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1.
Within the model of stable random matrices possessing translational invariance, a two-dimensional (on a square lattice) disordered oscillatory system with random strongly fluctuating bonds is considered. By a numerical analysis of the dynamic structure factor S(q, ω), it is shown that vibrations with frequencies below the Ioffe-Regel frequency ωIR are ordinary phonons with a linear dispersion law ω(q) ∝ q and a reciprocal lifetime б ~ q3. Vibrations with frequencies above ωIR, although being delocalized, cannot be described by plane waves with a definite dispersion law ω(q). They are characterized by a diffusion structure factor with a reciprocal lifetime б ~ q2, which is typical of a diffusion process. In the literature, they are often referred to as diffusons. It is shown that, as in the three-dimensional model, the boson peak at the frequency ωb in the reduced density of vibrational states g(ω)/ω is on the order of the frequency ωIR. It is located in the transition region between phonons and diffusons and is proportional to the Young’s modulus of the lattice, ω
b
≃E. 相似文献
2.
The random matrix theory has been used for analyzing vibrational spectra of amorphous solids. The random dynamical matrix
M = AA
T
with nonnegative eigenvalues ɛ = ω 2 has been investigated. The matrix A is an arbitrary square ( N-by- N) real sparse random matrix with n nonzero elements in each row, mean values 〈 A
ij
〉 = 0, and finite variance 〈 A
ij
2〉 = V
2. It has been demonstrated that the density of vibrational states g(ω) of this matrix at N, n ≫ 1 is described by the Wigner quarter-circle law with the radius independent of N. For n ≪ N, this representation of the dynamical matrix M = AA
T
makes it possible in a number of cases to adequately describe the interaction of atoms in amorphous solids. The statistics
of levels (eigenfrequencies) of the matrix M is adequately described by the Wigner surmise formula and indicates the repulsion of vibrational terms. The participation
ratio of the vibrational modes is approximately equal to 0.2–0.3 almost over the entire range of frequencies. The conclusions
are in qualitative and, frequently, quantitative agreement with the results of numerical calculations performed by molecular
dynamics methods for real amorphous systems. 相似文献
3.
The effective Debye temperatures Θ eff determined for solids by different physical methods have been analyzed and compared. Attention has been focused on the original
parameter of the Debye theory of heat capacity, i.e., the translational calorimetric Debye temperature Θ
c
t
(0), and the X-ray Debye temperature Θ
x
in the framework of the Debye-Waller theory for the C 60 fullerite. It has been established that the true Debye law T
3 is satisfied for the C 60 fullerite over a very narrow range of temperatures: 0.4 K ≤ T ≤ 1.8 K. For this reason, the experimental Debye temperatures Θ
c
t
(0) obtained for the C 60 fullerite by different authors in the range T > 4.2 K are characterized by a large scatter (by a factor of ∼5). It has been revealed that the value Θ
c
t
(0) = 77.12 K calculated in this paper with the use of the six-term Betts formula from the harmonic elastic constants $
\tilde C_{ijkl}
$
\tilde C_{ijkl}
of the C 60 single crystal in the limit T = 0 K is closest to the true Debye temperature. It has been demonstrated using the method of equivalent moments that the
real spectral frequency distribution of translational lattice vibrations g(ω) for the C 60 fullerite deviates from a parabolic distribution. The effective Debye temperatures Θ eff involved in applied problems of thermodynamics of crystals and elastic scattering of different radiations from lattice vibrations
have been determined. The quantitative measure of anharmonicity of translational and librational lattice vibrations of the
C 60 fullerite has been determined. This has made it possible to empirically evaluate the lattice thermal conductivity κ of the
C 60 fullerite at T ≈ 300 K: κ(300) = 0.80 W (m/K), which is in good agreement with the experimental thermal conductivity κ exp = 0.78 W (m/K) at T ≈ 250 K. 相似文献
4.
We have obtained IR absorption spectra of a C 2F 6 gas and a C 2F 6 cryosolution in Xe ( T = 163 K) in the fundamental and overtone ranges. We have interpreted 28 bands of 12C 12CF 6 and three bands of 13C 12CF 6. In the spectral ranges that correspond to vibrations that are combinations with ν 1, ν 7, and ν 5, we observe multiplets, which we attribute to interactions of the type of Fermi resonances between the states ν 1( A
1g
) ∼ ν 6( A
1g
), ν 7( E
g
) ∼ ν 6 + ν 11( E
g
) ∼ 2ν 8( E
g
), ν 5( A
2u
) ∼ ν 8 + ν 11( A
2u
). We reveal an anomalous intensity distribution in the spectrum of an asymmetric isotopologue. For the basic and isotopic
configurations of perfluoroethane, we calculate the coefficients of shapes of vibrations and the intensities of absorption
bands. We reveal that the behavior of the groups 12CF 3 and 13CF 3 is indifferent to the excitation of doubly degenerate stretching vibrations ν 7( E
g
) and ν 10( Eu). 相似文献
5.
Summary The spectral behaviour of the direct interband two-photon absorption coefficient α (2) in ZnO, CuCl and Bi 4Ge 3O 12 has been investigated in a large excitation energy range. The experimental results have shown that the α (2) spectral behaviour is well described by a parametric formula containing terms with different energy dependence. In particular,
for 2ħω- E
g>≈400 meV, the first experimental evidence of 2ħω- E
g) 5/2 dependence has been obtained. As a consequence, each of the various models proposed to predict the α (2) dispersion curve gives the correct energy dependence in a limited energy range, due to the poor approximation made in the
evaluation of dipole matrix elements. To explain the spectral dependence of the two-photon absorption coefficient, consideration
of all the intermediate states is required, with the energy dependence of the dipole matrix elements properly considered.
It is shown that the greatest contributions to the oscillator strength come from transitions totally allowed at the critical
points.
Work partially supported by M.P.I. 相似文献
6.
We solve the quantum mechanical problem of the inelastic scattering of phonons by a quadrupole defect in a crystal lattice
for the case of solid parahydrogen whose matrix contains pair complexes of H 2 orthomolecules. By employing the pseudospin approximation for the operator of the energy of quadrupole-quadrupole interaction
of the molecules in an orthopair we derive an effective Hamiltonian that describes the interaction of phonons with a pair
quadrupole orthodefect in the lattice. We set up the scattering matrix and calculate the effective phonon relaxation time
τ( ω, T) as a function of the frequency ω and the crystal temperature T. We also find that a pair quadrupole defect, which has a complicated system of levels, can be replaced by an effective two-level
system with temperature-dependent parameters. The fact that a pair quadrupole orthocluster has internal degrees of freedom
results in a resonant scattering peak near a certain critical temperature T
0. Our estimates for H 2 yield T
0≃ 6–7 K. Finally, we discuss the contribution of this mechanism to the low-temperature thermal conductivity of solid hydrogen.
Zh. éksp. Teor. Fiz. 114, 555–569 (August 1998) 相似文献
7.
Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose 𝔸
h
( M) is a 𝕌
h
( g)-equivariant quantization of the function algebra 𝔸( M) on M. We develop a method of building 𝕌
h
( g)-equivariant quantization on G-orbits in M as quotients of 𝔸
h
( M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in 𝕌 *
h
( g) and quotients of 𝔸
h
( M). It turns out that they are in one-to-one correspondence with characters of the algebra 𝔸
h
( M). We specialize our approach to the situation g= gl( n,ℂ), M=End(ℂ
n
), and 𝔸
h
( M) the so-called reflection equation algebra associated with the representation of 𝕌
h
( g) on ℂ
n
. For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and
bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the 𝕌( g)-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits.
Received: 28 April 2002 / Accepted: 3 October 2002 Published online: 24 January 2003
RID="*"
ID="*" This research is partially supported by the Israel Academy of Sciences grant no. 8007/99-01.
Communicated by L. Takhtajan 相似文献
8.
We focus the problem of establishing when a statistical mechanics system is determined by its free energy. A lattice system,
modelled by a directed and weighted graph (whose vertices are the spins and its adjacency matrix M will be given by the system transition rules), is considered. For a matrix A( q), depending on the system interactions, with entries which are in the ring Z[ a
q
: a∈ R
+] and such that A(0) equals the integral matrix M, the system free energy β
A
( q) will be defined as the spectral radius of A( q). This kind of free energy will be related with that normally introduced in Statistical Mechanics as proportional to the
logarithm of the partition function. Then we analyze under what conditions the following statement could be valid: if two
systems have respectively matrices A, B and β
A
= β
B
then the matrices are equivalent in some sense. Issues of this nature receive the name of rigidity problems. Our scheme,
for finite interactions, closely follows that developed, within a dynamical context, by Pollicott and Weiss but now emphasizing
their statistical mechanics aspects and including a classification for Gibbs states associated to matrices A( q). Since this procedure is not applicable for infinite range interactions, we discuss a way to obtain also some rigidity results
for long range potentials. 相似文献
9.
Corrections to scaling in the q-state Potts model due to departures of the initial condition from scaling
morphology are studied at zero temperature in phase-ordering kinetics within Gaussian closure approximation.
When the corrections to scaling are included, the equal time correlation function has the
form G(r,t) = g 0(r/L)+L -ωg 1(r/L) + ...,
where L is the coarsening length scale. Both the correction-to-scaling exponent ω and
the correction-to-scaling function g 1(x) are calculated for different values of q. The
correction-to-scaling exponent ω is found to be nontrivial and depends on q. The
corrections to scaling are found to be large (relative to scaling function g 0(x) itself) at large
scaling variable x. 相似文献
10.
The coefficient R( ν) of reflection from the surface of 6H-SiC single crystals is studied in the case in which the long-wavelength optical vibrations
of the lattice are coupled with the electron plasma. It is shown for the first time that the anisotropy of the properties
of electrons and phonons in 6H-SiC gives rise to special features in the spectrum of the coupled vibrations and the transparency
regions. It is found, in particular, that if the axis of the crystal lies in the polarization plane of the incident radiation
(0< θ<90°), for 30 cm −1⩽ ν
p⊥<320 cm −1 the spectrum of R( ν) acquires three regions of transparency and opacity, and for ν
p⊥⩾320 cm −1 four such regions, which are absent in an isotropic medium. The width of these regions is found to depend on the electron
concentration in the conduction band and on the angle θ.
Zh. éksp. Teor. Fiz. 116, 646–654 (August 1999) 相似文献
11.
Let ℳ be a von Neumann algebra with a cyclic and separating vector Ω and let ω(·) denote the corresponding vector state, i.e.,
ω( A)=(Ω, AΩ) A ∈ ℳ. We have proved that a positive semigroup τ on ℳ can induce the dynamical semigroup in the GNS representation associated
with ω if the state ω is a τ-invariant one. Some applications are given. 相似文献
12.
A theory of nonresonant acoustic absorption in Ising magnets is constructed by the nonequilibrium statistical operator method.
It is assumed that the spins are coupled with the sound via modulation of the Ising exchange integral, and the nonresonant
absorption is due to the interaction of the spin system with the thermal vibrations of the lattice. The frequency dependence
of the absorption χ″( ω), which has an analytical form different from that of the well-known Debye function, is determined. The temperature dependence
of χ″( ω), which is made up of 1) the averages of the vibrational variables and 2) the temperature dependence of the spin correlation
functions of the linear Ising model, is analyzed. It is shown that the cross-coupling of the two subsystems (Ising and Zeeman)
produces a second absorption peak at low frequencies together with the peak characteristic of the Debye curve.
Fiz. Tverd. Tela (St. Petersburg) 39, 516–521 (March 1997) 相似文献
13.
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, a 0 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
14.
The relaxation time τ( ω) for the scattering of the lattice waves of frequency ω by the paraelastic defects has been calculated by using the Feynman graph method, applied to a previous theoretical model
[8]. A simple expression for the resonance component of τ( ω) −1 has been derived.
Zusammenfassung Die Relaxationszeitτ(ω) für die Streuung der Gitterwellen der Frequenzω an den paraelastischen Defekten wurde nach der Methode der Feynmanschen Graphen berechnet, wobei ein früheres theoretisches
Modell [8] angewendet wurde. Ein einfacher Ausdruck für den Resonanzteil vonτ(ω)−1 wurde hergeleitet.
Résumé Nous avons calculé le temps de relaxationτ(ω) des ondes du réseau de fréquenceω, qui sont diffusées par des défauts para-élastiques, en appliquant la méthode des graphes de Feynman à un modèle théorique
antérieur [8]. Une simple expression pour la partie résonante deτ(ω)−1 a été dérivée.
相似文献
15.
The Fredholm representation theory is well adapted to the construction of homotopy invariants of non-simply-connected manifolds
by means of the generalized Hirzebruch formula [ σ( M)] = 〈 L( M)ch
A
f* ξ, [ M]〉 ∈ K
A
0(pt) ⊗ Q, where A = C*[ π] is the C*-algebra of the group π, π = π
1( M). The bundle ξ ∈ K
A
0( Bπ) is the canonical A-bundle generated by the natural representation π → A.
Recently, the first author constructed a natural family of Fredholm representations that lead to a symmetric vector bundle
on the completion of the fundamental group with a modification of the Higson-Roe corona, provided that the completion is a
closed manifold. 相似文献
16.
An investigation is reported of stimulated two-photon emission by Bose-condensed excitons accompanied by a coherent two-exciton
recombination, i.e., by simultaneous recombination of two excitons with opposite momenta leaving unchanged the occupation
numbers of exciton states with momenta p≠0. Raman light scattering (RLS) accompanied by a similar two-exciton recombination (or production of two excitons) is also
analyzed. The processes under consideration can occur only if a system contains Bose condensate, so their detection can be
used as a new method to reveal Bose condensation of excitons. The recoil momentum, which corresponds to a change in the momentum
of the electromagnetic field in the processes, is transferred to phonons or impurities. If the recoil momentum is transmitted
to optical phonons with frequency ω
0
s
, whose occupation numbers are negligible, and the incident light frequency satisfies ω<2Ω, where Ω_=Ω− ω
0
s
is the difference frequency and Ω is the light frequency corresponding to the recombination of an exciton with zero momentum,
stimulated two-photon emission and RLS with coherent two-exciton recombination give rise to a line at 2Ω_ − ω and an anti-Stokes component at ω+2Ω_, respectively. For ω2Ω_ the RLS spectrum contains Stokes and anti-Stokes components at frequencies ω±2Ω_, whereas stimulated two-photon emission is impossible. Formulas for the cross sections at finite temperatures are obtained
for the processes under consideration. Our estimates indicate that a spectral line at 2Ω_− ω, corresponding to the stimulated two-photon emission accompanied by coherent optical phonon-assisted two-exciton recombination
can be experimentally detected in Cu 2O.
Zh. éksp. Teor. Fiz. 115, 1353–1376 (April 1999) 相似文献
17.
The vibrational modes localized at the interface between two distinct crystals have been studied for a simple crystal model obeying all of the invariance conditions required for models used in studies of dynamical properties of crystal surfaces, and giving rise to Rayleigh surface waves. The two crystals are assumed to be semi-infinite simple cubic and to have the same lattice parameter a. They differ by their mass ( M and MA) and the central force interactions between first ( K and Ka) and second nearest neighbors and . The interface is obtained by coupling the (001) free surfaces of these distinct crystals by central force intractions ( K'). We find that the variation of the interaction conditions ( K') at the interface and of the parameter has the following qualitative effects on the properties of surface and bulk phonons. When ( K') increases from zero to a finite value, the frequencies of the surface phonons increase and are splitted in the case of two identical crystals. One can say that the surface phonons are transformed into interface modes. For some values of and parameters these interface phonons may be admixed with bulk phonons and thus become virtual interface states. 相似文献
18.
In this paper we give a complete characterization of Morita equivalent star products on symplectic manifolds in terms of
their characteristic classes: two star products ⋆ and ⋆' on ( M,ω) are Morita equivalent if and only if there exists a symplectomorphism ψ\colon M
M such that the relative class t(⋆, ψ ⋆(⋆')) is 2 π i-integral. For star products on cotangent bundles, we show that this integrality condition is related to Dirac's
quantization condition for magnetic charges.
Received: 19 July 2001 / Accepted: 23 January 2002 相似文献
19.
We consider bond percolation on the Z
d
lattice. Let M
n
be the number of open clusters in B( n)=[− n, n]
d
. It is well known that E
p
M
n
/(2 n+1)
d
converges to the free energy function κ( p) at the zero field. In this paper, we show that s 2p( Mn)/(2 n+1) d\sigma^{2}_{p}(M_{n})/(2n+1)^{d} converges to − p(1− p) κ′( p). 相似文献
20.
Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that
the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions
leads to significant variations in the spectral intensity A( k, ω) in the Brillouin zone. As a result, the modulation of A( k, ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by
the contour section, where A( k, ω) decreases according to the angle-resolved photoemission spectroscopy data. 相似文献
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