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1.
We investigate the quantum mechanical wave equations for free particles of spin 0, 1/2, 1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is S/ = p
dx
/, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple manageable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has exactly the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in . We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in . For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations. 相似文献
2.
It is shown that the standard WKB-approximation (the approximation of the first order in) to the propagator is not sufficient for the construction of the short-time propagator on curved spaces. The proper short-time propagator can be obtained by means of the second order (in) WKB-approximation and then no subtraction of a quantum correction proportional to
2 from the original Lagrangian is necessary.The authors are indebted to J. Tolar for valuable critical comments and advices. 相似文献
3.
J. T. Lue T. W. Nee J. J. Chu C. M. Chang 《Applied Physics A: Materials Science & Processing》1992,55(2):192-195
Optical reflectance of YBa2Cu3O7- thin films grown by laser ablation is measured within photon energies of 0.1 eV to 3.5 eV at room temperature. The spectra can be fit congruently with the anisotropic dielectric constants which take account of the intraband free carrier transition and interband transition. The anisotropic plasma frequencies are simulated to be pl=2.18 eV and ch=2.80 eV contributed from free carriers on the plane and in the chain, respectively. The interband transition occurs near 2.5 eV and is pertinent to a rather broad line width. 相似文献
4.
James Baugh David Ritz Finkelstein Andrei Galiautdinov Mohsen Shiri-Garakani 《Foundations of Physics》2003,33(9):1267-1275
Segal proposed transquantum commutation relations with two transquantum constants , besides Planck's quantum constant and with a variable i. The Heisenberg quantum algebra is a contraction—in a more general sense than that of Inönü and Wigner—of the Segal transquantum algebra. The usual constant i arises as a vacuum order-parameter in the quantum limit ,0. One physical consequence is a discrete spectrum for canonical variables and space-time coordinates. Another is an interconversion of time and energy accompanying space-time meltdown (disorder), with a fundamental conversion factor of some kilograms of energy per second. 相似文献
5.
Scott Allen 《Journal of statistical physics》1995,79(1-2):165-181
A detailed analysis is reported examining the local magnetic susceptibility (r), in relation to the correlation functionG(R) and correlation length , of a spherical model ferromagnet confined to geometry =L
d –d
×
d
(
d
2,d>2) under a continuous set oftwisted boundary conditions. The twist parameter
in this problem may be interpreted as a measure of the geometry-dependent doping level of interfacial impurities (or antiferromagnetic seams) in theextended system at various temperatures. For
j
0, jd-d, no seams are present except at infinity, whereas if
j
= 1/2, impurity saturation occurs. For 0 <
j
< 1/2 the physical domain
phys =D
d –d
×
d
(D>L), defining the region between seams containing the origin, depends on temperature above a certain threshold (T>T
0). Below that temperature (T>T
0), seams are frozen at the same position (DL/2,d-d'=1), revealing a smoothly varying largescale structural phase transition. 相似文献
6.
A nonzero 2-cocycle Z2(g, R) on the Lie algebra g of a compact Lie group G defines a twisted version of the Lie–Poisson structure on the dual Lie algebra g*, leading to a Poisson algebra C (g*()). Similarly, a multiplier c Z2(G, U(1)) on G which is smooth near the identity defines a twist in the convolution product on G, encoded by the twisted group C-algebra C*(G,c). Further to some superficial yet enlightening analogies between C (g*()) and C*(G,c), it is shown that the latter is a strict quantization of the former, where Plancks constant assumes values in (Z\{0})-1. This means that there exists a continuous field of C*-algebras, indexed by 0 (Z\{0})-1, for which A0= C0(g*) and A=C*(G,c) for 0, along with a cross-section of the field satisfying Diracs condition asymptotically relating the commutator in A to the Poisson bracket on C(g*()). Note that the quantization of does not occur for =0. 相似文献
7.
Davis-Mott and Tauc models of optical absorption at the absorption edge in the high absorption coefficient region (104cm–1) are carefully reviewed with regard to their theoretical foundations, assumptions, mathematical derivations, and results. The full implications of these models are exploited, and it is found that the Davis-Mott model for negligible matrix elements between localised states could account for the cubic power law behaviour of with photon energy of some amorphous semiconductors such as a-Si. A fractional power law to find the optical band gapE
opt, of the form [ (–E
opt)r; 2r3] based on Davis-Mott model is proposed in which the indexr can be a function of disorder. The Tauc model has further been extended to the case of negligible matrix elements between localised states, in which the same square power law for vs. with the same meaning of the optical gap as in the original Tauc model has resulted. A consideration of the case of unequal matrix elements for those transitions between localised states and those between extended states is also included. The meaning ofE
opt has been re-assessed and it is emphasized that it is an extrapolation of delocalised states to the zero of the density of states rather than a threshold energy for the onset of some kind of optical transitions.This paper is cordially dedicated to Professor C. A. Hogarth who taught us the Physics of amorphous materials. 相似文献
8.
To a gauge field on a principalG-bundlePM is associated a sequence of quantum mechanical Hamiltonians, as Planck's constant 0 and a sequence of representations
n
ofG is taken. This paper studies the associated quantum partition functions, trace exp (–tH
n
), and produces a complete asymptotic expansion, as 0, =1/n, of which the principal term, proportional to the classical partition function, is the familiar classical limit.Research supported in part by Deutsche Forschungsgemeinschaft and NSF grant NoPhy 81-09011A-01On leave of absence from Freie Universität, BerlinResearch supported by NSF grant MCS 820176A01 相似文献
9.
We investigate stochastic gravity as a potentially fruitful avenue for studying quantum effects in gravity. Following the approach of stochastic electrodynamics (sed), as a representation of the quantum gravity vacuum we construct a classical state of isotropic random gravitational radiation, expressed as a spin-2 field,h
µ
(x), composed of plane waves of random phase on a flat spacetime manifold. Requiring Lorentz invariance leads to the result that the spectral composition function of the gravitational radiation,h(), must be proportional to 1/
2. The proportionality constant is determined by the Planck condition that the energy density consist of/2 per normal mode, and this condition sets the amplitude scale of the random gravitational radiation at the order of the Planck length, giving a spectral composition functionh() =16c
2Lp/2. As an application of stochastic gravity, we investigate the Davies-Unruh effect. We calculate the two-point correlation function (R
iojo(O–/2)R
kolo(O,+/2)) of the measureable geodesic deviation tensor field,R
iojo, for two situations: (i) at a point detector uniformly accelerating through the random gravitational radiation, and (ii) at an inertial detector in a heat bath of the random radiation at a finite temperature. We find that the two correlation functions agree to first order ina/c provided that the temperature and acceleration satisfy the relationkT=a/2c. 相似文献
10.
The Wigner and Husimi distributions are the usual phase space
representations of a quantum state. The Wigner distribution has structures
of order 2. On the other hand, the Husimi distribution is a
Gaussian smearing of the Wigner function on an area of size and
then, it only displays structures of size . We have developed a
phase space representation which results a Gaussian smearing of the Wigner
function on an area of size , with 1. Within
this representation, the Husimi and Wigner functions are recovered when
=1 and
respectively. We treat the application of
this intermediate representation to explore the semiclassical limit of quantum
mechanics. In particular we show how this representation uncover
semiclassical hyperbolic structures of chaotic eigenstates. 相似文献
11.
G. Tauber 《General Relativity and Gravitation》1980,12(12):1043-1054
The spin-two particle is described by a symmetric tensorh
subject to the subsidiary conditionsh
=
h
=0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh
a symmetric third-rank tensor
=
as well as a vector fieldA
have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh
,
andA
independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh
as well as the generalization of the wave equationD
D
h
+ 2R
h
-R
h
-R
h
+g
R
h
+Rh
=m
2
h
Finally, variation with respect tog
yields the energy-momentum tensor. 相似文献
12.
G. Benfatto C. Marchioro E. Presutti M. Pulvirenti 《Journal of statistical physics》1980,22(3):349-362
We consider an anharmonic crystal described by variablesS
x
,x
d
,S
x
, with one-body interaction ¦S
x
¦
and nearest neighbor (n.n.) two body interaction ¦S
x
–S
y
¦. We prove that, for
d
bounded, , where
is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche. 相似文献
13.
In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {n(a)}n N
is a -convergent sequence, for each nN, when { (a)} convergent to 0, {n(a)} is -convergent, then when { (a)} convergent to 0, {n(a)} are -convergent uniformly with respect to nN 相似文献
14.
The temperature dependent exchange stiffnessD, defined for long wavelength spin waves by=Dq
2, is calculated for very weak itinerant ferromagnets. It is found that for a general single band of d-electrons,D reduces to a very simple form givingD(T)=D(0)/
0 in the limit
00. The stability condition for spin waves at finite temperatures is thenD(0) > 0 and/
0 > 0, where is the relative occupation ± spin sub-bands and
0 its value at 0°K.The authors are grateful to E. P. Wohlfarth for helpful discussions. 相似文献
15.
Selçuk Ş. Baym 《General Relativity and Gravitation》1990,22(2):179-192
In recent articles we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models were treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential, etc.). This model has the advantage of allowing us to determine the geometry of the universe by thermodynamic stability arguments. In this paper, in search for evidence for the definition of gravitational temperature, we will investigate a massless conformal scalar field in an Einstein universe in detail. We will argue that the gravitational temperature of the Einstein universe is given asT
g=1/2) (c/k) (1/R
0), where R0 is the radius of the Einstein universe. This is in accord with our definition of gravitational temperature in Friedmann thermodynamics and determines the dimensionless constant as 1/2. We discuss the limitations of the model we are using. We also suggest a method to generalize our gravitational temperature to arbitrary space-times granted that they are sufficiently smooth.Based on three essays awarded honorable mention in the years 1987, 1988 and 1989 by the Gravity Research Foundation—Ed. 相似文献
16.
J. -B. Suck H. Bretscher H. -J. Güntherodt 《Zeitschrift für Physik B Condensed Matter》1987,68(2-3):285-290
The total dynamic structure factorsS(Q, ) of icosahedral, glassy Pd58.8Si20.6U20.6, and the crystallized sample have been determined at room temperature using inelastic scattering of cold neutrons (IN6 of ILL). In contrast to the static structure factorS(Q), where the long range bond orientational order (BOO) leads to pronounced diffraction peaks with finite half width, the dynamic structure factor shows little or no influence of the long range BOO on the atomic dynamics of icosahedral PdSiU in the range of frequencies (0.525 meV) and momentum transfers Q(5Q30 nm–1 for inelastic scattering) investigated here. The wavelength-dependence of the atomic dynamics of icosahedral PdSiU is very similar to that of the metallic glass and is different from that of the crystallized sample. As for glassy PdSiU no well defined vibrational collective excitations are found as peaks in the inelastic part ofS(Q, ) of the icosahedral sample,-quite in contrast to theoretical expectations and to the dispersions of pronounced excitations determined under identical experimental conditions fromS(Q, ) of the crystallized sample. On structural relaxation of the metallic glass Pd58.8Si20.6U20.6 the largest amount of low energy modes is annealed out at lowest energy.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday 相似文献
17.
András Sütő 《Communications in Mathematical Physics》1987,111(3):409-415
The spectrum (H) of the tight binding Fibonacci Hamiltonian (H
mn=
m,n+1+
m+1,n
+
m,n
v(n),v(n)=
((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary 相似文献
18.
O. Costa De Beauregard Ch. Imbert J. Ricard 《International Journal of Theoretical Physics》1971,4(2):125-140
Fresnel's theory of the evanescent wave in total reflection entails that the propagation vectork and the momentum quanta
k have an imaginary component and, thus, a projection on the reflecting plane that is larger (in units such thatc=1) than the angular frequency and the energy quanta. We discuss the tachyon properties of these energy-momentum quanta and propose an experimental test using absorption or stimulated emission by an atomic or ionic beam. We then show that the Maxwell-Minkowski tensor (although certainly appropriate to discuss the macroscopic energy-momentum exchange between wave and diopter) does not describe adequately the energy-momentum density of the quanta in the evanescent wave, this stemming from its too remote connection with the generator i of space-time displacements. On the other hand de Broglie's energy-momentum tensorA
k[i]B
jk
is the density canonically associated with the generator of space-time displacements; we show that it describes quite satisfactorily both the energy fluxes (as measured through the longitudinal Goos-Hänchen and our new transverse shifts of the reflected beam in total reflection) and the momentum densities of the quanta inside the evanescent wave. Finally, we show that it is the gauge which is transverse in the diopter's rest frame that directly yields the physically measured energy fluxes. We take this fact as a new argument, strongly supported by experimental evidence, in favour of the physical reality of electromagnetic potentials. 相似文献
19.
We present exact explicit expressions for the row spin-spin correlation functions
00
n0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for
00
n0. 相似文献
20.
Gerald Rosen 《International Journal of Theoretical Physics》1980,19(7):557-560
Current experimental evidence supports the picture of three charged leptons (e
±,
±,
±), a triplet with mass splitting that bears a resemblance to the Gell-Mann-Okubo form. To elucidate the overall mass scale, a charged lepton is viewed as a mass point that engenders a local Reissner-Nordström spacetime geometry, and the Einstein-Maxwell action is evaluated through an invariant space-time region associated with the particle's radiation reaction interval 2e
2/3m. What emerge for the electron, muon, and tau are values of the Einstein-Maxwell action in the neighborhood of. The mean value of the three action integrals is =(140.93)e
2=(1.0284), and thus the apparent quantum condition sets the mass scale for the three charged leptons. 相似文献