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1.
We show that the non-relativistic quantum mechanicaln-body HamiltoniansT(k)=T+kV andT, the free particle Hamiltonian, are unitarily equivalent in the center of mass system, i.e.,T(k)=W
±
(k)TW
±
(k)
–1 fork sufficiently small and real.
, a sum ofn(n–1)/2 real pair potentials,V
i, depending on the relative coordinatex
i
R
3 of the pairi, whereV
i
is required to behave like |xi|– 2 – as |x
i
| and like |xi|– 2 + as |x
i
|0.T(k) is the self-adjoint operator associated with the form sumT+kV. There are no smoothness requirements imposed on theV
i
. Furthermore
are the wave operators of time dependent scattering theory and are unitary. This result gives a quantitative form of the intuitive argument based on the Heisenberg uncertainty principle that a certain minimum potential well depth and range is needed before a bound state can be formed. This is the best possible long range behavior in the sense that ifkV
i
C
i
|x
i
|–b
, 0<b2 for |x
i
|>R
i
(0<R
i
<) and allC
i
are negative thenT(k) has discrete eigenvalues andW
±(k) are not unitary. 相似文献
2.
We show that the inverse correlation lengthm(z) of the truncated spin-spin correlation function of theZ
d
Ising model with + or — boundary conditions admits the representationm(z) = –(4d–4)ln z(1–d1) + r(z) for smallz=e
–, i.e., large inverse temperatures
is ad-dependent analytic function atz = 0, already known in closed form ford = 1 and 2; ford = 3 bn can be computed explicitly from a finite number of the Zd limits of z = 0 Taylor series coefficients of the finite lattice correlation function at a finite number of points ofZ
d. 相似文献
3.
We associate a family of Hilbert spaces H
q
2;(D) of analytic functions on the unit disk D=z
:|z|<1 the q-continuous Gegenbauer polynomials C
n
(x;q) on the interval]–1;1[ and give a q-analogue of the unitary integral transform that Watanabe constructed from the Hilbert space L
2(]–1;1[;(1–x
2)–
dx onto the weighted Hilbert space H
2;(D). 相似文献
4.
Erik Balslev 《Communications in Mathematical Physics》1988,114(4):599-612
For potentialsV=V(x)=O(|x|–2–) for |x|,x3 we prove that if theS-matrix of (–, –+V) has an analytic extension
to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension
toO such that
for |Imk|<b. Consequently, the resolvent (–+V–z
2)–1 has an analytic continuation from + to {kOImk|<b} as an operator
from
b
={f=e
–b|x|
g|gL
2(3)} to –b
. Based on this, we define for potentialsW=o(e
–2b|x|) resonances of (–+V, –+V+W) as poles of
and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1) 相似文献
5.
This article is a study of the mapping from a potentialq(x) onR
3 to the backscattering amplitude associated with the Hamiltonian –+q(x). The backscattering amplitude is the restriction of the scattering amplitudea(, , k), (, , k)S
2×S
2×+, toa(,–, k). We show that in suitable (complex) Banach spaces the map fromq(x) toa(x/|x|, –x/|x|, |x|) is usually a local diffeomorphism. Hence in contrast to the overdetermined problem of recoveringq from the full scattering amplitude the inverse backscattering problem is well posed. 相似文献
6.
Waksjö Claes Rauch-Wojciechowski Stefan 《Mathematical Physics, Analysis and Geometry》2003,6(4):301-348
The method of separation of variables applied to the natural Hamilton–Jacobi equation
(u/q
i
)2+V(q)=E consists of finding new curvilinear coordinates x
i
(q) in which the transformed equation admits a complete separated solution u(x)=u
(i)(x
i
;). For a potential V(q) given in Cartesian coordinates, the main difficulty is to decide if such a transformation x(q) exists and to determine it explicitly. Surprisingly, this nonlinear problem has a complete algorithmic solution, which we present here. It is based on recursive use of the Bertrand–Darboux equations, which are linear second order partial differential equations with undetermined coefficients. The result applies to the Helmholtz (stationary Schrödinger) equation as well. 相似文献
7.
Quantitative universality for a class of nonlinear transformations 总被引:36,自引:0,他引:36
Mitchell J. Feigenbaum 《Journal of statistical physics》1978,19(1):25-52
A large class of recursion relationsx
n + 1 = f(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum
. With
sufficiently small),z > 1, the universal details depend only uponz. In particular, the local structure of high-order stability sets is shown to approach universality, rescaling in successive bifurcations, asymptotically by the ratio ( = 2.5029078750957... forz = 2). This structure is determined by a universal functiong
*(x), where the 2nth iterate off,f
(n), converges locally to
–n
g
*(
n
x) for largen. For the class off's considered, there exists a
n such that a 2n-point stable limit cycle including
exists;
–
n R~
–n ( = 4.669201609103... forz = 2). The numbers and have been computationally determined for a range ofz through their definitions, for a variety off's for eachz. We present a recursive mechanism that explains these results by determiningg
* as the fixed-point (function) of a transformation on the class off's. At present our treatment is heuristic. In a sequel, an exact theory is formulated and specific problems of rigor isolated.Research performed under the auspices of the U.S. Energy Research and Development Administration. 相似文献
8.
《Czechoslovak Journal of Physics》1986,36(11):1303-1310
We have observed the production of
andD
– mesons in neutron carbon interactions at 40–70 GeV/c. The experiment was performed with the spectrometer BIS-2 located in the neutron beam 4N of the Serpukhov accelerator.The signals of
mesons were detected in the effective mass spectraM(K
+ (890)
–) andM(K
+(890)
–
–). The kinematical region of detected
mesons is 30 GeV/c < pL < 60 GeV/c andp
T < 1 GeV/c. For this region the partial cross sections are
.
and(n +C D
– +X).BR(D
– K
+(890) ––) = (2·1 ± 0·7) b. The longitudinal momentum spectrum in the regionx > 0·5 can be described byF(x) (1 – x)
N
with
and
. The transverse momentum spectra were parametrized by the exponential function d/dp
T
2
exp (-Bp
T
2
) with
and
.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.The authors are grateful to A. M. Baldin, D. A. Cheplakov, Yu. N. Denisov, N. N. Golovin, Kh. Ya. Khristov, K. Lanius, A. A. Logunov, M. G. Meshheryakov, I. A. Savin, A. N. Sissakian, L. D. Soloviev, A. N. Tavkhelidze, N. E. Tyurin, I. S. Zlatev, I. P. Kolpakov and E. I. Maltsev for their support of these studies, to S. S. Gershtein, A. B. Kaidalov and A. K. Likhoded for useful discussions and remarks, to the staffs of the Serpukhov accelerator for their help in setting up and running this experiment, to E. M. Likhacheva for her constant participation in the experiment. 相似文献
9.
A. Möbius 《Zeitschrift für Physik B Condensed Matter》1990,79(2):265-273
A detailed phenomenological re-analysis of previously published conductivity data, (T, x), is presented. It is based on the investigation of differences, (T, x
1)–(T, x
2). In this way, the cusp-like low-temperature term is amplified against the other temperature dependent contributions. This term can be described by
wherep=0.19±0.03. It is present, if (4.2 K,x) exceeds 260 –1 cm–1, at least up to (4.2 K,x)1350 –1 cm–1 and forT60 K. But it is absent, if (4.2 K,x)180 –1 cm–1. The disappearance of this contribution should be related to the metal-semiconductor transition, taking place atx
c
0.14. On the other hand, the presence of a term proportional toT
1/2, as predicted by Altshuler and Aronov, seems unlikely.It is argued that the term
should be related to the interplay of electron-electron interaction and disorder. The comparison with data from the literature shows that this contribution might also be present in heavily doped crystalline semiconductors. 相似文献
10.
LetH=–+V onl
2(), whereV(x),x, are i.i.d.r.v.'s with common probability distributionv. Leth(t)=e
–itv
dv(v) and letk(E) be the integrated density of states. It is proven: (i) Ifh isn-times differentiable withh
(j)(t)=O((1+|t|)–) for some >0,j=0, 1, ...,n, thenk(E) is aC
n
function. In particular, ifv has compact support andh(t)=O((1+|t|)–) with >0, thenk(E) isC
. This allowsv to be singular continuous. (ii) Ifh(t)=O(e
–|t|) for some >0 thenk(E) is analytic in a strip about the real axis.The proof uses the supersymmetric replica trick to rewrite the averaged Green's function as a two-point function of a one-dimensional supersymmetric field theory which is studied by the transfer matrix method.Research partially supported by the NSF under grant MC-8301889 相似文献
11.
D. M. Kroll 《Zeitschrift für Physik B Condensed Matter》1978,31(3):309-320
A dispersion representation for the static energy-density correlation function
2 (q)
2(–q)
c
=C(q,T)=A+Bt
–h(z
2), wherez=q , t=(T—T)c/T
c and is the correlation length, is discussed.h(z
2) is calculated to order
2 in the zero-field critical region (T>T
c) for the standard isotropicn-component
4Ginzburg-Landau-Wilson model. Utilizing a procedure similar to that introduced by Bray for the two-point correlation function, the-expansion results are used in conjunction with an approximant for the spectral functionF(z/2) Imh(—z
2) based on the asymptotically exact short-distance expansion resulth
–1(z
2)z
/v[D
0+D
1
z
–(1 —)/v
+D
2
z
–1/v
] to predict quantitatively the full momentum dependence ofC(q,T) forT>T
c. In contrast to the two-point correlation function,C(q,T) is found to be a monotonic function as the critical temperature is approached at fixedq (forT>T
c). 相似文献
12.
François Dunlop 《Journal of statistical physics》1985,41(5-6):733-743
I give a proof of the Kosterlitz-Thouless transition for sufficiently anisotropic (J
zJ
x
–1
=J
zJ
y
–1
<2q
–(JKT)–J) two-dimensionalN-component rotators (N 3). The method is based on Wells' inequality and is related to mean field Gaussian inequalities. 相似文献
13.
M. M. El-Nahass B. A. Khalifa A. M. Abd El-Rahman R. El-Ariny 《Applied Physics A: Materials Science & Processing》1996,63(1):81-86
Solid solutions of ZnSe
x
Te1–x
(0. 1 x 1) were synthesized by vacuum fusion of stoichiometric proportions of ZnSe and ZnTe. X-ray diffraction data revealed that they have polycrystalline cubic zinc-blende structure. The calculated unit cell lattice constant (a) for the different compositions in powder form vary linearly, with molecular fractionx following Vegard's law:a(x) = 6.165 – 0.485x. Thin films of ZnSe
x
Te1–x
(0.1 x 1) solid solutions deposited onto glass or quartz substrates by thermal evaporation in a vacuum of 10–4 Pa were found to be polycrystalline with a preferred (1 1 1) orientation. The obtained data were confirmed by electron diffraction. The optical studies showed that ZnSe
x
Te1–x
polycrystalline films of different compositions have two direct transitions with corresponding energy gapsE
g andE
g +
so The variations in bothE
g andE
g +
so, withx indicate that ZnSe
x
Te1–x
solid solution belongs to an amalgamation-type following quadratic equations with bowing parameters 1.251 and 1.275, respectively. 相似文献
14.
Letw = {w(x)xZd} be a positive random field with i.i.d. distribution. Given its realization, letX
t be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w–1(Xt). The processX={X
t:t0} combined withw on a common probability space is an example of random walk in random environment. We consider the quantities
t
=(d/dt) E
(X
t
2
–M
–1
t and
t(w) = (d/dt)Ew(X
t
2
– M– 1t). Here Ew. is expectation overX at fixedw and E = Ew (dw) is the expectation over bothX andw. We prove the following long-time tail results: (1) limt td/2t= V2Md/2–3(d/2)d/2 and (2) limt td/4
st(w)= Zs weakly in path space, with {Zs:s>0} the Gaussian process with EZs=0 and EZrZs= V2Md/2–4(d)d/2 (r + s)–d/2. HereM and V2 are the mean and variance of w(0) under . The main surprise is that fixingw changes the power of the long-time tail fromd/2 tod/4. Since
, with
0 the stationary measure for the environment process, our result (1) exhibits a long-time tail in an equilibrium autocorrelation function. 相似文献
15.
G. Müller G. Mück M. Simon G. Winterling 《Applied Physics A: Materials Science & Processing》1982,29(2):63-68
The electrical properties ofn
+-window layers inp-i-n a-Si:H solar cells were characterised as a function ofn
+-layer thickness,
, by measuring firstly the activation energyE
a
of the dark conductivity and secondly the built-in potentialV
bi
of the cells.E
a
was found to increase with decreasing
attaining values as high as 0.8 eV for
5nm; bulk values, e.g.E
a
. 2eV in the amorphous andE
a<0.01 eV in the microcrystalline case, were only observed for
>20nm and for
>200nm, respectively. In contrast,V
bi
did not depend on
at all and was further found to be consistent with expectations based on the Fermi level positions in bulkn
+ andp
+-material. As a consequenceE
a
in very thin films can no longer be considered as a measure of (E
C
–E
F), the distance of the Fermi level from the conduction band edge. The apparent inconsistency inherent to theE
a
and theV
bi
results can be resolved by assuming that the deposition of then
+-material proceeds via the growth and coalescence of small islands. 相似文献
16.
17.
J. Dušek 《Czechoslovak Journal of Physics》1982,32(11):1195-1220
The operatorsT
C,l
E+i0)[–G
0(E+i0)]1–i
andT
C,l(E+i)G
0[–iG
0(E+i)]i acting on spaces of Hölder continuous, differentiable and analytic functions are investigated. The results of their action are expressed in terms of explicit singular factors and terms and Hölder (differentiable, analytic) functions. The most singular part of these operators is shown to be determined by a simple functional. 相似文献
18.
We prove that the Schrödinger operator –d
2/dx2+Fx+W(x) onL
2(R) withW bounded and analytic in a strip has no resonances in a region ImE–exp(–C/F). 相似文献
19.
H. Albrecht T. Hamacher R. P. Hofmann T. Kirchhoff R. Mankel A. Nau S. Nowak H. Schr?der H. D. Schulz M. Walter et al. 《Zeitschrift fur Physik C Particles and Fields》1995,68(2):215-220
Using the ARGUS detector at the storage ring DORIS II we have measured decays into three charged mesons containingK
* mesons. Exploiting the good particle identification capabilities of the detector we have determined the following branching ratios:
,B
r
(–K
*0
K
–
v
)= (0.20±0.05±0.04)%, andB
r
(–K
*–
X
0
v
) =(1.15±0.15–0.18
+0.13)%.Supported by the German Bundesministerium für Forschung und Technologie, under contract number 054DO51P. 相似文献
20.
J. Kvasnica 《Czechoslovak Journal of Physics》1985,35(11):1205-1208
Exact solutions of the wave equation for the propagation of electromagnetic waves in some inhomogeneous media are found. The first solution corresponds to the barometric model of the atmosphere, whose index of refraction can be expressed by the formulaN
2(z)=1+(N
0
2
-1) exp (–z/z
0). The other cases correspond toN
2(z)=1+(N
0
2
-1) ch–2(z) andN
2(z)=a-b. [1+exp(z/L)]–1.Dedicated to Academician Vladimír Hajko on the occasion of his 65th birthday. 相似文献