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1.
E. Korotyaev 《Communications in Mathematical Physics》1997,183(2):383-400
LetG
n=(A
n
−
, A
n
+
),n≧1, denote the gaps,M
n
±
be the effective masses and Σn=[A
n−1
+
,A
n
-
],A
0
+
=0, be the spectral bands of the Hill operatorT=−d
2/dx
2+V(x) inL
2 (R), whereV is a 1-periodic real potential fromL
2(0,1). Let the length gapL
n=|Gn|, hn be the height of the corresponding slit on the quasimomentum domain and Δn=π2(2n−1)−∣Σn∣>0 be the band reduction. Let
,n≧1, denote the gap length for the operator
. Introduce the sequencesL={Ln}, h={hn}, l={ln}, Δ={Δn},M
±={M
n
±
} and the norms
,m≧0. The following results are obtained: i) The estimates of‖V‖, ‖L‖, ‖h‖
1, ‖l‖1, ‖δ‖ in terms of ‖M±‖2, ii) identities for the Dirichlet integral of quasimomentum and integral of potentials and so on, iii) the generation of
i), ii) for more general potentials.
The research described in this publication was made possible in part by grant from the Russian Fund of Fundamental Research
and INTAS. 相似文献
2.
V. S. Rabinovich 《Russian Journal of Mathematical Physics》2009,16(2):300-308
We consider the class of matrix h-pseudodifferential operators Op h (a) with symbols a = (a ij ) i,j=1 N , where the coefficients a ij ∈ C ∞(? x n × ? ξ n ? C(0, 1] satisfy the estimates |? x β g6 ξ α α ij (x, ξ, h)| ? C αβ 〈ξ〉 m and 〈ξ〉 = (1 + |ξ|2)1/2 for every multi-indices α, β. We also assume that a ij (x, ξ) is analytically continued with respect to ξ to a tube domain ? n + i $ \mathcal{B} We consider the class of matrix h-pseudodifferential operators Op
h
(a) with symbols a = (a
ij
)
i,j=1N, where the coefficients a
ij
∈ C
∞(ℝ
x
n
× ℝ
ξ
n
⊗ C(0, 1] satisfy the estimates |ϖ
x
β
g6
ξ
α
α
ij
(x, ξ, h)| ⩽ C
αβ
〈ξ〉
m
and 〈ξ〉 = (1 + |ξ|2)1/2 for every multi-indices α, β. We also assume that a
ij
(x, ξ) is analytically continued with respect to ξ to a tube domain ℝ
n
+ i
, where is a bounded domain in ℝ
n
containing the origin. The main results of the paper are the local estimates for solutions of h-pseudodifferential equations.
Let H
h
s
(ℝ
n
, ℂ
N
) be the space of distributions with values in ℂ
N
which is equipped with the norm , let Ω ⊂ ℝ
n
be a bounded open set, let v ∈ C
∞(ℝ
n
), let ▿v(x) ∈ for any x ∈ Ω, and let . Let u
h
(∈ H
h
s
(ℝ
n
,‒
N
)) be a solution of the equation Op
h
(α)u = 0. In this case, for every ϕ ∈ C
0∞ (Ω) such that ϕ(x) = 1 on Supp v and for a sufficiently small h
0 > 0, there exists a constant C > 0 such that the following estimate holds for every h ∈ (0, h
0]:
We apply estimate (1) to local tunnel exponential estimates for the behavior as h → 0 of the eigenfunctions of matrix Schr?dinger, Dirac, and square-root Klein-Gordon operators.
To the memory of Professor V. A. Borovikov 相似文献
((1)) |
3.
E. A. Kataeva A. D. Bozhko S. V. Demishev 《Bulletin of the Lebedev Physics Institute》2010,37(11):347-351
The conductivity of carbon films grown by polymethylphenylsiloxane vapor decomposition in stimulated dc discharge plasma was
studied. It is found that the Mott hopping conductivity $
\sigma \left( T \right) = \sigma _0 \left( T \right)\exp \left\{ { - \frac{{T_0 }}
{T}^{{1 \mathord{\left/
{\vphantom {1 4}} \right.
\kern-\nulldelimiterspace} 4}} } \right\}
$
\sigma \left( T \right) = \sigma _0 \left( T \right)\exp \left\{ { - \frac{{T_0 }}
{T}^{{1 \mathord{\left/
{\vphantom {1 4}} \right.
\kern-\nulldelimiterspace} 4}} } \right\}
is characteristic of the samples under study in the temperature range of 80–400 K in the electric field E to 5 · 104 V/cm. An analysis of the pre-exponential factor σ
0(T) = σ
00(T
0)T
α allowed the conclusion that the hopping transport is most adequately described in the model with the exponential energy dependence
of the density of localized states for which α = −1/2 and the universal relation ln σ
00 −T
01/4 0 is valid, which is satisfied in the range where the parameter σ
00 varies by eight orders of magnitude. 相似文献
4.
It is shown that the slope of the upper critical field
in superconductors with d pairing drops rapidly with increasing concentration of normal impurities, while in superconductors with anisotropic s pairing
increases and reaches the well-known asymptotic level characteristic for the isotropic case. This difference makes it possible,
in principle, to employ measurements of H
c
2 in disordered superconductors as an experimental method for determining the type of pairing in high-T
c
superconductors and systems with heavy fermions.
Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 347–352 (10 March 1996) 相似文献
5.
S. G. Karshenboim 《Physics of Particles and Nuclei Letters》2009,6(6):450-454
Oscillations of neutral meson (K
0-$
\overline {K^0 }
$
\overline {K^0 }
, D
0-$
\overline {D^0 }
$
\overline {D^0 }
, and B
0-$
\overline {B^0 }
$
\overline {B^0 }
are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc
2—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct
for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field
of the galaxy center, we obtain the estimate from experimental data on K
0-$
\overline {K^0 }
$
\overline {K^0 }
oscillations:
$
\left| {\left( {\frac{{m_g }}
{{m_i }}} \right)_{K^0 } - \left( {\frac{{m_g }}
{{m_i }}} \right)_{\overline {K^0 } } } \right| \leqslant 8 \times 10^{ - 13} , at C.L. = 90\%
$
\left| {\left( {\frac{{m_g }}
{{m_i }}} \right)_{K^0 } - \left( {\frac{{m_g }}
{{m_i }}} \right)_{\overline {K^0 } } } \right| \leqslant 8 \times 10^{ - 13} , at C.L. = 90\%
相似文献
6.
Moments of the hadronic invariant mass and of the lepton energy spectra in semileptonic B decays have been determined with
the data recorded by the DELPHI detector at LEP. From measurements of the inclusive b-hadron semileptonic decays, and imposing constraints from other measurements on b- and c-quark masses, the first three moments of the lepton energy distribution and of the hadronic mass distribution, have been
used to determine parameters which enter into the extraction of |Vcb| from the measurement of the inclusive b-hadron semileptonic decay width. The values obtained in the kinetic scheme are:
and include corrections at order 1/mb3. Using these results, and present measurements of the inclusive semileptonic decay partial width of b-hadrons at LEP, an accurate determination of |Vcb| is obtained:
Received: 26 April 2005, Revised: 16 September 2005, Published online: 16 November 2005 相似文献
7.
Maximal Inequalities for CIR Processes 总被引:1,自引:0,他引:1
Let X be a Cox—Ingersoll—Ross (CIR) process given by
8.
N. I. Rukhadze P. Beneš Ch. Briançon V. B. Brudanin P. Čermák F. A. Danevich V. G. Egorov K. N. Gusev A. A. Klimenko V. E. Kovalenko A. Kovalik A. V. Salamatin I. Štekl V. V. Timkin V. I. Tretyak Ts. Vylov 《Physics of Atomic Nuclei》2006,69(12):2117-2123
A search for double electron capture of 106Cd was performed at the Modane Underground Laboratory (4800 m w.e.) using a low-background and high-sensitivity multidetector
spectrometer TGV-2 (Telescope Germanium Vertical). New limits on β
+/EC, EC/EC decays of 106Cd were obtained from preliminary calculations of experimental data accumulated for 4800 h of measurement of 10 g of 106Cd with enrichment of 75%. They are
> 9.1 × 1018 yr,
> 1.9 × 1019 yr for transitions to the first 2+, 511.9 keV excited state of 106Pd, and
> 1.3 × 1019 yr,
> 6.2 × 1019 yr for transitions to the ground 0+ state of 106Pd. All limits are given at 90% C.L.
The text was submitted by the authors in English. 相似文献
9.
Yu. S. Surovtsev T. Branz T. Gutsche V. E. Lyubovitskij 《Physics of Particles and Nuclei》2010,41(6):990-993
In a model-independent approach the data on ππ → ππ, K
$
\bar K
$
\bar K
, ηη, ηη′ in the I
G
J
PC
= 0+0++ channel and on the Kπ scattering in the $
I\left( {J^P } \right) = \frac{1}
{2}\left( {0^ + } \right)
$
I\left( {J^P } \right) = \frac{1}
{2}\left( {0^ + } \right)
channel are analyzed jointly for studying the status and QCD nature of the f
0- and the K*0-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q
$
\bar q
$
\bar q
). In the Kπ-scattering data analysis, the proof for the K*0(900) is given. 相似文献
10.
R. Orbach 《Hyperfine Interactions》1989,49(1-4):325-333
The excitation dynamics of site diluted magnets can be described at low energies (long length scales) by magnons, and above
a crossover frequency, ωc, (short length scales) by fractons. The density of fracton states is given by
, where
is the fracton dimensionality. Dilution gives rise to a characteristic length ξ∝(p−p
c)ν, wherep
c is the critical concentration for (magnetic) percolation. The crossover frequency ωc is proportional to ξ-1[1+(θ/2)], where θ is the rate at which the diffusion constant decays with distance for diffusion on an equivalent network. A fractal
dimensionD describes the density of magnetic sites on the infinite network, and
. For percolating networks,
for all dimensions ≥2. Neutron scattering structure factor measurements by Uemura and Birgeneau compare well with calculations
using fracton concepts.
Magnons are extended at low energies, while the fracton states are geometrically localized, with a wave function envelope
proportional to exp
. Here,
is the fracton length scale at frequency ω. The exponentd
ϕ lies between 1 andd
min, the chemical length index (of the order of 1.6 in three dimensions). The localization of the magnetic excitations causes
a spread in the NMR relaxation rates. A given nuclear moment will experience only a limited set of fracton excitations, resulting
in an overall non-exponential decay of the NMR relaxation signal. When strong cross-relaxation is present, the relaxation
will be exponential, but the temperature dependence will be strongly altered from the concentrated result. 相似文献
11.
The time-dependent and time-independent CP asymmetries $
A_{CP}^{B_q^0 \to f} \left( \tau \right)
$
A_{CP}^{B_q^0 \to f} \left( \tau \right)
and $
A_{CP}^{B_q^0 \to f} \left( {\hat s} \right)
$
A_{CP}^{B_q^0 \to f} \left( {\hat s} \right)
for rare semileptonic and radiative leptonic decays of B mesons are calculated by the method of helicity amplitudes. The sensitivity of CP asymmetries to various extensions of the Standard Model that have an operator basis that is identical to the operator basis
of the Standard Model is investigated. It is shown that, by combining information about the form of the charge lepton asymmetry
A
FB
at small values of the square of the invariant dilepton mass and information about the average value of the time-dependent
CP asymmetry, one can in principle determine the relative phases of the Wilson coefficients C
7γ
, C
9V
, and C
10A
in the effective Hamiltonian for b → {d, s}ℓ+ℓ− transitions. 相似文献
12.
In this paper, we deal with operators of the form
13.
C. Novotny B. Bernhardt G. Ewald C. Geppert G. Gwinner T. W. Hänsch R. Holzwarth G. Huber S. Karpuk H.-J. Kluge T. Kühl W. Nörtershäuser S. Reinhardt G. Saathoff D. Schwalm T. Udem A. Wolf 《Hyperfine Interactions》2006,171(1-3):57-67
The Doppler-free laser-spectroscopic frequency measurement of Doppler-shifted optical lines in forward and backward direction
of a fast ion beam permits a sensitive test of the relativistic Doppler-formula and, hence, the relativistic time dilation
factor . An experiment on metastable 7Li+, stored at a velocity of v = 0.064c in the Heidelberg heavy-ion storage ring TSR, has confirmed time dilation with unprecedented accuracy. Latest tests at two
different ion-velocities (v = 0.03c and v = 0.064c) will enhance these measurements. An improved version of this experiment will be carried out at the experimental storage
ring (ESR) at the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt. The ESR permits 7Li+ to be stored at v = 0.33c which promises an improvement of the sensitivity to deviations from γ
SR by an order of magnitude. A first test at the ESR has shown the feasibility for this kind of experiment. 相似文献
14.
15.
S. A. Nemov M. K. Zhitinskaya R. V. Parfen’ev D. V. Shamshur 《Physics of the Solid State》1998,40(7):1096-1097
A study is reported of the effect of low-level germanium additions (∼0.01–0.1 at. %) on the parameters of the superconducting
transition, viz. the critical temperature T
c, the second critical magnetic field H
c2, and
in PbTe doped with 2 at. % Tl, which are derived from the dependence of the electrical resistivity of a sample on temperature
(0.4–4.2 K) and magnetic field (0–1.3 T). The discontinuity revealed by experimental data is related to the onset of a Ge-induced
structural phase transition.
Fiz. Tverd. Tela (St. Petersburg) 40, 1204–1205 (July 1998) 相似文献
16.
A. P. Blinov 《Russian Physics Journal》2006,49(12):1283-1287
17.
18.
K. H. Hellwege S. Hüfner G. Schäfer S. Scheller 《Zeitschrift für Physik B Condensed Matter》1967,6(2):100-104
The paramagnetic resonance of Nd3+ in Y2O3 has been measured at 4.2°K and 9.25 kMe/s. The values of theg-tensors are: ions onC
3i
-sites:g
∥=2.434±0.007;g
⊥=0.702±0.005; ions onC
2-sites:g
x
=4.395±0.012;g
y
=0.433±0.009;g
z
=1.648±0.006.
Further measurements have been performed on La2O3 crystals doped with Ce3+, Dy3+, and Er3+; the results are (C
3v
-sites only):
.
相似文献
19.
E. V. Gryzlova A. N. Grum-Grzhimailo A. I. Magunov S. I. Strakhova 《Optics and Spectroscopy》2010,109(1):59-65
Optical activity of xenon atoms in the vacuum UV range induced by circularly polarized laser light is studied theoretically.
The optical activity arises in the vicinity of the autoionizing state 5p
5(2
P
1/2)8s′$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
as a result of its coupling via the laser field with the discrete state 5p
5(2
P
3/2)7p
$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
. Polarization variations of the vacuum UV radiation upon its propagation through the atomic medium are calculated, and the
possibility of controlling this polarization is discussed. Manifestations of nonresonant coupling of the discrete state with
the broad autoionizing state 5p
5(2
P
1/2)6d′$
\left[ {\frac{1}
{2}} \right]_1
$
\left[ {\frac{1}
{2}} \right]_1
induced by the overlap of the Rydberg autoionizing series in xenon are studied. 相似文献
20.
Carl M. Bender 《Czechoslovak Journal of Physics》2006,56(9):1047-1062
In this paper, two independent methods are used to show that the non-Hermitian
-symmetric wrong-sign quartic Hamiltonian H = (1/2m)p
2 − gx
4 is exactly equivalent to the conventional Hermitian Hamiltonian
. First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated
by using functional-integration methods. As the linear term in the Hermitian Hamiltonian
is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly
is a consequence of the broken parity symmetry of the original non-Hermitian
-symmetric Hamiltonian. The anomaly term in
remains unchanged if an x
2 term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in
are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states. 相似文献
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