共查询到20条相似文献,搜索用时 93 毫秒
1.
All complete sets of symmetry operators of the wave equation in Minkowski space containing one isotropic first-order operator of the form /x0+/x3 and two second-order operators are obtained. Privileged coordinates corresponding to these sets are given. The variables are separated in the wave equation and in the free Schrödinger equation in three-dimensional spacetime.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 44–48, February, 1991. 相似文献
2.
We investigate the band-gap structure of some second-order differential operators associated with the propagation of waves in periodic two-component media. Particularly, the operator associated with the Maxwell equations with position-dependent dielectric constant (x),xR
3, is considered. The medium is assumed to consist of two components: the background, where (x) =
b
, and the embedded component composed of periodically positioned disjoint cubes, where (x) =
a
. We show that the spectrum of the relevant operator has gaps provided some reasonable conditions are imposed on the parameters of the medium. Particularly, we show that one can open up at least one gap in the spectrum at any preassigned point provided that the size of cubesL, the distancel=L betwen them, and the contrast =
b
/
a
are chosen in such a way thatL
–2, and quantities -1-3/2 and 2 are small enough. If these conditions are satisfied, the spectrum is located in a vicinity of widthw(3/2)-1 of the set {2
L
-2
k
2:kZ3}. This means, in particular, that any finite number of gaps between the elements of this discrete set can be opened simultaneously, and the corresponding bands of the spectrum can be made arbitrarily narrow. The method developed shows that if the embedded component consists of periodically positioned balls or other domains which cannot pack the space without overlapping, one should expect pseudogaps rather than real gaps in the spectrum. 相似文献
3.
Successive band-splitting transitions occur in the one-dimensional map xi+1=g(xi),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2n) bands to 2Nbands is given by=(2)1/N (n=0, 1,2,...). The time-correlation function
i=xix0/(x0)2,xi xi–xi is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2,
i–[(10–42)/17] i,0-[(102-8)/51]i,1 + [(7 + 42)/17](–1)ie–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for
i has been obtained by deriving an analytic form of
i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)1/N, the damping constant of
i fori N is given by
N=2(N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results. 相似文献
4.
Michael G. Mürmann 《Journal of statistical physics》1987,48(3-4):769-788
We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (2/dq2){F([1/1(q)]), with F= –. 相似文献
5.
O. Costa de Beauregard 《Foundations of Physics》1986,16(9):937-939
Bohr's 1930 derivation of the uncertainty relation c
2
m th bears a close relationship to Einstein's 1913 derivation of the gravitational redshift via the equivalence principle. A rewording of Bohr's argument is presented here, not taking the last step of acceleration as equivalent to a uniform gravity field, thus yielding a derivation of the formula c
2
m th, avoiding Treder's 1971 objection. 相似文献
6.
We consider the Laplacian
m
in 3 (or in a bounded region of 3) with Dirichlet boundary conditions on the surfaces of some identical (small) neighborhoods ofm randomly distributed points, in the limit whenm goes to infinity and their linear size decreases as 1/m. We give here a stronger form of the result showing the convergence of the above operator to – C(x), whereC(x) is the limit density of electrostatic capacity of the obstacles. In particular results on the rate of convergence and on the fluctuations of
m
around the limit operator are given. 相似文献
7.
Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA
is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA
generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation 1 and 2 are two derivations both satisfying the hypotheses on , and 1 and 2 have the same restriction toA
, then there exists a one-parameter subgroup of the action with generator 0 such thatD(1)D(2)D(0) is a joint core for the three derivations, and 2=1+0 on this core. 相似文献
8.
Salvador Miracle-Sole 《Journal of statistical physics》1995,79(1-2):183-214
Some aspects of the microscopic theory of interfaces in classical lattice systems are developed. The problem of the appearance of facets in the (Wulff) equilibrium crystal shape is discussed, together with its relation to the discontinuities of the derivatives of the surface tension (n) (with respect to the components of the surface normaln) and the role of the step free energy step(m) (associated with a step orthogonal tom on a rigid interface). Among the results are, in the case of the Ising model at low enough temperatures, the existence of step(m) in the thermodynamic limit, the expression of this quantity by means of a convergent cluster expansion, and the fact that 2step(m) is equal to the value of the jump of the derivative / (when varies) at the point =0 [withn=(m
1 sin ,m
2 sin , cos )]. Finally, using this fact, it is shown that the facet shape is determined by the function step(m). 相似文献
9.
Ola Bratteli Richard H. Herman Derek W. Robinson 《Communications in Mathematical Physics》1978,59(2):167-196
For automorphism groups of operator algebras we show how properties of the difference
t
– '
t
are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if t – 't 0.28 for smallt, then = 0(+)°-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference
t
– '
t
=O(t) ast ; 0, then = + and if
t
– '
t
0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC
0,C
0
*
groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation 相似文献
10.
Carl Bender Fred Cooper L. M. Simmons Jr. Pinaki Roy Greg Kilcup 《Journal of statistical physics》1991,64(1-2):395-428
We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx
1+2. The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t(
n))
f
as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and. 相似文献
11.
V. N. Folomeshkin 《International Journal of Theoretical Physics》1974,11(6):387-394
A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions:
k
(-gg
0k
)=0 and
ik
0
0g
ik
-
ik
k
0g
0i
=0. In aT-orthogonal metricgs
2=g
00
dt
2 -g
dx
dx
these conditions take a simple form: 0(detg
)=0 and (0
g
)(0
g
)=0. 相似文献
12.
Emil Straube 《Communications in Mathematical Physics》1981,81(1):27-30
Let (, , ) be a measure space with normalized measure,f: a nonsingular transformation. We prove: there exists anf-invariant normalized measure which is absolutely continuous with respect to if and only if there exist >0, and , 0<<1, such that (E)< implies (f
–k(E))< for allk0. 相似文献
13.
L. V. Ermakova V. N. Strekalovskii É. G. Vovkotrub V. G. Bamburov 《Journal of Applied Spectroscopy》2002,69(1):152-154
The Raman scattering spectra of isostructural Bi2O3 and Bi1.8Tm0.2O3 in the course of heating have been investigated. It is shown that the sequences of structural changes with increase in temperature differ: and * , respectively. In the hightemperature region, the structure takes the form of a disordered cube irrespective of the previous history of specimens. 相似文献
14.
Giuseppe Albertini 《Journal of statistical physics》1998,90(3-4):853-871
The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative. 相似文献
15.
We review the construction of topological Yang–Mills theory (TYMT) from the point of view of an operator satisfying d = [, b] with b the BRST operator. We focus our attention on a situation in which [, d] 0 and show how this leads us to consider a more general derivative ~d = b + d +
k 2
k
1–k
. 相似文献
16.
We consider the following problem as a model for the slow passage through a steady bifurcation: dy/dt = (t) y – y3 +, where is a slowly increasing function oft given by=
i + t (
i,<0). Both and are small parameters. This problem is motivated by laser experiments as well as theoretical studies of laser problems. In addition, this equation is a typical amplitude equation for imperfect steady bifurcations with cubic nonlinearities. When=0, we have found that=0 is not the point where the bifurcation transition is observed. This transition appears at a value =
j > 0. We call j the delay of the bifurcation transition. We study this delay as a function of
i, the initial position of, and, the imperfection parameter. To this end, we propose an asymptotic study of this equation as 0, small but fixed. Our main objective is to describe this delay in terms of the relative magnitude of and. Since time-dependent imperfections are always present in experiments, we analyze in the second part of the paper the effect of a small-amplitude but time-periodic imperfection given by (t) = cos(t). 相似文献
17.
C. J. K. Batty 《Communications in Mathematical Physics》1979,68(1):39-43
It is shown that if is the generator of a strongly continuous oneparameter group of *-automorphisms of aC*-algebraA and is an unbounded *-derivation ofA with the same domain as , then + is also a generator for all sufficiently small real numbers . 相似文献
18.
V. V. Kuryshkin 《International Journal of Theoretical Physics》1973,7(6):451-466
In order to clarify physical consequences due to the presence of a set of auxiliary functions
k
(q,t) in quantum mechanics with a non-negative phase-space distribution function, the simplest quantum-mechanical problems are solved. It is shown that
k
(q,t) influence upon the results of a problem. Therefore it is supposed that
k
(q, t) reflect some physical reality (subquantum situation), interacting with a mechanical system. In particular the subquantum situation determines the minimum coordinate and momentum uncertainties ((q)2 and (p)2) as well as the coordinate distribution of a fixed system and the momentum distribution of a free system. These results provide the opportunity to formulate the notion of a stationary homogeneous isotropic subquantum situation. Supposing thatq andp are small an attempt is made to develop an approximate method of solutions (quasi-orthodox approximation). Energy spectrum of an electron in a hydrogen atom is found in the second order of this approximation.On leave of absence from Peoples' Friendship University, Chair of Theoretical Physics, 3, Ordjonikidze Street, B-302, Moscow, U.S.S.R. 相似文献
19.
In addition to the realization of atomically abrupt interfaces in III–V semiconductors by molecular beam epitaxy, the confinement of donor and acceptor impurities to an atomic plane normal to the crystal growth direction, called-doping, is important for the fabrication of artifically layered semiconductor structures. The implementation of-function-like doping profiles by using Si donors and Be acceptors generates V-shaped potential wells in GaAs and AlxGa1–xAs with a quasi-two-dimensional (2D) electron (or hole) gas. In this review we define three areas of fundamental and device aspects associated with-doping. (i) The prototype structure of-doping formed by a single atomic plane of Si donors in GaAs allows to study the 2D electron gas by magnetotransport and tunneling experiments, to study the metal-insulator transition, and to study central-cell and multivalley effects. In addition, non-alloyed ohmic contacts to GaAs and GaAs field-effect transistors (-FETs) with a buried 2D channel of high carrier density can be fabricated from-doped material. (ii) GaAs sawtooth doping superlattices, consisting of a periodic sequence of alternating n- and p-type-doping layers equally spaced by undoped regions, emit light of high intensity at wavelengths of 0.9 < <1.2 [m], which is attractive for application in photonic devices. The observed carrier transport normal to the layers due to tunneling indicates the feasibility of this superlattice as effective-mass filter. (iii) The confinement of donors (or acceptors) to an atomic (001) plane in selectively doped AlxGa1–xAs/GaAs heterostructures leads to very high mobilities, to high 2D carrier densities, and to a reduction of the undesired persistent photo-conductivity. These-doped heterostructures are thus important for application in transistors with improved current driving capabilities.Extended version of a paper presented at the18th Int. Symp. GaAs Related Compounds (Heraklion, Crete, 1987) 相似文献
20.
The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency
0)within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic equation with a free parameter h with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h>0. The exact solutions for which h<h are called sub-Heisenberg states. These nonperturbative solutions appear in the form of Gaussian, non-Heisenberg states for which the initial classical uncertainty relation takes the form (x
2)(p)
2
=(h/2)
2,which includes the limit of zero indeterminacy (h 0). We show how the radiation reaction and the vacuum fields govern the evolution of these non-Heisenberg states in phase space, guaranteeing their decay to the stationary state with average energy h
0
/2 and (x)
2
(p)
2
=h
2
/4 at zero temperature. Environmental and thermal effects-are briefly discussed and the connection with similar works within the realm of quantum electrodynamics is also presented. We suggest some other applications of the classical non-Heisenberg states introduced in this paper and we also indicate experiments which might give concrete evidence of these states. 相似文献