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1.
The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like
an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V
HC
(x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with
〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q
o| = π/d) and experience a mutual repulsive force (zero point repulsion) f
o
=h
2/2md
3 which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual
collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining
a correct microscopic understanding of widely different many-body systems. 相似文献
2.
The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations
described by tree graphs. This implies classical representability of any set of correlations 〈A
i
〉, 〈B〉, 〈A
i
B〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for
the unmeasurable correlation 〈A
1
A
2〉 associated to different choices for B. The same analysis applies to the Hardy model and to the “perfect correlations” discussed by Greenberger, Horne, Shimony
and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical
representation is the only basis for arguments about violations of locality and causality. 相似文献
3.
The depolarisation ratio for the Raman-active phenyl stretching mode has been measured over the whole of the mesophase range,
and the orientational order parameters deduced, in the uniaxial nematic liquid crystal octylcyanobiphenyl (8CB). Linearly
polarised light was incident normally on a homogeneously aligned sample and a χ2 minimisation routine performed on the 360° depolarisation ratio profile. The order parameters 〈P
200〉 and 〈P
400〉 , together with the differential polarisability ratio, r , are used as fitting parameters and measured as a function of temperature. Interestingly, we show that the value for r , conventionally measured in the isotropic phase and assumed to remain constant, has a clear temperature dependence, ranging
from -0.032±0.008 in the isotropic phase through to -0.245±0.015 at the nematic-to-smectic A phase transition. The measured
order parameters 〈P
200〉 and 〈P
400〉 varied from 0.35- 0.55±0.02 and 0.180- 0.245±0.02 , respectively, across the 8 ° C wide nematic phase range. The values of both 〈P
200〉 and 〈P
400〉 are in excellent agreement with theory, but it is noteworthy that 〈P
400〉 shows a much better quantitative match than has been reported in previous work. Crucially the temperature dependence of
r is shown to be a contributing factor in the low 〈P
400〉 values that have been conventionally reported from Raman scattering measurements. The potential for fitting the entire angular
depolarisation ratio distribution in liquid crystalline systems that are described by more order parameters, specifically
biaxial materials, is discussed. 相似文献
4.
Wenwei Ge Hong Liu Xiangyong Zhao Xiaobing Li Xiaoming Pan Di Lin Haiqing Xu Xiangping Jiang Haosu Luo 《Applied Physics A: Materials Science & Processing》2009,95(3):761-767
In this paper, a single crystal of 0.96Na0.5Bi0.5TiO3-0.04BaTiO3 with dimensions of Φ 30×10 mm was grown by the top-seeded-solution growth method. X-ray powder diffraction results show that the as-grown crystal
possesses the rhombohedral perovskite-type structure. The dielectric, piezoelectric and electrical conductivity properties
were systematically investigated with 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples. The room-temperature dielectric constants
for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples are found to be 650, 740 and 400 at 1 kHz. The (T
m, ε
m) values of the dielectric temperature spectra are almost independent of the crystal orientations; they are (306°C, 3718),
(305°C, 3613) and (307°C, 3600) at 1 kHz for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal. The optimum poling conditions were
obtained by investigating the piezoelectric constants d
33 as a function of poling temperature and poling electric field. For the 〈001〉 and 〈110〉 crystal samples, the maximum d
33 values of 146 and 117 pC/N are obtained when a poling electric field of 3.5 kV/mm and a poling temperature of 80°C were applied
during the poling process. The as-grown 0.96Na0.5Bi0.5TiO3-0.04BaTiO3 crystal possesses a relatively large dc electrical conductivity, especially at higher temperature, having a value of 1.98×10−11 Ω−1⋅m−1 and 3.95×10−9 Ω−1⋅m−1 at 25°C and 150°C for the 〈001〉 oriented crystal sample. 相似文献
5.
Shi-Min Xu Xing-Lei Xu Hong-Qi Li 《International Journal of Theoretical Physics》2008,47(6):1654-1662
The intermediate representation (namely intermediate coordinate-momentum representation) |x〉
λ,ν
are introduced and employed to research the expression of the operator
in intermediate representation |x〉
λ,ν
. The systematic Hamilton operator
of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ,ν,τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate
representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained
in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon
transformation of Wigner operator is just the projectional operator |x〉
λ,ν
λ,ν
〈x|, and the Radon transformation of Wigner function is just a margin distribution. 相似文献
6.
Using the general formulation for obtaining chemical potentialμ of an ideal Fermi gas of particles at temperature T, with particle rest mass m0 and average density 〈N〉/V, the dependence of the mean square number fluctuation 〈ΔN
2〉/V on the particle mass m0 has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energym
0c2 is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy kBT. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any
of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate
experimental measurements of their momentum distribution one can extract, someday, not only the density 〈N
v〉/V but also the mean square fluctuation 〈Δ
v
2
〉/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis
leads to a scaled neutrino massm
v
instead of the actual massm
0v
. 相似文献
7.
Wen-jian Yu Ye-jun Xu Hong-chun Yuan Ji-suo Wang 《International Journal of Theoretical Physics》2011,50(9):2871-2877
We first deduce the s-ordered expansion of the Wigner operator. Since Radon transformation of Wigner operator is just the intermediate representation
|x〉
λ,ν projector, we naturally obtain the s-ordered product of |x〉
λ,νλ,ν〈x|. Accordingly, the completeness relation is still preserved under the s-ordering. Finally, based on it, we obtain the s-ordered expansion of some useful operator in quantum optics, and some new operator identities are revealed accordingly. 相似文献
8.
Yu. A. Abrahamian G. G. Karamian V. I. Serago V. I. Stafeyev 《International Journal of Infrared and Millimeter Waves》1997,18(12):2315-2322
Photoconductivity of single crystal Pb1−xSnxTe〈In〉, (0.24≤x≤0.25), films at 4.2K in the wavelength region 4÷5 mm and magnetic fields up to 8 T was studied. Preparation
technology of the films with high photoconductivity (PFEP ≤ 10−12 W×Hz1/2) and photoresponsiveness (τ ≤ 10−6 s), as well as the measurements procedure are described in the paper. Also the mechanism of photoconductivity is discussed. 相似文献
9.
The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p
c ∼ N
-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition
from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N
2. In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas
particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field
theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of
an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p
c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p
c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N
2
f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained.
Thus, the two ensembles are manifestly inequivalent in these systems.
An erratum to this article is available at . 相似文献
10.
Measurements have been made of the Hall coefficientR of some alloys of silver in palladium over the temperature range 1°K to 120°K. The alloys contain between ∼1 and ∼10 at.-%
silver. Values ofR were also obtained at room temperature and these were in good agreement with earlier published work. The values ofR are negative in all the alloys, and |R| increases both on reducing the temperature and increasing the silver concentration,c. Below ∼10°K, |R| becomes independent of temperature but shows a linear dependence onc, increasing by a factor of 2.5 over the concentration range measured.
This increase is too great to be accounted for in terms of band structure changes alone, so we have examined the effects of
anisotropic impurity scattering. To a first approximation it can be shown thatR is proportional to an anisotropy parameterA, defined asA=〈τ
2(k)〉/〈τ(k)〉2, whereτ(k) represents the relaxation time of an electron in a statek, and 〈〉 is an average over the Fermi surface. In palladium we assume that the majority of the current is carried by the s-electrons.
In the presence of silver impurities these electrons can be scattered into s-states or d-states with relaxation times given
byτ
ss
α1/c(1−c) andτ
sd
α1/c
2(1−c) respectively. FollowingPlate we have assumed thatτ
ss is isotropic and thatτ
sd is anisotropic, leading to an overall anisotropic relaxation time for impurity scattering. We then find the parameterA increases approximately linearly with silver content, in accordance with our experimental results. 相似文献
11.
We investigate numerically and analytically the statistics of Markov chains on so-called braid (B
n
) and locally free (ℒℱ
n
) groups. Namely, we compute the mean length 〈μ〉 and the variance 〈μ2〉−〈μ〉2 of the shortest word which remains after applying of all group relations to the randomly generatedN-letter word (Markov chain). We express the conjecture (numerically justified) that the mean value 〈μ〉 for the random walk
on the groupB
n
(n≫1) coincides with high accuracy with the same value for the random walk on the “locally free group weth errors” if the number
of errors is of order of 20%. 相似文献
12.
We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled
as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure,
pc ∼ N-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N2. The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is
found, in which 〈A〉 ∼ N3/2. For p ≫ pc we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state. 相似文献
13.
M. E. Guzhva V. V. Lemanov P. A. Markovin W. Kleemann 《Physics of the Solid State》1997,39(4):618-624
Temperature-induced variations of light refraction and dielectric permittivity in single-crystal Sr1−x
BaxTiO3 (x=0.02, 0.05, 0.07, and 0.14), Sr1−x
CaxTiO3 (x=0.014), and in nominally pure strontium titanate have been studied within the 17–300 K temperature range. The spontaneous
polar contribution to the refractive index has been isolated. It was used to calculate the temperature and concentration dependences
of the polarization autocorrelation function 〈P
s
2〉
in the Sr1−x
BaxTiO3 system. For x⩽0.07, the polarization P
s=〈P
s
2
〉1/2 varies proportional to (x−x
g)1/2, where x
g=0.0027 is the new critical concentration in Sr1−x
BaxTiO3, below which short-range polar order vanishes.
Fiz. Tverd. Tela (St. Petersburg) 39, 704–710 (April 1997) 相似文献
14.
Studies of quantum fields and gravity suggest the existence of a minimal length, such as Planck length. It is natural to ask
how the existence of a minimal length may modify the results in elementary quantum mechanics (QM) problems familiar to us.
In this paper we address a simple problem from elementary non-relativistic quantum mechanics, called “particle in a box”,
where the usual continuum (1+1)-space-time is supplanted by a space-time lattice. Our lattice consists of a grid of λ
0×τ
0 rectangles, where λ
0, the lattice parameter, is a fundamental length (say Planck length) and, we take τ
0 to be equal to λ
0/c. The corresponding Schroedinger equation becomes a difference equation, the solution of which yields the q-eigenfunctions and q-eigenvalues of the energy operator as a function of λ
0. The q-eigenfunctions form an orthonormal set and both q-eigenfunctions and q-eigenvalues reduce to continuum solutions as λ
0→0. The corrections to eigenvalues because of the assumed lattice is shown to be O(l02)O(\lambda_{0}^{2}). We then compute the uncertainties in position and momentum, Δx, Δp for the box problem and study the consequent modification of Heisenberg uncertainty relation due to the assumption of space-time
lattice, in contrast to modifications suggested by other investigations. 相似文献
15.
P. Zh. Aslanyan V. N. Emelyanenko G. G. Rikhkvitzkaya 《Physics of Particles and Nuclei Letters》2007,4(1):60-66
The experimental data from the 2-m propane bubble chamber have been analyzed for pC → Λ(K
s
0
)X reactions at 10 GeV/c. The estimation of experimental inclusive cross sections for Λ and K
s
0
production in the p
12C collision is equal to σΛ = (13.3 ± 1.7) mb and σ
K
s
0
= (4.6 ± 0.6) mb, respectively. The measured 〈Λ〉/〈π+〉 ratio from pC reaction is equal to (5.3 ± 0.8) × 10−2, and it is approximately two times larger than the 〈Λ〉/〈π+〉 ratio simulated by the FRITIOF model and than that of experimental pp reactions at the same energy.
The text was submitted by the authors in English. 相似文献
16.
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
17.
Michael O’Carroll 《Journal of statistical physics》2012,146(4):864-869
We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (β≪1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter α=〈s
4〉−3〈s
2〉2>0, i.e. in the region which we call Gaussian subjugation, where 〈s
k
〉 denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle
of asymptotic mass −lnβ and a bound state below the two-particle threshold. We develop a β analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show
that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex
spectral parameter and the coefficients of its Laurent expansion are analytic in β. 相似文献
18.
N. M. Agababyan V. V. Ammosov M. Atayan N. Grigoryan H. Gulkanyan A. A. Ivanilov Zh. Karamyan V. A. Korotkov 《Physics of Atomic Nuclei》2007,70(10):1739-1742
Using the data obtained with the SKAT bubble chamber, the total yields of K*(892)+, Σ+(1385), and Σ0 are estimated for the first time in neutrino-induced reactions at moderate energy 〈E
v〉 = 10.4 GeV. It is shown that the recently observed enhancement of the K
0 and Λ yields in vA interactions as compared to vN interactions is contributed only slightly by the K*(892)+ and Σ+(1385) production. The contribution of resonances to the K
0 and Λ yields is found to be in qualitative agreement with higher energy (〈E
v〉 ≳ 40 GeV) data. It is shown that the energy dependence of the K*(892)+ mean multiplicity in vN interactions is approximately linear in the range of 〈E
v〉 ≈ 10−60 GeV, while that for Σ0 in vA interactions (A = 20−21) is approximately logarithmic in the range of 〈E
v〉 ≈ = 10−150 GeV.
The text was submitted by the authors in English. 相似文献
19.
A local quantum statistics based on a finite temperature field theory in an arbitrary Riemann space-time is considered. The
expressions have been derived for the partition functions, the grand thermodynamic potential and the particle distributions
〈n
k〉 of massive scalar gas and fermion gas in arbitrary space-time. It is shown that the chemical potential depends on the geometry
of manifold. 相似文献
20.
A. S. Barabash 《Physics of Atomic Nuclei》2010,73(1):162-178
The present status of double-beta-decay experiments (including the search for 2β
+, ECβ
+, and ECEC processes) are reviewed. The results of the most sensitive experiments are discussed. Average and recommended half-life
values for two-neutrino double-beta decay are presented. Conservative upper limits on effective Majorana neutrino mass and
the coupling constant of the Majoron to the neutrino are established as 〈m
ν
〉 < 0.75 eV and 〈g
ee
〉 < 1.9 × 10−4, respectively. Proposals for future double-betadecay experiments with a sensitivity for the 〈m
ν
〉 at the level of 0.01–0.1 eV are considered. 相似文献