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1.
We present the numbers of spanning trees on the Sierpinski gasket SG
d
(n) at stage n with dimension d equal to two, three and four. The general expression for the number of spanning trees on SG
d
(n) with arbitrary d is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket SG
d,b
(n) with d = 2 and b = 3,4 are also obtained. 相似文献
2.
Abdullah Algin Metin Arik Deniz Kocabicakoglu 《International Journal of Theoretical Physics》2008,47(5):1322-1332
We construct a two-parameter deformed SUSY algebra for the system of n ordinary fermions and n(q
1,q
2)-deformed bosons called Fibonacci oscillators with
-symmetry. We then analyze the Fock space representation of the algebra constructed. We obtain the total deformed Hamiltonian
and the energy levels together with their degeneracies for the system. We also consider some physical applications of the
Fibonacci oscillators with
-symmetry, and discuss the main reasons to consider two distinct deformation parameters. 相似文献
3.
Abdullah Algin 《International Journal of Theoretical Physics》2009,48(1):71-84
We discuss the algebras, representations, and thermodynamics of quantum group bosonic gas models with two different symmetries:
GL
p,q
(2) and
. We establish the nature of the basic numbers which follow from these GL
p,q
(2)- and
-invariant bosonic algebras. The Fock space representations of both of these quantum group invariant bosonic oscillator algebras
are analyzed. It is concisely shown that these two quantum group invariant bosonic particle gases have different algebraic
and high-temperature thermo-statistical properties. 相似文献
4.
We study various statistical properties of real roots of three different classes of random polynomials which recently attracted
a vivid interest in the context of probability theory and quantum chaos. We first focus on gap probabilities on the real axis,
i.e. the probability that these polynomials have no real root in a given interval. For generalized Kac polynomials, indexed by
an integer d, of large degree n, one finds that the probability of no real root in the interval [0,1] decays as a power law n
−θ(d) where θ(d)>0 is the persistence exponent of the diffusion equation with random initial conditions in spatial dimension d. For n≫1 even, the probability that they have no real root on the full real axis decays like n
−2(θ(2)+θ(d)). For Weyl polynomials and Binomial polynomials, this probability decays respectively like
and
where θ
∞ is such that
in large dimension d. We also show that the probability that such polynomials have exactly k roots on a given interval [a,b] has a scaling form given by
where N
ab
is the mean number of real roots in [a,b] and
a universal scaling function. We develop a simple Mean Field (MF) theory reproducing qualitatively these scaling behaviors,
and improve systematically this MF approach using the method of persistence with partial survival, which in some cases yields
exact results. Finally, we show that the probability density function of the largest absolute value of the real roots has
a universal algebraic tail with exponent −2. These analytical results are confirmed by detailed numerical computations. Some
of these results were announced in a recent letter (Schehr and Majumdar in Phys. Rev. Lett. 99:060603, 2007). 相似文献
5.
G. Gritzner J. Ammer K. Kellner V. Kavečanský M. Mihalik S. Maťaš M. Zentková 《Applied Physics A: Materials Science & Processing》2008,90(2):359-365
La0.67Pb0.33(Mn1-xCox)O3-δ ceramics with x=0, 0.01, 0.03, 0.06, 0.1 and 0.15 have been prepared in a two-step procedure. Precursor gels were made by
the wet chemical malic acid method. The gels were calcined and then converted into ceramics by heat treatment at 950 °C and
1000 °C in air. X-ray diffraction showed that the compounds were phase pure. The crystal structure symmetry of the compounds
was confirmed to be rhombohedral (space group R3̄c) for the whole investigated range of x. All compounds undergo a paramagnetic–ferromagnetic
phase transition between 335 K and 225 K. The basic magnetic characteristics such as the Curie temperature , the paramagnetic Curie temperature θ, the effective magnetic moment and the saturated magnetization decrease with increasing Co doping. The ferromagnetic transition is accompanied by an anomaly in the electrical resistance
for all compounds. The high-temperature insulator–metal transitions () do not coincide with the relevant . A large magnetoresistance peak of about 15% was observed for all compounds at .
PACS 72.80.Ga; 75.47.Lx; 75.60.Ej 相似文献
6.
Dong Li 《Journal of statistical physics》2007,129(2):265-287
It has been shown in E and Li (Comm. Pure. Appl. Math., 2007, in press) that the Andersen dynamics is uniformly ergodic. Exponential convergence to the invariant measure is established
with an error bound of the form
where N is the number of particles, ν is the collision frequency and κ(ν)→const as ν→0. In this article we study the dependence on ν of the rate of convergence to equilibrium. In the one dimension and one particle case, we improve the error bound to be
In the d-dimension N-particle free-streaming case, it is proved that the optimal error bound is
It is also shown that as ν→∞, on the diffusive time scale, the Andersen dynamics converges to a Smoluchowski equation. 相似文献
7.
We present the numbers of dimer-monomers Md(n) on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four. The upper and lower bounds for the asymptotic growth constant, defined as zSGd=limv→∞lnMd(n)/v where v is the number of vertices on SGd(n), are derived in terms of the results at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of zSGd can be evaluated with more than a hundred significant figures accurate. From the results for d=2,3,4, we conjecture the upper and lower bounds of zSGd for general dimension. The corresponding results on the generalized Sierpinski gasket SGd,b(n) with d=2 and b=3,4 are also obtained. 相似文献
8.
We find the limit of the variance and prove the Central Limit Theorem (CLT) for the matrix elements φ
jk
(M), j,k=1,…,n of a regular function φ of the Gaussian matrix M (GOE and GUE) as its size n tends to infinity. We show that unlike the linear eigenvalue statistics Tr φ(M), a traditional object of random matrix theory, whose variance is bounded as n→∞ and the CLT is valid for Tr φ(M)−E{Tr φ(M)}, the variance of φ
jk
(M) is O(1/n), and the CLT is valid for
. This shows the role of eigenvectors in the forming of the asymptotic regime of various functions (statistics) of random
matrices. Our proof is based on the use of the Fourier transform as a basic characteristic function, unlike the Stieltjes
transform and moments, used in majority of works of the field. We also comment on the validity of analogous results for other
random matrices. 相似文献
9.
The following hydrogen and oxygen concentration cells using the oxide protonic conductors,
\textCaZ\textr0.98\textI\textn0.02\textO3 - d {\text{CaZ}}{{\text{r}}_{0.98}}{\text{I}}{{\text{n}}_{0.02}}{{\text{O}}_{3 - \delta }} and
\textCaZ\textr0.9\textI\textn0.1\textO3 - d {\text{CaZ}}{{\text{r}}_{0.{9}}}{\text{I}}{{\text{n}}_{0.{1}}}{{\text{O}}_{{3} - \delta }} , as the solid electrolyte were constructed, and their polarization behavior was studied,
( \textreversible: - )\text Pt,\textH2 + \textH2\textO/\textCaZ\textr1 - y\textI\textny\textO3 - d( y = 0.02\text or 0.1 )/\textAr( + \textH2 + \textO2 ),\text Pt( + :\textirreversible ) \left( {{\text{reversible}}: - } \right){\text{ Pt}},{{\text{H}}_2}{ + }{{\text{H}}_2}{\text{O}}/{\text{CaZ}}{{\text{r}}_{1 - y}}{\text{I}}{{\text{n}}_y}{{\text{O}}_{3 - \delta }}\left( {y = 0.02{\text{ or }}0.1} \right)/{\text{Ar}}\left( { + {{\text{H}}_2} + {{\text{O}}_2}} \right),{\text{ Pt}}\left( { + :{\text{irreversible}}} \right) 相似文献
10.
Vinod Chandra V. Ravishankar 《The European Physical Journal C - Particles and Fields》2009,59(3):705-714
We study the viscosity and thermodynamic properties of QGP at RHIC by employing the recently extracted equilibrium distribution
functions from two hot QCD equations of state of O(g
5) and O(g
6ln (1/g)), respectively. After obtaining the temperature dependence of the energy density and the entropy density, we focus our attention
on the determination of the shear viscosity for a rapidly expanding interacting plasma, as a function of temperature. We find
that the interactions significantly decrease the shear viscosity. They decrease the viscosity to entropy density ratio,
as well. 相似文献
11.
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
12.
M. Kreuzer R. C. Rashkov M. Schimpf 《The European Physical Journal C - Particles and Fields》2009,60(3):471-480
The non-linear nature of string theory on non-trivial backgrounds, related to the AdS/CFT correspondence, force one to look
for simplifications. Two such simplifications proved to be useful in studying string theory. These are the pp-wave limit,
which describes point-like strings, and the so-called “near-flat space” limit which connects two different sectors of string
theory—pp-wave and “giant magnons”. Recently another example of AdS/CFT duality emerged—AdS
4/CFT
3, which suggests duality between
CS theory and superstring theory on
. In this paper we study the “near-flat space” limit of strings on an
background and discuss possible applications of the limiting theory.
R.C. Rashkov is on leave from Department of Physics, Sofia University, Bulgaria. 相似文献
13.
For a quasi-Fuchsian group Γ with ordinary set Ω, and Δ
n
the Laplacian on n-differentials on Γ\Ω, we define a notion of a Bers dual basis for ker Δ
n
. We prove that det , is, up to an anomaly computed by Takhtajan and the second author in (Commun. Math Phys 239(1-2):183–240, 2003), the modulus
squared of a holomorphic function F(n), where F(n) is a quasi-Fuchsian analogue of the Selberg zeta function Z(n). This generalizes the D’Hoker–Phong formula det , and is a quasi-Fuchsian counterpart of the result for Schottky groups proved by Takhtajan and the first author in Analysis
16, 1291–1323, 2006.
相似文献
14.
We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on strip graphs G of the honeycomb lattice for a variety of transverse widths equal to L
y
vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary
conditions. These partition functions have the form
, where m denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for N
Z,G,j
for arbitrary L
y
. We also present plots of zeros of the partition function in the q plane for various values of v and in the v plane for various values of q. Plots of specific heat for infinite-length strips are also presented, and, in particular, the behavior of the Potts antiferromagnet
at
is investigated. 相似文献
15.
Several modifications of the faradaic efficiency and electromagnetic field (EMF) methods, taking electrode polarisation resistance
into account, were considered based on the analysis of ion transport numbers and p-type electronic conductivity of ceramics at 973–1,223 K. In air, the activation energies for p-type electronic and oxygen ionic transport are 115 ± 9 and
71 ± 5 kJ/mol, respectively. The oxygen ion transference numbers vary in the range 0.992–0.999, increasing when oxygen pressure
or temperature decreases. The apparent electronic contribution to the total conductivity, estimated from the classical faradaic
efficiency and EMF techniques was considerably higher than true transference numbers due to a non-negligible role of interfacial
exchange processes. The modified measurement routes give reliable and similar results when p(O2) values at the electrodes are high enough, whilst decreasing the oxygen pressure leads to a systematic error for all techniques
associated with measurements of concentration cell EMF. This effect, presumably due to diffusion polarisation, increases with
decreasing temperature. The most reliable results in the studied p(O2) range were provided by the modified faradaic efficiency method. 相似文献
16.
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}
17.
V. V. Shelkovnikov Z. M. Ivanova A. I. Plekhanov E. V. Spesivtsev S. V. Rykhlitsky 《Journal of Applied Spectroscopy》2009,76(1):66-72
Thin-film formation of J-aggregated pseudoisocyanine iodide with long alkyl substituents C18H37 (PIC 2-18) and C10H21 (PIC 2-10) and ethyl substituents (PIC 2-2) with added anion was studied by spectrophotometry directly during spin-coating of its solutions. It is found that a bathochromic shift
of the monomer dye absorption band maximum and extensive growth of a J-peak that is not compensated by the monomer decrease
take place as the dye film forms. The refractive index and absorption coefficient of a solid dye thin film in monomeric (n
max = 2.1) and J-aggregated (n
max = 3.05) forms were measured as functions of the dispersion by spectral ellipsometry. The influence of a change in the local
field factor on the spectral properties of the pseudoisocyanine dye solution in the course of both spin-coating and solid
J-aggregated thin-film formation is considered.
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 76–83, January–February, 2009. 相似文献
18.
We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W
n
(S), and rooted self-avoiding polygons P
n
(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P
n
(S), and W
n(S) for an arbitrary point S on the lattice. These are used to compute the averages ,, and over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent are the same for the annealed and quenched averages. However, , and , where the exponents and , take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives and , to be compared with the known annealed values and . 相似文献
19.
Analysis of edge-state energies in the integer quantum
Hall effect is carried out within the semiclassical approximation.
When the system is wide so that each edge can be considered
separately, this problem is equivalent to that of a one dimensional
harmonic oscillator centered at x = xc and an infinite wall at
x = 0, and appears in numerous physical contexts. The eigenvalues
En(xc) for a given quantum number n are solutions of the
equation S(E,xc)=π[n+ γ(E,xc)] where S is the WKB
action and 0 < γ < 1 encodes all the information on the
connection procedure at the turning points.
A careful implication of the WKB connection formulae results in an
excellent approximation to the exact energy eigenvalues. The
dependence of γ[En(xc),xc] ≡γn(xc)
on xc is analyzed between its two extreme values
as xc ↦-∞ far inside the sample
and as xc ↦∞ far outside the sample.
The edge-state energiesEn(xc) obey an almost exact scaling
law of the form
and the scaling function f(y) is explicitly elucidated. 相似文献
20.
S. Majid 《Czechoslovak Journal of Physics》1997,47(1):79-90
We obtain new family of quasitriangular Hopf algebras
via the author's recent double-bosonisation construction for new quantum groups. They are versions of U
q(su
n+1) with a fermionic rather than bosonic quantum plane of roots adjoined to U
q(su
n). We give the n = 2 case in detail. We also consider the anyonic-double of an anyonic (
) braided group and the double-bosonisation of the free braided group in n variables. 相似文献
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