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1.
M. W. Evans 《Foundations of Physics Letters》1996,9(4):397-405
The equations of free-space electrodynamics are derived directly from the Riemann curvature tensor and the Bianchi identity of general relativity by contracting on two indices to give a novel antisymmetric Ricci tensor. Within a factore/h, this is the field-strength tensor G of free-space electrodynamics. The Bianchi identity for G describes free-space electrodynamics in a manner analogous to, but more general than, Maxwell's equations for electrodynamics, the critical difference being the existence in general and special relativity of the Evans-Vigier fieldB
(3). 相似文献
2.
Results from percolation theory are used to study phase transitions in one-dimensional Ising andq-state Potts models with couplings of the asymptotic formJ
x,y const/¦x–y¦2. For translation-invariant systems with well-defined lim
x
x
2
J
x
=J
+ (possibly 0 or ) we establish: (1) There is no long-range order at inverse temperatures withJ
+1. (2) IfJ
+>q, then by sufficiently increasingJ
1 the spontaneous magnetizationM is made positive. (3) In models with 0<J
+< the magnetization is discontinuous at the transition point (as originally predicted by Thouless), and obeysM(
c
)1/(
c
J
+)1/2. (4) For Ising (q=2) models withJ
+<, it is noted that the correlation function decays as xy()c()/|x–y|2 whenever<
c
. Points 1–3 are deduced from previous percolation results by utilizing the Fortuin-Kasteleyn representation, which also yields other results of independent interest relating Potts models with different values ofq. 相似文献
3.
M. W. Evans 《Foundations of Physics Letters》1995,8(4):381-388
It is shown that the longitudinal vacuum fieldB
(3) emerges from the Biot-Savart-Ampère law governing the motion of an electron with intrinsic spin moving at the speed of light, in which case the expression forB
(3) is identical with that obtained from the Dirac equation of one electron accelerated to the speed of light by an electromagnetic field. Use of an O(3), non-Abelian, gauge geometry forB
(3) identifies the quantized photon momentum appearing in the Dirac equation witheA
(0), wheree is the charge on the electron andA
(0) the amplitude of the vector potential. The condition =eA
(0) can be obtained in turn from the relativistic Hamilton-Jacobi equation of an electron accelerated to the speed of light by an electromagnetic field. 相似文献
4.
C. Quesne 《International Journal of Theoretical Physics》2004,43(2):545-559
We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson q-exponential of the sum of two non-q-commuting operators as an (in general) infinite product of q-exponential operators involving repeated q-commutators of increasing order, Eq(A+B) = Eq0(A)Eq1 (B)
i=2
Eqi. By systematically transforming the q-exponentials into exponentials of series and using the conventional Baker–Campbell–Hausdorff formula, we prove that one can make any choice for the bases qi, i=0, 1, 2, ..., of the q-exponentials in the infinite product. An explicit calculation of the operators C
i in the successive factors, carried out up to sixth order, also shows that the simplest q-Zassenhaus formula is obtained for 0 = 1 =1, and 2 = 2, and 3 = 3. This confirms and reinforces a result of Sridhar and Jagannathan, on the basis of fourth-order calculations. 相似文献
5.
For a -dimensional system of particles with the two-body potentialq(r)+
v
K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density
which was found in Part I. 相似文献
6.
In this paper we define a new q-special function A
n
(x, b, c; q). The new function is a generalization of the q-Laguerre function and the Stieltjes–Wigert function. We deduced all the properties of the function A
n
(x, b, c; q). Finally, lim
q1
A
n
((1 – q)x, –, 1;q) gives L
n
(,)(x,q), which is a -modification of the ordinary Laguerre function. 相似文献
7.
We give a realization of the quantum affine Lie algebras
and
in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter q being related to the statistical parameter of the anyons by q = ei. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel [1] fermionic construction of undeformed affine Lie algebras. 相似文献
8.
Walter Wyss 《Foundations of Physics Letters》1991,4(3):235-246
Fractional noiseN(t),t 0, is a stochastic process for every , and is defined as the fractional derivative or fractional integral of white noise. For = 1 we recover Brownian motion and for = 1/2 we findf
–1-noise. For 1/2 1, a superposition of fractional noise is related to the fractional diffusion equation. 相似文献
9.
We give the algebra
q
/*
dual to the matrix Lorentz quantum group
q
of Podles-Woronowicz, and Watamuraet al. As a commutation algebra, it has the classical form
q
/*
U
q
(sl(2, )) U
q
(sl(2, )). However, this splitting is not preserved by the coalgebra structure which we also give. For the derivation, we use a generalization of the approach of Sudbery, viz. tangent vectors at the identity. 相似文献
10.
We study the behaviour of time evolved quantum mechanical expectation values in Lagrangian states in the limit 0 and t. We show that it depends strongly on the dynamical properties of the corresponding classical system. If the classical system is strongly chaotic, i.e. Anosov, then the expectation values tend to a universal limit. This can be viewed as an analogue of mixing in the classical system. If the classical system is integrable, then the expectation values need not converge, and if they converge their limit depends on the initial state. An additional difference occurs in the timescales for which we can prove this behaviour; in the chaotic case we get up to Ehrenfest time, t ln (1/), whereas for integrable system we have a much larger time range. 相似文献
11.
We find the asymptotic decrease of correlations <
A +y
,
B
>,yZ
v
+1, |y|, in the Ising model at high temperatures. For the case when monomials
A
and
B
both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials
A
,
B
we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory. 相似文献
12.
We calculate the moments t
q
, whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t
q
~L
(q) asL, then we show that there is a phase transition atq=q
c
such that whenq<q
c
,(g)=0, and forq>q
c
, (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions. 相似文献
13.
H. W. Diehl 《Zeitschrift für Physik B Condensed Matter》1987,66(2):211-218
Systems representable as a time-dependent Ginzburg-Landau model with nonconserved order parameter are considered in a block (V=L
d) geometry with periodic boundary conditions, both for space dimensionalitiesd4 andd=4–. A systematic approach for studying finite size effects on dynamic critical behavior is developed. The method consists in constructing an effective reduced dynamics for the lowest-energy (q=0) mode by integrating out the remaining degrees of freedom, and generalizes recent analytic approaches for studying static finite size effects to dynamics. Above four dimensions, the coupling to the other (q0) modes is irrelevant and the probability densityP(,t) for the normalized order parameter=dd
x(x,t)/V satisfies a Fokker-Planck equation. The dynamics is equivalently described by the Langevin equation for a particle moving in a ||4 potential or by a supersymmetric quantum mechanical Hamiltonian. Dynamic finite size scaling is found to be broken, e.g. the order parameter relaxation rate varies at the bulk critical temperatureT
c, as (T
c,
L)L
–d/2 asL. By contrast, ford<4, the coupling to the other (q0) modes cannot be ignored and dynamic finite size scaling is valid. The asymptotic behavior of correlation and response functions can be studied within the framework of an expansion in powers of 1/2. The scaling function associated with is computed to one-loop order. Finally, the many component (n) limit is briefly considered. 相似文献
14.
We prove exponential convergence to equilibrium (L
2 geometric ergodicity) for a random walk with inward drift on a sub-Cayley rooted tree. This randomwalk model generalizes a Monte Carlo algorithm for the self-avoiding walk proposed by Berretti and Sokal. If the number of vertices of levelN in the tree grows asC
N
~
N
N
–1
, we prove that the autocorrelation time satisfies N2 N1+ 相似文献
15.
We use a quite concrete and simple realization of sl
q
(2, ) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the noncommutative scheme 1 II 1* as the counterpart of the standard 1 = Sl(2, )/B. 相似文献
16.
LetS be a bounded region inR
N
and letP={S
l
}
i=1
m
be a partition ofS into a finite number of closed subsets having piecewiseC
2 boundaries of finite (N–1)-dimensional measure. Let :SS be piecewiseC
2 onP and expanding in the sense that there exists 0<<1 such that for anyi=1,2,...,m, DT
i
–1<, whereDT
i
–1 is the derivative matrix ofT
i
–1 and · is the Euclidean matrix norm. We prove that for some classes of such mappings, for example, Jabtonski transformations or convexity-preserving transformations, the number of crossing points constitutes a bound for the number of ergodic absolutely continuous -invariant measures. We give examples showing that in general the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we show that it is possible to construct piecewise expandingC
2 transformations on a fixed partition with a finite number of elements but which have an arbitrarily large number of ergodic, absolutely continuous invariant measures. 相似文献
17.
H. Ghafoori-Shiraz 《Optical and Quantum Electronics》1988,20(2):153-163
A parabolic model of the formg =n
2 +n + has been suggested for long-wavelength InGaAsP laser diode peak-grain coefficient variations with the carrier density. The parameters, and, which are dependent on doping, bandgap-wavelength and temperature, have been calculated by applying the least-mean-square method to fit the results of the Lasher and Stern theory of the recombination in semiconductors. p ]This model is superior to the commonly used linear model in accuracy and range of applicability. 相似文献
18.
Frederic Bisshopp 《International Journal of Theoretical Physics》1974,11(1):5-29
The nonlinear wave equation,
tt
–+3=0, has many solutions that are periodic in time and localized in space, all with infinte energies. The search for spherically symmetric solutions that are well represented by the simple approximation, (r, t)A(r) sin t, leads to a discrete spectrum of solutions{
N
(r, t; )}. The solutions are nonlinear wavepackets, and they can be regarded as particles. The asymptotic theory () of the motion of the guiding center of theNth wavepacket, in the presence of a specified potential, is characterized by an infinite mechanical mass and an infinte interaction mass, and they are compatible. The rest mass in the classical relativistic mechanics of guiding centers ism
0
c
2=
N
; i.e. the spectrum {
N
} determines a spectrum of Planck's constants.On leave (1972–73) Université de Paris VI, Département de Mécanique, 75 Paris 5e, France. 相似文献
19.
A. B. Sushkov E. A. Tishchenko 《International Journal of Infrared and Millimeter Waves》1993,14(12):2555-2568
Development of an ellipsometry to the case of a coherent far infrared irradiation, low temperatures and small samples is described, including a decision of the direct and inverse problems of the convergent beam ellipsometry for an arbitrary wavelength, measurement technique and a compensating orientation of cryostat windows. Experimental results are presented: for a gold film and UBe13 single crystal at room temperature (=119m), temperature dependencies of the complex dielectric function of SrTiO3 (=119, 84 and 28m) and of YBa2Cu3O7– ceramic (A=119m). 相似文献
20.
Tom Kennedy 《Journal of statistical physics》1984,37(5-6):529-559
We study a classical charge symmetric system with an external charge distributionq in three dimensions in the limit that the plasma parameter zero. We prove that ifq is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field(x) where is given by-+ 2z sinh() =q This is the mean field equation of Debye and Hückel. The proof uses the sine-Gordon transformation, the Mayer expansion, and a correlation inequality.Work partially supported by NSF Grant MCS 82-02115. 相似文献