum transfer and scattering in the forward direction and at arbitrary angles. 相似文献
9.
M. Böhm 《Nuclear Physics B》1975,91(3):494-508
Current conservation in the form of the Ward identity between the electromagnetic vertex and the propagator implies that the energy dependence of the BS kernel is restricted and that the propagator cannot be chosen independently from the kernel. It is rather determined from the BS kernel in terms of an integral equation. Convolution type, energy-independent kernels are compatible with current conservation. We study the propagator and form factor resulting from smooth kernels. 相似文献
10.
We study the baryons containing a heavy quark in the framework
of Bethe-Salpeter (BS) equation. The most general forms of
the BS wavefunctions are given. In the heavy-quark limit we simplify the
BS equations and we show clearly that the spin symmetry exists in heavy
baryon states. 相似文献
11.
《Nuclear Physics B》1988,296(2):462-492
Using a new type of harmonic superspace variables, we reduce the N = 2, D = 10 Brink-Schwarz (BS) superparticle to a system whose constraints are (i) first class, (ii) functionally independent and (iii) Lorentz covariant. We show that these features are essential for a correct covariant quantization. QBRST is first rank. By using it to second quantize the system, we obtain a covariant off-shell unconstrained superfield action of the linearized D = 10 type IIB supergravity. A corresponding procedure for the Green Schwarz (GS) superstring is conjectured. 相似文献
12.
多组份纠缠是量子信息处理的重要资源,它的产生通常涉及到许多复杂的线性和非线性过程.本文从理论上提出了一种利用两个独立的四波混频过程和线性分束器产生真正的四组份纠缠的方案,其中,线性分束器的作用是将两个独立的四波混频过程联系起来.首先应用部分转置正定判据研究了强度增益对四组份纠缠的影响,结果表明,在整个增益区域内都存在真正的四组份纠缠,并且随着强度增益的增加,纠缠也在增强.然后研究了线性分束器的透射率对四组份纠缠的影响,发现只要线性分束器的透射率不为0或1,该系统也可以产生真正的四组份纠缠.最后,通过研究该系统可能存在的三组份纠缠和两组份纠缠来揭示该系统的纠缠结构.本文理论结果为实验上利用原子系综四波混频过程产生真正的四组份纠缠提供了可靠的方案. 相似文献
13.
We consider the topology of the BS causal completion, and show that it is not distorted in the causal direction. Using this
result, we show that the causal completion with spacelike causal boundary in the sense of the BS construction satisfies the
formal definition of the global hyperbolicity. We also show that any two causally related points in the causal completion
can be connected by a causal geodesic. 相似文献
14.
15.
Influence of multi-photon pulses on practical differential-phase-shift quantum key distribution
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The influence of multi-photon pulses on practical differcBtial-phase-shift quantum key distribution (DPS-Qt(D) is analysed. We have estimated the information which Eve obtained by PNS (photon-number splitting) attack and BS (beam splitting) attack. The result indicates that the PNS attack and BS attack will not limit the transmission distance as long as we select an appropriate mean photon number. Also, the maximum mean photon number under BS attack in practical DPS-QKD system and the set of practical assumptions about Eve's capabilities are presented.[第一段] 相似文献
16.
G. Thiamová J. Paldus 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,46(3):453-461
The singlet stability of symmetry adapted (SA), restricted
Hartree-Fock (RHF) solutions, and the implied symmetry breaking for several
planar, π-electron systems, is investigated using the semiempirical
Pariser-Parr-Pople Hamiltonian in the whole range of the coupling constant.
We focus here on highly symmetric cyclic polyenes
C10H10 and C14H14 and their various distorted analogues of
lower symmetry, in particular on the perimeter models of naphthalene and
anthracene (p-naphthalene and p-anthracene) modeling the so-called
[n]-annulenes. Relying on earlier results for general systems with
conjugated double-bonds, we explore the character and properties of both
the SA and broken-symmetry (BS) RHF solutions for these systems and relate
their behavior to those of highly symmetric cyclic polyenes and corresponding
polyacenes. In this way we are able to provide a better understanding of
the spontaneous symmetry breaking in these systems at the Hartree-Fock level
of approximation. 相似文献
17.
An entangled coherent state(ECS) is one type of entanglement, which is widely discussed in the application of quantum information processing(QIP). In this paper, we propose an entanglement concentration protocol(ECP) to distill the maximally entangled W-type ECS from the partially entangled W-type ECS. In the ECP, we adopt the balanced beam splitter(BS) to make the parity check measurement. Our ECP is quite different from the conventional ECPs. After performing the ECP, not only can we obtain the maximally entangled ECS with some success probability, but also we can increase the amplitude of the coherent state. Therefore, it is especially useful in long-distance quantum communication, if the photon loss is considered. 相似文献
18.
A new method is suggested for analyzing the scattering of particles whose interaction is mediated by the exchange of field quanta. The conventional approach uses the Lehmann, Symanzik, and Zimmerman (LSZ) method for formulating the asymptotic boundary condition constraints. Then after making the appropriate renormalization subtractions one finds Bethe-Salpeter (BS) equations for the transition amplitudes. The covariant form of the BS equations makes the construction of solutions arduous. Approximate reductions to noncovariant form are generally employed. Our method is based on an alternative to the LSZ technique and leads directly to a set of coupled noncovariant integral equations for the transition operators. No approximation is required to achieve this result. Our equations are similar to the Lippmann-Schwinger equations for many-body scattering. The complexity of these equations is governed by the maximum number of field quanta permitted to be present at any instant. 相似文献
19.
20.
A. F. Rozenfeld K. Laneri E. V. Albano 《The European physical journal. Special topics》2007,143(1):3-8
A dynamic scaling Ansatz for the approach to stationary states in complex systems
is proposed and tested by means of extensive simulations applied to both
the Bak-Sneppen (BS) model, which exhibits robust Self-Organised
Critical (SOC) behaviour, and the Game of Life (GOL) of J. Conway,
whose critical behaviour is under debate. Considering the dynamic scaling behaviour of the density of
sites (ρ(t)), it is shown that i) by starting the dynamic measurements with configurations
such that ρ(t=0) →0, one observes an initial increase of the
density with exponents θ= 0.12(2) and θ= 0.11(2) for the BS and GOL models, respectively;
ii) by using initial configurations with ρ(t=0) →1, the density decays with exponents δ= 0.47(2) and δ= 0.28(2) for the BS
and GOL models, respectively.
It is also shown that the temporal autocorrelation decays with exponents
Ca = 0.35(2) (Ca = 0.35(5)) for the BS (GOL) model.
By using these dynamically determined critical exponents
and suitable scaling relationships, we also obtain the dynamic
exponents z = 2.10(5) (z = 2.10(5)) for the
BS (GOL) model.
Based on this evidence we conclude that the dynamic
approach to stationary states of the investigated models
can be described by suitable power-law functions
of time with well-defined exponents. 相似文献