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1.
Levinson theorem for Dirac particles in one dimension 总被引:1,自引:0,他引:1
Qiong-gui Lin 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1999,7(4):515-524
The scattering of Dirac particles by symmetric potentials in one dimension is studied. A Levinson theorem is established.
By this theorem, the number of bound states with even(odd)-parity, n+ (n-), is related to the phase shifts [] of scattering states with the same parity at zero momentum as follows: The theorem is verified by several simple examples.
Received 26 August 1998 and Received in final form 18 January 1999 相似文献
2.
The approximately analytical bound and scattering state solutions of the arbitrary l-wave Klein-Gordon equation for the mixed Manning-Rosen potentials are carried out by an improved new approximation to the
centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Manning-Rosen potentials are presented and the corresponding energy equations for
bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states,
reduce to the bound states of those at the poles of the scattering amplitude. Some useful figures are plotted to show the
improved accuracy of our results and the special case for wave is studied briefly.
相似文献
3.
We study the localization length lc of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle. For a pair with many bound states N the localization length is proportional to N, independently of the form of the two particle interaction. For the case of two bound states, we present an exact solution for the corresponding Fokker–Planck equation and demonstrate that lc depends sensitively on the shape of the interaction potential and the symmetry of the bound state wave functions. 相似文献
4.
In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric (r–r
0) potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of r
0 can be established by an SO(2) transformation. We obtain a transcendental equation for calculating the energy of the bound state from the matching condition in the configuration space. The condition for existence of bound states is determined by the Sturm-Liouville theorem. 相似文献
5.
Shi-Hai Dong 《International Journal of Theoretical Physics》2000,39(6):1529-1541
The Levinson theorem for the one-dimensional Schrödinger equation with both local and the nonlocal symmetric potentials is established by the Sturm–Liouville theorem. The critical case where the Schro;audinger equation has a finite zero-energy solution is also analyzed. It is shown that the number n
+ (n
–) of bound states with even (odd) parity is related to the phase shift +(0)[–(0)] of the scattering states with the same parity at zero momentum as
and
The problems on the positive-energy bound states and the physically redundant state related to the nonlocal interaction are also discussed. 相似文献
6.
Instability of nonlinear bound states 总被引:17,自引:0,他引:17
We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,u
tt–u+f(u)=0, and the nonlinear Schrödinger equation, –iu
t–u+f(u)=0.Supported in part by NSF Grants MCS 81-21487 and MCS 82-01599 相似文献
7.
Gao-Feng Wei Xu-Yang Liu Wen-Li Chen 《International Journal of Theoretical Physics》2009,48(6):1649-1658
The approximately analytical scattering state solutions of the l-wave Klein-Gordon equation with the unequal scalar and vector Hulthén potentials are carried out by an improved new approximate
scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Hulthén potentials are presented and the corresponding calculation formula of phase
shifts is derived. It is well shown that the energy levels of the continuum states reduce to those of the bound states at
the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and two
special cases for s-wave (l=0) and for l=0 and equal scalar and vector Hulthén potentials are also studied briefly. 相似文献
8.
G. Montambaux 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,1(3):377-383
The stability of a Charge Density Wave (CDW) in a one-dimensional ring pierced by a Aharonov-Bohm flux is studied in a mean-field
picture. It is found that the stability depends on the parity of the number N of electrons. When the size of the ring becomes as small as the coherence length , the CDW gap increases for even N and decreases for odd N. Then when N is even, the CDW gap decreases with flux but it increases when N is odd. The variation of the BCS ratio with size and flux is also calculated. We derive the harmonics expansion of the persistent
current in a presence of a finite gap.
Received: 16 September 1997 / Received in final form: 12 November 1997 / Accepted: 13 November 1997 相似文献
9.
Jelena Šamonina-Kosicka 《Isotopes in environmental and health studies》2013,49(3):357-364
Diamine oxidase (DAO), the enzyme that is responsible for amine biodegradation in animals, plants and humans, catalyses the biotransformation of amines such as histamine (HA), putrescine, 1-phenylethylamine, tyrosine, tryptamine, serotonine and spermine. The kinetic and solvent isotope effects (SIEs) were applied to study the mechanism of the biotransformation using HA and its methylderivatives. The SIE for the biotransformation of HA, Nτ-methylhistamine and Nπ-methylhistamine was found to be 3.58, 2.22 and 5.70 on Vmax, and 1.58, 1.06 and 1.14 on Vmax/KM, respectively. On the other hand, the kinetic isotope effect for oxidation of stereospecifically deuterium-labelled [(α R)-2H]-Nτ-methylhistamine and [(α R)-2H]-Nπ-methylhistamine was 0.69 and 0.62 on Vmax, and 15.06 and 7.50 on Vmax/KM, respectively. These results demonstrate that DAO catalyses amine biotransformation by stereospecifically cleaving the αC\bond H bond in the pro-S position. Moreover, the oxidation of amine to aldehyde involves several transition states, including hybridisation change from sp3 (Schiff base) to sp2 (imine), then back again to sp3 to give a final product with hybridisation sp2 (aldehyde). 相似文献
10.
R. Zeyher A. Greco 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(4):473-485
The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for
the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions
into account. Classifying the order parameter according to irreducible representations of the point group C4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs
only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature Tc is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term
and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. Tc increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. Tc is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of Tc is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity
in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation
involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded
term) so that singular properties in momentum or frequency are averaged out very effectively.
Received: 16 June 1998 / Accepted: 14 July 1998 相似文献
11.
P. Bonville J. A. Hodges Z. Hossain R. Nagarajan S. K. Dhar L. C. Gupta E. Alleno C. Godart 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(3):377-383
We present magnetic properties of the three-band Hubbard model in the para- and antiferromagnetic phase on a hypercubic lattice
calculated with the Dynamical Mean-Field Theory (DMFT). To allow for solutions with broken spin-symmetry we extended the approach
to lattices with AB-like structure. Above a critical sublattice magnetization one can observe rich structures in the spectral-functions similar to the t-J model which can be related to the well known bound states for one hole in the Neél-background. In addition to the one-particle
properties we discuss the static spin-susceptibility in the paramagnetic state at the points and for different dopings . The -T-phase-diagram exhibits an enhanced stability of the antiferromagnetic state for electron-doped systems in comparison to hole-doped.
This asymmetry in the phase diagram is in qualitative agreement with experiments for high-Tc materials.
Received: 28 May 1998 / Revised and Accepted: 14 September 1998 相似文献
12.
Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves
a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition
for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization
(one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent
state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution.
Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M
* (M* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find
that: 1) for M
* ≪ M ≪ M
*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t1, t2, t3 and t*; 2) there are transient regimes (t
1 ≲ t ≲ t
3) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter
than t2. The chain growth is auto-accelerated for t
1 ≲ t ≲ t
2 : the cut-off chain length (= polymerization degree 〈n〉w
N
1 ∝ t
2 in this regime. 4) For t
2 < t < t
3 the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N1 is decreasing with time in this regime, while the length scale N2 of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t*, shows a sharp maximum in the vicinity of M*; the effective exponent
is as high as ∼ σ-1/3 just above M*. 相似文献
13.
Nonlinear quantum theory of interaction of charged particles and monochromatic radiation in a medium
G. K. Avetisyan A. Kh. Bagdasaryan G. F. Mkrtchyan 《Journal of Experimental and Theoretical Physics》1998,86(1):24-31
We study the quantum theory of nonlinear interaction of charged particles and a given field of plane-transverse electromagnetic
radiation in a medium. Using the exact solution of the generalized Lamé equation, we find the nonlinear solution of the Mathieu
equation to which the relativistic quantum equation of particle motion in the field of a monochromatic wave in the medium
reduces if one ignores the spin-spin interaction (the Klein-Gordon equation).We study the stability of solutions of the generalized
Lamé equation and find a class of bounded solutions corresponding to the wave function of the particle. On the basis of this
solution we establish that the particle states in a stimulated Cherenkov process form bands. Depending on the wave intensity
and polarization, such a band structure describes both bound particle-wave states (capture) and states in the continuous spectrum.
It is obvious that in a plasma there can be no such bands, since bound states of a particle with a transverse wave whose phase
velocity v
ph is higher than c are impossible in this case. The method developed in the paper can be applied to a broad class of problems reducible to the
solution of the Mathieu equation.
Zh. éksp. Teor. Fiz. 113, 43–57 (January 1998) 相似文献
14.
We study the asymptotic behavior of the ratio of Pauli and Dirac electromagnetic nucleon form factors, F2/F1, in time-like region, for different parametrizations built for the space-like region. We investigate how fast the ratio F2/F1 approaches the asymptotic limits according to the Phragmèn-Lindel?f theorem. We show that the QCD-inspired logarithmic behavior
of this ratio results in very far asymptotics, experimentally unachievable. This is also confirmed by the normal component
of the nucleon polarization, Py, in e+ + e-↦N + ˉ (in collisions of unpolarized leptons), which is a very interesting observable, with respect to this theorem. Finally
we observe that the 1/Q parametrization of F2/F1 contradicts this theorem. 相似文献
15.
C.-K. Siu S. J. Reitmeier I. Balteanu V. E. Bondybey M. K. Beyer 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,43(1-3):189-192
Pt4
- catalyses the conversion of CO and
N2O to CO2 and N2 in the gas phase, as observed by Fourier
transform ion cyclotron (FT-ICR) mass spectrometry. The partial pressures of
CO and N2O determine the extent of poisoning and the turnover numbers
that can be achieved. The catalytic conversion terminates as soon as two CO
are adsorbed on the cluster. With N2O, the reactivity of
Pt4O2
- and Pt4O3
- is reduced to 41% and
34% compared to Pt4O-, respectively, and with
Pt4O4
- this value is reduced to 1%. In contrast,
Pt4
+ shows no apparent catalytic activity. Density functional
theory calculations of Pt4
+/- with CO and N2O adsorbates
reveal significantly different stabilities of the reaction intermediates for
the different charge states. 相似文献
16.
G. Seibold F. Becca F. Bucci C. Castellani C. Di Castro M. Grilli 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(1):87-97
The concept of frustrated phase separation is applied to investigate its consequences for the electronic structure of the
high T
c
cuprates. The resulting incommensurate charge density wave (CDW) scattering is most effective in creating local gaps in k-space when the scattering vector connects states with equal energy. Starting from an open Fermi surface we find that the
resulting CDW is oriented along the (10)- and (or) (01)-direction which allows for a purely one-dimensional or a two-dimensional
“eggbox type” charge modulation. In both cases the van Hove singularities are substantially enhanced, and the spectral weight
of Fermi surface states near the M-points, tends to be suppressed. Remarkably, a leading edge gap arises near these points, which, in the eggbox case, leaves
finite arcs of the Fermi surface gapless. We discuss our results with repect to possible consequences for photoemission experiments.
Received 14 June 1999 相似文献
17.
《Journal of Macromolecular Science: Physics》2013,52(2):147-156
A linear β-(1→3)-d-glucan PCM3 (pachyman), a major polysaccharide in Poria cocos mycelia, formed aggregates in aqueous solution or dimethyl sulfoxide (DMSO) with absorbed moisture, thereby considerably complicating its fractionation and study of solution properties. In this work, the pachyman PCM3 having narrow polydispersity (M w/M n = 1.9) was carefully fractionated by a preparative size exclusion chromatography (SEC) using dehydrated DMSO as the mobile phase. The weight-average molecular mass M w and intrinsic viscosity [η] of the fractions were measured by static and dynamic laser light scattering, SEC combined with light scattering, and viscometry in DMSO at 25°C, thus eliminating the aggregation. The Mark-Houwink equation for the pachyman in DMSO is established to be: [η] = 6.79 × 10?4 M w 0.95 (mL/g) in the M w range from 1.2 to 3.5 × 105. The characteristic ratio C ∞ of the PCM3 in DMSO at 25°C, from light scattering by using Flory theory, was obtained to be 10.1, thus indicating that it behaves as a relatively expanded, flexible coil. In addition, the M w of the pachyman from Poria cocos mycelia was 1.68 × 105, obviously larger than that from the sclerotium (8.9 × 104). 相似文献
18.
L. Alff S. Kleefisch U. Schoop M. Zittartz T. Kemen T. Bauch A. Marx R. Gross 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):423-438
Andreev bound states at the surface of superconductors are expected for any pair potential showing a sign change in different
k-directions with their spectral weight depending on the relative orientation of the surface and the pair potential. We report
on the observation of Andreev bound states in high temperature superconductors (HTS) employing tunneling spectroscopy on bicrystal
grain boundary Josephson junctions (GBJs). The tunneling spectra were studied as a function of temperature and applied magnetic
field. The tunneling spectra of GBJ formed by YBa2Cu3O (YBCO), Bi2Sr2CaCu2O(BSCCO), and La1.85Sr0.15CuO4 (LSCO) show a pronounced zero bias conductance peak that can be interpreted in terms of Andreev bound states at zero energy
that are expected at the surface of HTS having a d-wave symmetry of the order parameter. In contrast, for the most likely s-wave HTS Nd1.85Ce0.15CuO4-y (NCCO) no zero bias conductance peak was observed. Applying a magnetic field results in a shift of spectral weight from zero
to finite energy. This shift is found to depend nonlinearly on the applied magnetic field. Further consequences of the Andreev
bound states are discussed and experimental evidence for anomalous Meissner currents is presented.
Received: 17 February 1998 / Revised: 27 April 1998 / Accepted: 23 June 1998 相似文献
19.
在球坐标系中研究了具有离心项的Manning-Rosen型标量势与矢量势的Klein-Gordon方程.在标量势等于矢量势的条件下,运用合适的指数近似将具有离心项的径向Klein-Gordon方程转化成超几何微分方程,从而获得了系统的任意l波Klein-Gordon方程解析束缚态径向波函数.最后,对l=0和α=0或1两种特殊情况进行了简单讨论.
关键词:
Manning-Rosen势
Klein-Gordon方程
束缚态
近似解析解 相似文献
20.
The determinant of the wave operator or its transposed operator (source operator) works as a measure for resonance and bound
states in one-dimensional potential scattering system. This fact is based on an identity proved here: the determinant of the
wave or source operator equals to the transmission coefficient, which represents the field amplitude in the forward side of
the scatterer. Utilizing this measure, resonance and bound states in one-dimensional system are properly assigned without
solving wave equation. In future, local enhancement of optical near-field in three-dimensional system, i.e., local plasmon
resonance will be treated, generalizing the present method. 相似文献