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1.
Suresh Chandra 《Pramana》2004,62(5):1181-1185
Kaur and Mahajan [1] have claimed to derive a universal relation InG = 1.91578(±0.09727) + 0.97111(±0.03809) In Δ between the Sutherland parameter Δ(=ω
er
e
2
/2De) and the dimensionless parameterG(= 8ω
exe/Be) for the ground as well as excited electronic states of diatomic molecules. Validity of this relation is checked and we find
that the relation is not correct. Next, we checked the validity of the relation Δ = 2.2re for the alkali group diatomic molecules. This relation is also found not to be correct. 相似文献
2.
Suresh Chandra 《Pramana》2001,56(4):585-587
When observed spectrum of a diatomic molecule is expressed in terms of the Dunham coefficients Y
00, Y
10, Y
20, Y
01 and Y
11 only, dissociation energy of the molecule is given by Y
00+Y
10
2
/(−4Y
20). Kaur and Mahajan [1] have used the Dunham coefficients Y
10, Y
20, Y
01, and Y
11, for 15 vibrational states of 12 diatomic molecules (Y
00 is zero for the cases accounted for), but their dissociation energy cannot be reproduced by the expression Y
10
2
/(−4Y
20). Probable reason for the discrepancy has been discussed. 相似文献
3.
We consider a Gaussian diffusion X
t
(Ornstein-Uhlenbeck process) with drift coefficient γ and diffusion coefficient σ
2, and an approximating process YetY^{\varepsilon}_{t} converging to X
t
in L
2 as ε→0. We study estimators [^(g)]e\hat{\gamma}_{\varepsilon}, [^(s)]2e\hat{\sigma}^{2}_{\varepsilon} which are asymptotically equivalent to the Maximum likelihood estimators of γ and σ
2, respectively. We assume that the estimators are based on the available N=N(ε) observations extracted by sub-sampling only from the approximating process YetY^{\varepsilon}_{t} with time step Δ=Δ(ε). We characterize all such adaptive sub-sampling schemes for which [^(g)]e\hat{\gamma}_{\varepsilon}, [^(s)]2e\hat{\sigma}^{2}_{\varepsilon} are consistent and asymptotically efficient estimators of γ and σ
2 as ε→0. The favorable adaptive sub-sampling schemes are identified by the conditions ε→0, Δ→0, (Δ/ε)→∞, and NΔ→∞, which implies that we sample from the process YetY^{\varepsilon}_{t} with a vanishing but coarse time step Δ(ε)≫ε. This study highlights the necessity to sub-sample at adequate rates when the observations are not generated by the underlying
stochastic model whose parameters are being estimated. The adequate sub-sampling rates we identify seem to retain their validity
in much wider contexts such as the additive triad application we briefly outline. 相似文献
4.
J. K. Baria 《Czechoslovak Journal of Physics》2004,54(4):469-485
A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic
interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C
11,C
12 andC
44), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C
12–C
44), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y
1), limiting value in the [110] direction (Y
2), degree of elastic anisotropy (A), maximum frequencyω
max, mean frequency 〈ω〉, 〈ω
2〉1/2=(〈ω〉/〈ω
−1〉)1/2, fundamental frequency 〈ω
2〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons
is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into
account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar
et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever
possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model
potential for predicting a large number of physical properties of transition metals. 相似文献
5.
T. Mercouris C.A. Nicolaides 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,14(2):241-248
By implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT), cycle-averaged complex eigenvalues
were obtained for the He atom, whose real part gives the field-induced energy shift, Δ(ω
1, F
1;ω
2, F
2,ϕ), and the imaginary part is the multiphoton ionization rate, Γ(ω
1, F
1;ω
2, F
2,ϕ), where ω is the frequency, F is the field strength and ϕ is the phase difference. Through analysis and computation we show that, provided the intensities
are weak, the dependence of Γ(ω
1, F
1;ω
2, F
2,ϕ) on ϕ is simple. Specifically, for odd harmonics, Γ varies linearly with cos(ϕ) whilst for even harmonics it varies linearly
with cos(2ϕ). In addition, this dependence on ϕ holds for Δ(ω
1, F
1;ω
2, F
2,ϕ) as well. These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of
the weak field regime in the dichromatic case. When the combination of (ω
1, F
1) and (ω
2, F
2) is such that higher powers of cos(ϕ) and cos(2ϕ) become important, these rules break down and we reach the strong field
regime. The herein reported results refer to Γ(ω
1, F
1;ω
2, F
2,ϕ) and Δ(ω
1, F
1;ω
2, F
2,ϕ) for He irradiated by a dichromatic ac-field consisting of the fundamental wavelength λ = 248 nm and its 2nd, 3rd and 4th
higher harmonics. The intensities are in the range 1.0×1012-3.5×1014 W/cm2, with the intensity of the harmonics being 1-2 orders of magnitude smaller. The calculations incorporated systematically
electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for 1S, 1P, 1D, 1F, 1G, and 1H two-electron states of even and odd parity.
Received 9 July 2000 and Received in final form 2 November 2000 相似文献
6.
A universal relation between the Sutherland parameter, Δ (= k
e
r
e
/2
/2D
e) and the dimensionless parameter G (= 8ω
e
x
e
/B
e
), has been established using 40 electronic states, which include ground as well as excited states of polar and non-polar
molecules. This relation is used to predict the dissociation energy of four lowest electronic states of S
2 molecule. The respective values for the states X
3Σ
g
/−
, a
1Δ
g
, b
1Σ
g
/+
and B
3Σ
u
/−
turn out to be 36557, 31431, 28247 and 13429 cm−1, and are in good agreement with the experimental values. Furthermore, metastable states a
1Δ
g
and b
1Σ
g
/+
of S
2 are shown to dissociate into 3
P
1 + 3
P
1 as against the dissociation of X
3Σ
g
/−
into 3
P
2 + 3
P
1. In addition, a relation between Sutherland parameter Δ and internuclear distance r
e
, viz., Δ=2.2r
e
has been obtained for the ground state of alkali diatomic molecules. 相似文献
7.
Lei Gao Yanyan Huang 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(2):165-171
The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions
are distributed in shape, are investigated. The shape distribution function P(L
x, L
y) is assumed to be 2Δ-2θ(L
x - 1/3 + Δ/3)θ(L
y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L
x - L
y), where θ( . . . ) is the Heaviside function, Δ is the shape variance and Li are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ
on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α
∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ(3)
e|/χ(3)
1 exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement
bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the
crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As
Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ(3)
e|/χ(3)
1 on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute
limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the
exact results better than old mean field one does.
Received 10 December 2002 Published online 4 June 2003
RID="a"
ID="a"e-mail: lgaophys@pub.sz.jsinfo.net 相似文献
8.
V. K. Balkhanov Yu. B. Bashkuev 《Journal of Experimental and Theoretical Physics》2010,110(3):469-472
The temperature dependences of the ac resistivity R and ac capacitance C of arsenic selenide were measured more than four decades ago [V. I. Kruglov and L. P. Strakhov, in Problems of Solid State Electronics, Vol. 2 (Leningrad Univ., Leningrad, 1968)]. According to these measurements, the frequency dependences are R ∝ ω−0.80±0.01 and ΔC ∝ ω−0.120±0.006 (ω is the circular frequency and ΔC is measured from the temperature-independent value C
0). According to fractal-geometry methods, R ∝ ω1−3/h
and ΔC ∝ ω−2+3/h
, where h is the walk dimension of the electric current in arsenic selenide. Comparison of the experimental and theoretical results
indicates that the walk dimensions calculated from the frequency dependences of resistivity and capacitance are h
R
= 1.67 ± 0.02 and h
C
= 1.60 ± 0.08, which are in agreement with each other within the measurement errors. The fractal dimension of the distribution
of conducting sections is D = 1/h = 0.6. Since D < 1, the conducting sections are spatially separated and form a Cantor set. 相似文献
9.
R. Mélin D. Feinberg 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(1):101-114
We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several
spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be
well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic
cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact.
The maximal conductance of a two-channel contact is proportional to (e
2/h)(a
0/D)2exp[-D/ξ(ω*)], where D is the distance between the contacts, a0 the lattice spacing, ξ(ω) is the superconducting coherence length, and ω* is the cross-over frequency between a perturbative regime ( ω < ω*) and a non perturbative regime ( ω* < ω < Δ).
Received 18 June 2001 and Received in final form 17 January 2002 相似文献
10.
Aldo Procacci Benedetto Scoppola Victor Gerasimov 《Communications in Mathematical Physics》2003,235(2):215-231
Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy
per site W
r
(𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe
3
/q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated
in [16 and 19], based on which a sufficient condition for W
r
(𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice.
Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003
RID="*"
ID="*" Partially supported by CNPq (Brazil)
RID="**"
ID="**" Partially supported by CNR, G.N.F.M. (Italy)
Communicated by H. Spohn 相似文献
11.
R. Hakalla R. Kępa W. Szajna M. Zachwieja 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,38(3):481-488
Three bands of the A1Π- X1Σ+ system
in the 12CH+ ion radical have been rephotographed under
high resolution as an emission spectra using a Geissler-type
discharge tube. The conventional technique of spectroscopy has
been implemented. Using the Th lines as a standards, as well as an
interferometric comparator equipped with a photoelectric scanning
device, the 0-0 , 0-1 and 2-1 bands have been
reanalyzed. By means of much longer bands (Jmax = 17 in the
Q(J) branch of the 0-0 band; Jmax = 16 in the R(J)
branch of the 0-1 band; Jmax = 14 in the P(J) and
Q(J) branches of the 2-1 band), than have been observed so
far, as well as the merged calculations, using another five bands
given by Carrington et al. [A. Carrington, D.A. Ramsay, Phys.
Scripta 25, 272 (1982)] additionally, more accurate molecular
constants for the X1Σ+ state, the improved reduced
band system origin Te = 24118.726 (14) cm-1 as well as for
the first time the equilibrium molecular constants with their one
standard deviation for the A1Π state in the CH+ molecule
have been computed: ωe'=1864.402(22),
ωexe'=115.832(14), ωeye'= 2.6301(24),
Be'=11.88677(72), αe'= 0.9163(18), γe'=
-2.29(12)×10-2, εe'= 4.95(20)×10-3,
De'=1.92960(31)×10-3, βe'=
1.0733(50)×10-4, δe'= -1.312(16)×10-5,
, αqe'=
-3.14(16)×10-3, and qDe'= -2.20(14)×10-5
cm-1. Only in our research the addition to the zero-point
energy Y'00=-1.9430 cm-1 and
cm-1
have been calculated. The equilibrium bond lengths of
r'e=1.235053(37) ? and
? for the
A1Π and X1Σ+ states, respectively have been
computed. Full quantum-mechanics characteristic of the A-X
bands system in the 12CH+ molecule, i.e. RKR turning
points, the Franck-Condon factors and r-centroids have been
obtained. Dissociation energies DeX1 Σ+=(38470±
3503) cm-1 and DeA1 Π= (14415 ±3509) cm-1
for the molecule under consideration have been estimated. 相似文献
12.
For the first time submillimetric microwaves (λ<1 mm) are used to observe Azbel' Kaner cyclotron resonance in metals. The very high frequency used (typicallyF≅400 GHz) gives a large value ofωτ (typically 500) and therefore very sharp peaks. The fundamental resonance fieldH
c=m
*
cω/e is rather high (typically 200 KG), so subharmonicsH
c/n can be observed at many values ofH in the field region 0–27 KG. If relatively few electrons participate in the resonance and ifω
cτ≧50 (ω
c=eH/m
*
c,τ relaxation time) thenChambers has shown that the line shapes are independent of relaxation time while the fractional linewidthΔH/H varies as l/ωτ. For the belly orbit in pure copper the conditions of Chambers' theory are satisfied forH≧20 KG parallel to [111] axis.m
* is a minimum andτ=1.8×10−10 s. 相似文献
13.
C. Monthus T. Garel 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(1):39-45
The directed polymer in a 1+3 dimensional
random medium is known to present a disorder-induced phase
transition. For a polymer of length L, the high temperature
phase is characterized by a diffusive behavior for the end-point
displacement R2 ∼L and by free-energy fluctuations of order
ΔF(L) ∼O(1). The low-temperature phase is characterized by
an anomalous wandering exponent R2/L ∼Lω and
by free-energy fluctuations of order ΔF(L) ∼Lω
where ω∼0.18. In this paper, we first study the scaling
behavior of various properties to localize the critical temperature
Tc. Our results concerning R2/L and ΔF(L) point towards
0.76 < Tc ≤T2=0.79, so our conclusion is that Tc is equal
or very close to the upper bound T2 derived by Derrida and
coworkers (T2 corresponds to the temperature above which the ratio
remains finite as L ↦
∞). We then present histograms for the free-energy, energy and
entropy over disorder samples. For T ≫Tc, the free-energy
distribution is found to be Gaussian. For T ≪Tc, the free-energy
distribution coincides with the ground state energy distribution, in
agreement with the zero-temperature fixed point picture. Moreover the
entropy fluctuations are of order ΔS ∼L1/2 and follow a
Gaussian distribution, in agreement with the droplet predictions,
where the free-energy term ΔF ∼Lω is a near
cancellation of energy and entropy contributions of order L1/2. 相似文献
14.
Coherent propagation of atomic-matter waves in a one-dimensional optical lattice is studied. Wave packets of cold two-level
atoms propagate simultaneously in two optical potentials in a dressed-state basis. Three regimes of the wave-packet propagation
are specified by the quantity Δ2
/ω
D
, where Δ and ω
D
are the dimensionless atom–laser detuning and the Doppler shift, respectively. At Δ2
/ω
D
≫ 1, the propagation is essentially adiabatic, at Δ2
/ω
D
≪ 1, it is (almost) resonant, and at Δ2 ≃ ω
D
, the wave packets propagate nonadiabatically, splitting at each node of the standing wave. The latter means that the atom
makes a transition from one potential to the other one when crossing each node, and the probability of that transition is
given by a Landau–Zener-like formula. All the regimes of propagation are studied with δ-like and Gaussian wave packets in the momentum and position spaces. Varying the control parameters, we can create wave packets
trapped in a well of optical potentials and moving ballistically in a given direction in close analogy with point-like atoms.
Within some range of the parameters, we force the atom to move in a pure quamtum-mechanical manner in such a way that a part
of the packet is trapped in a well, and the other part propagates ballistically. The propagation modes are found to be characterized
by different types of time evolution of the uncertainty product and the Wigner function. 相似文献
15.
The value of adjustable parameterC in the four-parameter potentialU(r) =D
e [(1 - exp[-b(r -r
e)])/(1 -C exp[-b(r -r
e)])]2 has been expressed in terms of molecular parameters and its significance has been brought out. The potential so constructed,
withC derived from the molecular parameters, has been applied to ten electronic states in addition to the states studied by Wei
Hua. Average mean deviation for these 25 states has been found to be 3.47 as compared to 6.93, 6.95 and 9.72 obtained from
Levine, Varshni and Morse potentials, respectively. Also Dunham’s method has been used to express rotation-vibration interaction
constant (αe) and anharmonicity constant (ωexe) in terms ofC and other molecular constants. These relations have been employed to determine these quantities for 37 electronic states.
For αe, the average mean deviation is 7.2% compared to 19.7% for Lippincott’s potential which is known to be the best to predict
these values. Average mean deviation for (ωexe) turns out to be 17.4% which is almost the same as found from Lippincott’s potential function. 相似文献
16.
A microscopic theory of the Efetov supermatrix sigma-model type is constructed for the low-lying electron states in a mixed
superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a
vortex in a moderately clean superconductor with τ
−1≫ω
0∼Δ2/E
F
. At low energies ε≪ω
Th∼ (ω
0/τ)1/2, the energy level statistics is described by the “zero-dimensional” limit of this supermatrix theory, and the result for
the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma
model increase the mean interlevel distance by the relative amount [2 ln (1/ω
0
τ)]−1.
Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 78–83 (10 July 1998)
Published in English in the original Russian journal. Edited by Steve Torstveit. 相似文献
17.
Effect of the molecular structure on the gas-surface scattering
studied by supersonic molecular beam
T. Kondo H. S. Kato T. Yamada S. Yamamoto M. Kawai 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,38(1):129-138
The experimental apparatus for investigating the gas-surface interaction has
been newly developed. The coherent length of the helium, the energy
resolution and the angular spread of the beam in the apparatus were
established as ω= 16 nm,
DE/E = 2.4%\Delta E/E = 2.4{\%}
and Δθ= 0.5○, respectively, through the
measurements of the time-of-flight of He beam and of the angular intensity
distributions of He scattered from LiF(001). The angular intensity
distributions of Ar, N2 and CO scattered from the LiF(001) surface
along the [100] azimuthal direction were then measured as a function of
incident translational energy. The effects of the molecular structural
anisotropy and center-of-mass position on the gas-surface inelastic
collision at the corrugated surface are discussed with predictions based on
a recently developed simple classical theory of the ellipsoid-washboard
model. 相似文献
18.
X. G. Wu M. J. Wan C. Q. Song T. Gao 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2010,60(2):263-267
Electronic structure and spectroscopic properties B
e, ωe, ωe
x
e, αe, T
e
of ground state and the low-lying excited states of HF+ and HF- molecular ions were
investigated within scalar relativistic multireference configuration
interaction with single and double excitations framework using the GAMESS-US
program package. All potential energy curves (PECs) were calculated using
the relativistic complete active space self-consistent field/spin-orbit
multi-configuration quasi-degenerate perturbation theory (CASSCF/SO-MCQDPT).
The curves are all fitted to the analytical potential energy function
(APEF), from which accurate spectroscopic constants are derived. The
spin-orbit splitting was also been studied, the split value of X2P^{2}{\rm \Pi} state of HF+ is determined to be 288.38 cm-1. The calculated properties are in good agreement with the available experimental value.
Spectroscopic constants of the ground states of HF- that have never
been observed in experiment are obtained. These curves provide an
interpretation of the known experimental observations on this system and
suggest a number of further experiments which possible provide a critical
test of this data. 相似文献
19.
L. Bartosch P. Kopietz 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(1):29-36
We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals
for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln2-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions
to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e
4 appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω
2 which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω
1)1/2exp(- Ω
1/|ω|) at T = 0, where Ω
1 is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance
that can be compared with experiments.
Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002 相似文献
20.
Space-time dispersion of graphene conductivity 总被引:1,自引:0,他引:1
L. A. Falkovsky A. A. Varlamov 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(4):281-284
We present an analytic calculation of the conductivity of pure graphene as a
function of frequency ω, wave-vector k, and temperature for the
range where the energies related to all these parameters are small in
comparison with the band parameter γ≃3 eV, but much larger than
the collision rate τ-1. The simple asymptotic expressions are given
in various limiting cases. For instance, the conductivity for kv0≪
T≪ω is equal to σ(ω,k)=e2/4ħ and independent
of the band structure parameters γ and v0. Our results are also
used to explain the known dependence of the graphite conductivity on
temperature and pressure. 相似文献