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1.
A locally finite, causal, and quantal substitute for a locally Minkowskian principal fiber bundle
of modules of Cartan differential forms over a bounded region X of a curved C
-smooth spacetime manifold M with structure group G that of orthochronous Lorentz transformations L
+ := SO(1,3), is presented.
is usually regarded as the kinematical structure of classical Lorentzian gravity when the latter is viewed as a Yang-Mills type of gauge theory of a sl(2, {})-valued connection 1-form
. The mathematical structure employed to model this replacement of
is a principal finitary spacetime sheaf
of quantum causal sets
with structure group G
n, which is a finitary version of the continuous group G of local symmetries of General Relativity, and a finitary Lie algebra g
n-valued connection 1-form
on it, which is a section of its subsheaf
.
is physically interpreted as the dynamical field of a locally finite quantum causality, whereas its associated curvature
as some sort of finitary and causal Lorentzian quantum gravity. 相似文献
2.
A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n
, n
, S
z
n
, S
z
n
, S
z (n
–n
), n
n
and S
+
a
+
a
as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors. 相似文献
3.
G. Kurtze W. Maier G. Blattner C. Klingshirn 《Zeitschrift für Physik B Condensed Matter》1980,39(2):95-98
Two photon Raman scattering (TPRS) via virtually excited biexcitons is observed in CdS over a rather large spectral region in a scattering configuration which favours stimulated emission. We observe either a pure longitudinal exciton or-for the first time—a bound exciton (I
2) as final state particles. Furthermore, the anomaly in the relation between exc and R at exc=
Eblex is observed for the first time in a II–VI compound, indicating an energy of the 1 biexciton level of 5.098 eV in agreement with two photon absorption measurements. With an applied magnetic fieldB, the corresponding shift of the exciton eigenenergies can be observed. For the longitudinal
exciton, the diamagnetic shift is 0.35 meV atB=10T forBc in agreement with theoretical predictions. In this configuration also a stimulated one photon spin flip Raman scattering is observed, yielding the well known electronicg-value of 1.78. 相似文献
4.
Let be a closed * derivation in aC* algebra
which commutes with an ergodic action of a compact group on
. Then generates aC* dynamics of
. Similar results are obtained for non-ergodic actions on abelianC* algebras and on the algebra of compact operators.Research supported by N.S.F. 相似文献
5.
K. Golden 《Communications in Mathematical Physics》1992,143(3):467-499
The bulk conductivity
*(p) of the bond lattice in
d
is considered, where the bonds have conductivity 1 with probabilityp or 0 with probability 1-p Various representations of the derivatives of
*(p) are developed. These representations are used to analyze the behavior of
*(p) for =0 near the percolation thresholdp
c
, when the conducting backbone is assumed to have a hierarchical node-link-blob (NLB) structure. This model has loops on arbitrarily many length scales and contains both singly and multiply connected bonds. Exact asymptotics of
for the NLB model are proven under some technical assumptions. The proof employs a novel technique whereby
for the NLB model with =0 andp nearp
c
is computed using perturbation theory for
*(p) (for two- and three-component resistor lattices) aroundp=1 with a sequence of s converging to 1 as one goes deeper in the hierarchy. These asymptotics establish convexity of
*(p) (for the NLB model) nearp
c
, and that its critical exponentt obeys the inequalities 1t2 ford=2,3, while 2t3 ford4. The upper boundt=2 ind=3, which is realizable in the NLB class, virtually coincides with two very recent numerical estimates obtained from simulation and series expansion for the original model.Supported in part by NSF Grant DMS-8801673 and AFOSR Grant AFOSR-90-0203 相似文献
6.
Julien Berestycki 《Journal of statistical physics》2003,113(3-4):411-430
Let (S(t),t0) be a homogeneous fragmentation of ]0,1[ with no loss of mass. For x]0,1[, we say that the fragmentation speed of x is v if and only if, as time passes, the size of the fragment that contains x decays exponentially with rate v. We show that there is v
typ>0 such that almost every point x]0,1[ has speed v
typ. Nonetheless, for v in a certain range, the random set
v
of points of speed v, is dense in ]0,1[, and we compute explicitly the spectrum vDim(
v
) where Dim is the Hausdorff dimension. 相似文献
7.
R. F. Bilyalov 《Russian Physics Journal》1976,19(9):1136-1138
Four classes of solutions are found to the equations R=–2; ; and g ;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations Rij=0 in a vacuum for the metric
. The metric ds2 assumes axial symmetry and symmetry with respect to the reflection
.Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976. 相似文献
8.
The positron lifetime and DSC measerments for EBBA and DOBAMBC have been made with heating and cooling clycles. The experimental results show that a shorter lifetime (1) is essentially independent of temperature while the longer lifetime (2) and the intensity (I
2) change abruptly double or triple with temperature. Consequently, the EBBA has only nematic phases while the DOBAMBC has two liquid-crystalline phases (smectic C* and smectic A) with transition temperatures as follows: for EBBA, solid nematic (304.5 K), nematic isotropic (356.5 K), isotropic nematic (356.5 K), nematic solid (301 K); and for DOBAMBC, solid smectic C* (346 K), smectic C* smectic A (357.5 K), smectic A isotropic (389 K). These critical temperatures are in accordance with the transition temperatures measured by DSC. In addition, the difference in the solid-nematic transition temperature in the heating and cooling cycles was also observed. A discussion about the correlation of the observed changes in lifetime (2) with the changes in molecular orientational order (S) and dielectric anisotropy () is presented. 相似文献
9.
Norbert Kalus 《Journal of statistical physics》1981,25(4):635-643
We describe a new class of single spin measures on then-dimensional sphereS
r
n
of radiusr (n 4) for which Lebowitz-type [J. Lebowitz,J. Stat. Phys.
16:463 (1977)] inequalities hold. This is achieved by an appropriate parametrization ofS
r
n
. The above class includes the uniform measures onxs Rn ¦x¦ r for any 0 p r. The second topic of this paper is an abstract formulation of the first Griffiths inequality [R. B. Griffiths,J. Math. Phys.
8:478 (1967)] and the underlying symmetry property. 相似文献
10.
Using results from conformal field theory, we compute several universal amplitude ratios for the two-dimensional Ising model at criticality on a symmetric torus. These include the correlation-length ratio x
=lim
L
(L)/L and the first four magnetization moment ratios V
2n
=
2n
/
2
n
. As a corollary we get the first four renormalized 2n-point coupling constants for the massless theory on a symmetric torus, G*2n
. We confirm these predictions by a high-precision Monte Carlo simulation. 相似文献
11.
The tensor product of two supersingleton representations
n of the Lie superalgebraosp (1, 2n) is studied forn2. The main results are as follows: (a) anticommutators and commutators of the odd generators in
n
n form a skew-symmetric representation of the Lie algebrau(n, n); (b) simple explicit form of all irreducible components of
n
n, which are labelled by a single parameterJ=0, 1, ..., has been found. Each of them is a*-representation ofosp (1, 2n) for which assertion (a) is valid. The dimension of its vacuum subspace equals
, i.e., the nondegenerate vacuum occurs for J=0 only. Basic property of this family of irreducible*-representations of osp(1, 2n) are analogous to those of massless representations of osp(1, 4).Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday. 相似文献
12.
Giancarlo Benettin Luigi Galgani Antonio Giorgilli 《Communications in Mathematical Physics》1989,121(4):557-601
As in Part I of this paper, we consider the problem of the energy exchanges between two subsystems, of which one is a system of harmonic oscillators, while the other one is any dynamical system ofn degrees of freedom. Such a problem is of interest both for the realization of holonomic constraints of classical mechanics, and for the freezing of the internal degrees of freedom in molecular collisions. The results of Part I, which referred to the particular case =1, are here extended to the more difficult case >1. For the rate of energy transfer we find exponential estimates of Nekhoroshev's type, namely of the form exp (*/)1/a
, where is a positive real number giving the size of the involved frequencies, and * anda are constants. For the particularly relevant constanta we find in generala=1/ however, in the particular case when the frequencies are equal (collision of identical molecules), we finda=1 independently of , as conjectured by Jeans in the year 1903. 相似文献
13.
We consider site percolation on Z
d, directed edges going from any sZ
d to s+A
1,..., s+A
n, where A
1,..., A
n are the same for all sites and at least two of them are noncollinear. A site is closed if it belongs to p+Block, where p is a point in a Poisson distribution in R
dZ
d with a density and Block={sL: |s|M}+{sR
d: |s|}, where L is a linear subspace of R
d, |·| is the Euclidean norm, =max(|A
1|,..., |A
n|) and M is a parameter. We study the behavior of *, the critical value, and P
closed*, corresponding critical percentage of closed sites, when M. Denote R
d/L the factor space. Call two nonzero vectors U, V codirected if U=kV, where k>0. Theorem. If there are A
i and A
j whose projections to R
d/L are not codirected, then *1/M
dim(L) and P
closed* remains separated both from 0 and 1 when M. If projections of all A
1,..., A
n to R
d/L are codirected, then *1/M
dim(L)+1 and P
closed*1/M when M. 相似文献
14.
Giampiero Esposito Hugo Morales-Técotl Giuseppe Pollifrone 《Foundations of Physics Letters》1994,7(3):303-308
Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal
e
n
A/A
to the boundary and a pair of independent spinor fields
A
and
. This paper studies the corresponding classical properties, i.e., the classical boundary-value problem and boundary terms in the variational problem. If
is set to zero on a 3-sphere bounding flat Euclidean 4-space, the modes of the massless spin–1/2 field multiplying harmonics having positive eigenvalues for the intrinsic 3-dimensional Dirac operator onS
3 should vanish onS
3. Remarkably, this coincides with the property of the classical boundary-value problem when spectral boundary conditions are imposed onS
3 in the massless case. Moreover, the boundary term in the action functional is proportional to the integral on the boundary of
A
e
n
AA
A
. 相似文献
15.
Intense picosecond light pulses of a mode-locked Nd: glass laser at
L
=1054 nm (fundamental wavelength) and
SH
=527 nm (second harmonic wavelength) are passed through a sample of D2O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (1 + 1 3 + 4) and stimulated Raman scattering (1
R
+ ), which occur concurrently (1=
L
or
SH
angular pump frequency, #x03C9;
R
first Stokes frequency, #x03C9; signal frequency, #x03C9;3 signal frequency, #x03C9;4 idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type 1 +
R
3 + 4, coherent antiStokes Raman scattering (CARS, 1 + 1 – 4 3), inverse Raman scattering (
A
+ 1 + ), and cascading light up-conversion of the type 1 +
(i)
–
R
(i+1). 相似文献
16.
H. Allrecht H. Ehrlichmann T. Hamacher A. Krüger A. Nau A. Nippe M. Reidenbach M. Sch?fer H. Schr?der H. D. Schulz et al. 《Zeitschrift fur Physik C Particles and Fields》1992,54(1):13-19
We have measured theR value in non-resonante
+
e
– annihilation using the ARGUS detector at the storage ring DORIS II. At a centre-of-mass energy
GeV the ratio of the hadronic cross-section to the -pair cross section in lowest order QED has been determined to beR=3.46±0.03±0.13. In addition, we have measured the charged-particle multiplicities in non-resonant hadron production at
GeV just below theB
threshold and in (4S) resonance decays. For the average charged-particle multiplicities in continuum events and (4S)B
decays we obtain n>cont=8.35±0.02±0.20 and n>(4s)=10.81±0.05±0.23.Supported by the German Bundesministerium für Forschung und Technologie, Contract no. 054DO51P 相似文献
17.
We consider the diffusion of a particle at Xt in a drift field derived from a smooth potential of the formV+B, whereV is periodic andB is a bump of compact support. With no bump,B=0, the mean squared displacementE(t) E |X
t
– X0|2 =D(V)t +C +O(e
–t
),>0, in any dimension. WhenB0, we establish in one dimension the asymptotic expansion
, 0, ast. Our analysis relies on the Nash estimates developed in previous work for the transition density of the process and their consequences for the analytic structure,of the Laplace transform
ofE(t). 相似文献
18.
Florin Constantinescu 《Communications in Mathematical Physics》1968,8(4):345-352
It is known that a complex-valued continuous functionS(x) and a Schwartz distribution can both be extended to an analytic function(z) in the complex plane minus the support ofS. Conditions are given for the existence of limits
(x+i), in the ordinary sense, at certain points of the support ofS, for the case in which(z) is the Cauchy representation. In this way we obtain local Plemelj and dispersion relations. Possible generalizations and applications are discussed. 相似文献
19.
Shahen Hacyan 《General Relativity and Gravitation》1994,26(1):85-96
The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices. 相似文献
20.
Steady-State Spectroscopic and Fluorescence Lifetime Measurements of New Two-Photon Absorbing Fluorene Derivatives 总被引:2,自引:0,他引:2
Kevin D. Belfield Mikhailo V. Bondar Olga V. Przhonska Katherine J. Schafer 《Journal of fluorescence》2002,12(3-4):449-454
Steady-state excitation anisotropy, lifetimes, and time-resolved emission spectra of new 2-photon absorbing fluorene derivatives were measured in aprotic solvents at room temperature. Excitation anisotropy spectra in viscous silicon oil allowed the determination of the spectral position of three electronic transitions S0 S1, S0 S2, S0 S3 (Si, i = 1, 2, 3 are the singlet electronic states) and the angles ( 30°) between absorption S0 S1 and emission S1 S0 dipole moments for the first electronic transition. Solvate relaxation processes in the first excited state of the investigated fluorene molecules affect the lifetimes of these states, 1, so that experimental values of 1 do not correspond to those calculated by Strickler and Berg theory. The influence of the molecular concentration on the fluorescence quantum yields and 1 have been investigated. 相似文献