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1.
Bound states and critical behavior of the Yukawa potential 总被引:1,自引:0,他引:1
We investigate the bound states of the Yukawa potential V (r)=−λexp(−αr)/r, using different algorithms: solving the Schr?dinger equation numerically and our Monte Carlo Hamiltonian approach. There
is a critical α = αC, above which no bound state exists. We study the relation between αC and λ for various angular momentum quantum number l, and find in atomic units, αC(l) = λ[A
1 exp(−l/B
1) + A
2 exp(−l/B
2)], with A
1 = 1.020(18), B
1 = 0.443(14), A
2 = 0.170(17), and B
2 = 2.490(180). 相似文献
2.
O.L. Safronov 《Communications in Mathematical Physics》1998,193(1):233-243
Given two selfadjoint operators A and V=V
+ -V
-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let α>0 and let λ be a regular point for A. We consider the quantities N
+(λ,α), N
-(λ,α), N
0(λ,α) defined as the number of the eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right or change the direction of their motion exactly
at point λ, respectively, as t increases from 0 to α>0. An abstract theorem on the asymptotics for these quantities is presented. Applications to Schr?dinger
operators and its generalizations are given.
Received: 9 April 1997 / Accepted: 26 August 1997 相似文献
3.
Oleg Safronov 《Communications in Mathematical Physics》2001,218(1):217-232
Let A be a periodic Schr?dinger operator and let V
0≥ 0 be a decaying potential. We study the number of the eigenvalues of the operator A(α) =A−αV
0 inside a fixed interval (λ1,λ2). We obtain an asymptotic formula for as α→∞.
Received: 12 September 2000 / Accepted: 22 November 2000 相似文献
4.
V. Bezák 《Czechoslovak Journal of Physics》1998,48(5):529-535
The linear stochastic equation dx
β
/dt+[1+f
β
(t)]x
β
(t)=A sin (Ωt) is discussed. The functionƒ
β
(t) is defined as a Poissonian noise dependent on a parameterβ>0,ƒ
β
(t)=β Σ
j
[δ(t − t
j
+
) −δ (t − t
j
−
)]. The mean frequency of the delta-pulses is chosen asβ-dependent in the formλ(β)=2γ(β
−2 + 1) exp(−β) whereγ is a constant from the interval (0, 0.974). With the stochastic functionƒ
β
(t) defined in this way, attention is paid on the oscillational term of the averaged function 〈x(t)〉, 〈x(t)〉osc=Āsin(Ωt − α). It is found that the dependenceĀ=Ā(β) exhibits one maximum and one minimum. The occurrence of these extrema seems to affirm the presence of stochastic resonance.
This work has been supported by the Slovak Grant Agency VEGA under contract No. 1/4319/97. 相似文献
5.
Shimon Brooks 《Communications in Mathematical Physics》2010,293(1):231-255
We study semiclassical measures, or quantum limits, for quantized hyperbolic automorphisms of
\mathbbT2{\mathbb{T}^2} . We show that any quantum limit has the following property: if a weight α is carried on ergodic components of low entropy (say, entropy less than h
0), then a weight ≥ α must be carried on ergodic components of high entropy (≥ h
max−h
0, where h
max is the maximal entropy). This combines some existing partial results towards the classification of quantum limits. 相似文献
6.
A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach
can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational
wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r
12, r
13, r
14, r
23, r
24, r
34) and ten (r
12, r
13, r
14, r
15, r
23, r
24, r
25, r
34, r
35 and r
45) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial
wave functions for the 1
S states in four-electron atomic systems include the two independent spin functions χ1 = αβαβ + βαβα − βααβ − αββα and χ2 = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited
23
S states in four- electron atomic systems. 相似文献
7.
Benjamin Fain 《Foundations of Physics Letters》1997,10(3):221-233
The prerequisite of quantum measurement is a transformation of an initially off-diagonal density matrix
ρmα;nβ
describing an interacting measured object and measuring device into a diagonal density matrix
ρmα;mαδmnδαβ
. The latter density matrix describes a proper mixture of states having definitem-values. On the other hand, the irreversible relaxation (towards the thermodynamic equilibrium) is also characterized by transformation
of an initially off-diagonal matrix into a diagonal one. It has been shown that the process of irreversible relaxation can
be used to perform quantum measurement, provided the duration Δt of the measurement is much larger thanT
2, the phase relaxation time, and much smaller thanT
1, the population relaxation time:T
2 ≪ Δt ≪T
1. Agedanken experiment describing this kind of measurement is provided. Aπ/2-pulse transforms an initials
z
= −1/2 state into superposition ofs
z
= ±1/2 states. The irreversible relaxation leads to the proper mixture ofs
z
= 1/2 ands
z
= −1/2 state. Results of the measurements are verified by the second electromagnetic pulse. 相似文献
8.
M R M Witwit 《Pramana》1994,42(2):159-165
Eigenenergies are calculated for the potentialsV
1(r)=−(a/r)[1+(1+br)e−2br
] andV
2(r)=−(v/r)[1 −λr(1−Z
−1)(1+λr)−1], using renormalized series technique. Accurate results produced here for various eigenstates agree with those available
in the literature. 相似文献
9.
Bi4V2O11 exists in three phases viz. α, β, and γ. High temperature γ-phase can be stabilized to room temperature owing to its higher
conductivity by the partial substitution of metallic cations for vanadium in Bi4V2O11. Phase transitions from α → β and β → γ are composition and temperature-dependent. Mn2+-doped compounds Bi4V2−x
Mn
x
O11−
δ
(0 ≤ x ≤ 0.4) have been synthesized by solid state reaction technique and investigated by X-ray diffraction and ionic conductivity
measurement. High ionic conducting γ-phase is stabilized for x ≥ 0.2. The ionic conductivity of the series of Bi4V2−x
Mn
x
O11−
δ
samples has been measured by using ac impedance spectroscopy technique. The conductivity data do show departure from its
simple Arrhenius behavior for all of the compositions. The highest conductivity observed for x = 0.2 sample can be attributed to lower activation energy. 相似文献
10.
We have recorded and investigated the ESR spectrum of vanadium-doped α-RbTiOPO4 single crystals in the temperature interval 77–300 K. Two types of structurally distinct centers, V1 and V2, with a 4:1 ratio
of the peak intensities were observed. The angular dependences of the resonance magnetic fields are described by a spin Hamiltonian
corresponding to axial symmetry with the parameters g
∥1=1.9305, g
⊥1=1.9565, A
∥1=−168.2×10−4cm−1, and A
⊥1=−54.3×10−4cm−1 for V1 centers and g
∥2=1.9340, g
⊥2=1.9523, A
∥2=−169.0×10−4cm−1, and A
⊥2=−55.2×10−4cm−1 for V2 centers. A model of a paramagnetic center is proposed: The vanadium ions replace titanium ions in two structurally
distinct positions Ti1 and Ti2 (V1 and V2 centers, respectively). The possibility that a VO2+ ion forms when α-RbTiOPO4 crystals and crystals of the KTP group (KTiOPO4, NaTiOPO4, α-and β-LiTiOPO4), studied earlier, are doped with vanadium is discussed.
Fiz. Tverd. Tela (St. Petersburg) 40, 534–536 (March 1998) 相似文献
11.
Among von Neumann algebras, the Weyl algebra W{\mathcal{W}} generated by two unitary groups {U(α)} and {V(β)}, the algebra U{\mathcal{U}} generated by a completely non-unitary semigroup of isometries {U
+(α)} and the Weyl algebra W+h{\mathcal{W}_{+}^{h}} pertaining to a semi-bounded space with homogeneous spectrum of the generator of {V(β)}, all share the property that their representations are completely reducible and the irreducible representations are equivalent.
We trace this fact to the identity of these algebras, in the sense that any of them contains a representation of any of the
remaining two algebras, which in turn contains the original algebra. We prove this statement by explicit construction. The
aforementioned results about the representations of the algebras follow immediately from the proof for any of them. Also,
by the above construction we prove for Wh+{\mathcal{W}^{h}_{+}} the analog of a theorem by Sinai for W{\mathcal{W}} : given {V(β)} with semi-bounded homogeneous spectrum, there exists a completely non-unitary semigroup {U
+(α)} such that {V(β)} and {U
+(α)} generate W+h{\mathcal{W}_{+}^{h}}. 相似文献
12.
Let (A,α) be a C*-dynamical system. We introduce the notion of pressure P
α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra
? of A such that for all pairs a,b∈? the C*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α
j
(a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P
α(H) is the supremum of the quantities h
φ(α) −φ(H), where h
φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P
α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism
group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h
φ(α), and any state of finite maximal entropy is a trace.
Received: 19 April 2000 / Accepted: 14 June 2000 相似文献
13.
P. Thakur R. Dogra A. K. Bhati S. C. Bedi R. P. Singh S. Muralithar R. K. Bhowmik 《Hyperfine Interactions》2000,131(1-4):103-109
The electric quadrupole moments of the 9/2− and 21/2− isomeric states of 173Ta at 165.8 keV and 1713.2 keV, respectively, were measured as Q(9/2−)=2.92(15) b and Q(21/2−)=6.23(18) b for the first time using the TDPAD technique. A 66 MeV pulsed 12C ion beam from the 15UD pelletron accelerator facility of the Nuclear Science Centre at New Delhi was used in the reaction
165Ho(12C, 4nγ)173Ta. The experimental values of equilibrium deformations β2(9/2−)=0.251(7) and β2(21/2−)=0.391(7) were extracted.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
We report on the lattice location of indium in and the magnetic ordering of manganese in its α- and β-phases, as seen by perturbed
angular correlation. Quadrupole interaction spectra show that indium prefers to replace Mn atoms of type I in α-Mn, but replaces
type II atoms in the β-Mn structure. The interaction strength equalseQV
zz
/h=3.6 (6) MHz in α-Mn and 172.3 (3) MHz with ν=0.13 (1) in β-Mn. No magnetic ordering down to 4.2 K was observed in β-Mn, while
belowT
N
=95 K in the α-Mn phase, a magnetic hyperfine interaction appears indicating two distinct magnetic probe environments. The
hyperfine field, when measured atT=4.2 K, equals for 70% of the probes 6.33 (1) T, while the remaining fraction senses a 3.10 (4) T field. The magnitudes of
the hyperfine fields are essentially unaffected by a variety of conditions in the sample preparation. The ordering temperature,
on the contrary, turns out to be rather sensitive to residual impurities especially any oxygen contamination. 相似文献
15.
A. L. Kataev 《JETP Letters》2012,94(11):789-794
The generalized Crewther relations in the channels of the non-singlet and vector quark currents are considered. These relations
follow from the double application of the operator product expansion approach to the same axial vector-vector-vector triangle
amplitude in two regions, adjoining to the angle sides (x, y) (or p
2, q
2). We assume that the generalized Crewther relations in these two kinematic regimes result in the existence of the same perturbation
expression for two products of the coefficient functions of annihilation and deepinelastic scattering processes in the non-singlet
and vector channels. This feature explains the conformal symmetry motivated cancellations between the singlet α
s
3 corrections to the Gross-Llewellyn Smith sum rule S
GLS of νN deep inelastic scattering and the singlet α
s
3 correction to the e
+
e
−-annihilation Adler function D
A
V
in the product of the corresponding perturbative series. Taking into account the Baikov-Chetyrkin-Kuhn fourth order result
for S
GLS and the perturbative effects of the violation of the conformal symmetry in the generalized Crewther relation, we obtain the
analytical contribution to the singlet α
s
4 correction to the D
A
V
function. Its a-posteriori comparison with the recent result of direct diagram-by-diagram evaluation of the singlet fourth
order corrections to D
A
V
function demonstrates the coincidence of the predicted and obtained ζ32-contributions to the singlet term. They can be obtained in the conformal invariant limit from the original Crewther relation.
Therefore, on the contrary to previous belief, the appearance of ζ3-terms in the perturbative series in quantum field theory gauge models does not contradict to the property of the conformal
symmetry and can be considered as regular feature. The Banks-Zaks motivated relation between our predicted and the obtained
directly fourth order corrections is mentioned. It confirms the expectation, previously made by Baikov-Chetykin-Kuhn, that
at the 5-loop level the generalized Crewther relation in the channel of vector currents may receive additional singlet contribution,
which in this order of perturbation theory is proportional to the first coefficient of the QCD β function. 相似文献
16.
A. V. Guskov 《Physics of Particles and Nuclei Letters》2010,7(3):192-200
The electromagnetic structure of charged pions can be described by the electric (απ) and magnetic (βπ) polarizabilities that depend on the rigidity of pion’s internal structure as a composite particle. It is shown that the
values of απ and βπ can be precisely measured via the Primakoff reaction π− + (A, Z) → π− + (A, Z) + γ in the COMPASS experiment at CERN. 相似文献
17.
Fritzsch like mass matrices with non-zero 22-elements both in U sector and D sector have been investigated in the context
of latest data regardingm
t
phys
, |V
ub|, |V
cb|, |V
td| and |V
ts|. Unlike several other phenomenological models, the present model not only accommodates the value ofm
t
phys
in the range 150–240 GeV, encompassing the CDF and D0 values, but is also able to reproduce |V
cb| ≊0.040 and |V
ub/Vcb| = 0.08±0.02 and |V
td| is predicted to lie in the range 0.005–0.014. Further, the angles of the unitarity triangle, related to the CP-violating
asymmetries, are calculated to be in the ranges −1.0⩽sin2α⩽−0.1, 0.6 ⩽sin2α⩽1.0 and 0.48⩽sin2β⩽0.56, which are in agreement
with other recent calculations. 相似文献
18.
M. M. Malamud 《Russian Journal of Mathematical Physics》2010,17(1):96-125
Diverse closed (and selfadjoint) realizations of elliptic differential expressions A = Σ0⩽|α|,|β|⩽m
(−1)
α
D
α
a
α,β
(x)D
β
, a
α,β
(·) ∈ C
∞($
\bar \Omega
$
\bar \Omega
) on smooth (bounded or unbounded) domains Ω in ℝ
n
with compact boundary ∂Ω are considered. Trace-ideal properties of powers of resolvent differences for these closed realizations of A are proved by using the concept of boundary triples and operator-valued Weyl-Titchmarsh functions, and estimates for negative
eigenvalues of certain selfadjoint extensions of the nonnegative minimal operator are derived. Our results extend classical
theorems due to Vishik, Povzner, Birman, and Grubb. 相似文献
19.
The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension
4≤L≤8. The exponents in the finite-size scaling relations for the order parameter and the magnetic susceptibility at the finite-lattice
critical temperature are computed to be β=0.49(7), β=0.49(5), β=0.50(1) and γ=1.04(4), γ=1.03(4), γ=1.02(4) for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the
obtained results are consistent with the renormalization group predictions of β=0.5 and γ=1. The values for the critical temperature of the infinite lattice T
c
(∞)=6.6788(65), T
c
(∞)=6.6798(69), T
c
(∞)=6.6802(70) are obtained from the straight-line fit of the magnetic susceptibility maxima using 4≤L≤8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained
results are in very good agreement with the series expansion results of T
c
(∞)=6.6817(15), T
c
(∞)=6.6802(2), the dynamic Monte Carlo result of T
c
(∞)=6.6803(1), the cluster Monte Carlo result of T
c
(∞)=6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm result of T
c
(∞)=6.6802632±5×10−5. 相似文献
20.
Quantitative correlations between the intensity of the crystalline band at 1144 cm−1 (A
1144) normalized to the intensity of the C–O stretching band at 1094 cm−1 (A
1094) in IR spectra of PVA films and the degree of crystallinity (α) of these films measured by an x-ray diffraction method were
investigated. It was found that α and A
1144/A
1094 were related by the linear dependence α (%) = a + b(A
1144/A
1094) with correlation coefficient 0.999 for α values in the range 18–60%. 相似文献