Entropy andp-particle observables. I. The general program

An information-theoretic notion of entropy is proposed for a system ofN interacting particles which assesses an observer's limited knowledge of the state of the system, assuming that he or she can measure with arbitrary precision all one-particle observables and correlations involving some numberp of the particles but is completely ignorant of the form of any higher-order correlations involving more thanp particles. The idea is to define a generic measure of entropyS[ ] = –Tr log for an arbitrary density matrix or distribution function , and then, given the trueN-particle, to define a reduced _R ^P which reflects the observer's partial knowledge. The result, at any timet, is a chain of inequalitiesS[ _R ¹ ]S[ _R ² ]...S[ _R ^N ]S[], with true equalityS[ _R ^p ]=S[ _R ^p+1 ] if and only if the true factorizes exactly into a product of contributions involving all possiblep-particle groupings. It follows further than (1) if, at some initial timet ₀, the true factorizes in this way, thenS[ _R ^p (]S[ _R ^p (t ₀)] for all finite timest>t ₀, with equality if and only if the factorization is restored, and (2) the initial response of the system must be to increase itsp-particle entropy.     

Isotope dependence of particle-decay rates of muonic molecular ions (d3,4Heμ) J=1 below (dμ)1s-3,4He threshold

Rates of particle-emitting decay of the resonant state of the muonic molecular ion (dHe) _J=1 lying below the (d)_1s-He threshold can decay to the d-He scattering state. The resonant state is estimated by scattering calculations with the non-adiabatic coupled-rearrangement-channel method. Strong isotope dependence of the decay rates of (d³He) _J=1 and (d⁴He) _J=1 is predicted, though the calculated radiative decay rates of the states are almost the same. In (d³He) _J=1, the particle decay width is three times larger than the radiative decay width, while the two types of decay widths are almost the same in (d⁴He) _J=1. This results in a strong hindrance of the branching ratio of the radiative decay of (d³He) _J=1 compared with the case of (d⁴He) _J=1. This is consistent with a recent observation of the radiative decay of the two molecular states.     

New cascade laser transitions in CH2F2 pumped with the 9R32 line of a cw CO2 laser

New cascade laser transitions of¹²CH₂F₂ at 172.50m, 208.83m, 220.44m, 223.99m and 250.61m are reported. A waveguide FIR laser was pumped with a quasi cw¹²C¹⁶O₂ laser operating on the 9R32 line. Together with the already known lines at 184.3m, 196.1m and 235.9m, the laser lines can be assigned to rotational transitions in the ₉ vibrational band of¹²CH₂F₂ and to refill transitions of the vibrational ground state ₀.     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Experimental survey of the sticking problem in muon catalyzed dt fusion

The sticking process dt + n, which constitutes the most severe limit to the number of fusions which a muon can catalyze, is reviewed. Many attempts were made to determine by calculations and measurements the probability for initial sticking _s ⁰ (immediately after dt fusion) and for final sticking _s (after the came to rest). Previous results based on neutron disappearance rates and on the observation of -X-rays were controversial and also in some disagreement with theory. New data are reported from PSI on direct observation of final sticking, using a setup with the St. Petersburg ionization chamber. These data mark a significant improvement in reliability and may clarify questions concerning previous discrepancies. The new results is _s(0.56±0.04)%, lower than the theory prediction _s=(0.65±0.03)%, at medium density.     

Singularity theorems and the [General Relativity + additional matter fields] formulation of metric theories of gravitation

By using the [General Relativity + additional matter fields] formulation (which depends on a redefined metrich ) of metric theories of gravitation, the study of singularities characterized by incomplete nonspacelike geodesics is simplified, but may be used only if (at least) the non-spacelike geodesics of the original metricg are conserved under the transformation betweeng and the new metrich . In order that every class of geodesies of a diagonal Bianchi I metric correspond to the same class of geodesies of a diagonal metrich , it is necessary that the transformation between these two metrics be a constant (positive) conformal transformation. We analyse the implications of the previous results for the singularitiesg when the latter is a solution of theories with a quadratic or polynomial Lagrangian.     

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

In this paper, we paraquantize the spinning string theory in the Neveu-Shwarz model. Unlike the Ardalan and Mansouri work [Phys. Rev. D, Vol. 9, (1974) 3341], the paraquantum system is such that both the center of mass variables and the excitation modes of the string verify paracommutation relations. The commutators of the Poincaré algebra are satisfied, except the [p ,p ] one, since one can only write [p ,p ]= 0, for Q1. Because of the relation [x ,x ] =,0 and with the sole use of the trilinear relations, we find existence possibilities of spinning strings defined in a noncommutative space-time at space-time dimensions other than D=10.     

The paramagnetic state (μ+e−) in silicon and tellurium at high temperature

The paramagnetic state (⁺e^–) in Si and Te was observed in a longitudinal magnetic field. The mean lifetimes of these states were obtained: _Si = 1.45(3) s, _Te = 12.5(8) s at 290 K, _Te = 12(2) s at 250 K.     

A μSR study of spin density wave condensation in Cr85Mo15

Zero field SR spectra from Cr₈₅Mo₁₅ are well described by the sum of a lightly damped (0.02s^–1<₁<0.2s^–1) and a heavily damped (2s^–1<₂<15s^–1) exponential. The temperature dependence of these components is discussed in relation to the condensation of the incommensurate spin density wave and the onset of the antiferromagnetic state in this Cr-like alloy below T_N=120K. Evidence is presented for the nucleation of the spin density wave at temperatures greater than 1.5T_N.     

The magnetic moment of103Ru

The nuclear magnetic moment of¹⁰³Ru has been determined using the technique of low-temperature nuclear orientation on¹⁰³Ru as a dilute impurity in Fe. The Fe lattice was cooled to 1.7 mK using a PrNi₅ enhanced nuclear demagnetisation stage precooled with a³He–⁴He dilution refrigerator. The¹⁰³RuFe system was observed to have a long nuclear spin-lattice relaxation time, but analysis of the relaxation indicates that the¹⁰³Ru nuclei are close to thermal equilibrium with the Fe lattice at times>200 min after demagnetising. From the near thermal equilibrium anisotropy of the 497 keV -ray in¹⁰³Rh we have deduced the nuclear magnetic moment as |(¹⁰³Ru)|=0.18(2)_N. This value is almost independent of the choice of spinI=3/2 or 5/2 for the nucleus, but is only consistent with systematics ifI(¹⁰³Ru)=3/2 and <0. UsingI=3/2 we obtain the E2/M1 mixing ratio of the 497 keV -ray as =–0.42(4). The sign of the anisotropy of the 610 keV -ray from the 650 keV level in¹⁰³Rh is only consistent with an allowed -decay to the state ifI(650 keV,¹⁰³Rh)=5/2. The E2/M1 mixing ratio of the 610 keV -ray is then =+0.15(3) or +60( _–40 ⁺ ), <–80. From the initial rise in -ray anisotropy following demagnetisation we determine the Korringa constant for¹⁰³RuFe to beC=5.7(5) K·s.     

Nuclear magnetic moment of 12 d 11/2− 131mXe

NMR-ON measurements were performed on^131mXe (I=11/2^–; T_1/2=12.0 d) in Fe, the sample being prepared by recoil implantation after the¹³⁰Te(,3n)^131mXe compound reaction at E=40 Mev. The hyperfine splitting _NB_HF/h¦, extrapolated to zero external magnetic field, was found to be 209.9(1) MHz. Taking B_HF=+1523(8) kG for the hyperfine field of XeFe, the magnetic moment of^131mXe is deduced to be (–)0.994(5) _N. As a byproduct, the zero-field hyperfine splitting of^129mXe (I=11/2^–; T_1/2=8.9d) in Fe was measured as 188.1(1) MHz, with which a magnetic moment of (–)0.891(5) _N is deduced for^129mXe.     

μ+SR in magnetically ordered BCC metals: Local fields, μ+ sites,quantum diffusion,and strain effects

The paper gives a critical discussion of the procedures for extracting from the ⁺SR signals obtainable on magnetically ordered metals information on ⁺ sites, on local lattice distortions induced by the ⁺, on the local magnetic fields felt by the ⁺, and on quantum diffusion. Results for-Fe are: ⁺ occupy O sites, the tetragonality of the elastic double-force tensor isA–B 2eV, the dipolar magnetic field acting on the ⁺ isB _dip=(0.66±0.02)T. Using this information ⁺ hopping rates and diffusivities in Fe are deduced and compared with diffusivities obtained for hydrogen and deuterium. From this it is concluded that hydrogen in Fe diffuses via the adiabatic mechanism. In addition, the paper contains a brief summary of the theoretical background required for taking advantage of the rather large ¦A– B¦ values expected for ⁺ at O sites in bcc metals in order to gain information on the effects of energy asymmetries between neighbouring ⁺ sites on the ⁺ hopping rates.     

Systematic study of muon transfer to sulphur dioxide

In a systematic study of the transfer process to sulphur dioxide, in seven different H₂ + SO₂ gas mixtures, the time spectra of the muonic sulphur X-rays yield muon transfer rates to the SO₂ molecule, deduced from the lifetimes of the p atoms, which agree all well with each other. The muonic oxygen time spectra show an additional structure as if p atoms of another kind were present. Reduced transfer rates_O are reproducible if one uses the model of ephemeral p atoms. The intensity ratios between the different kinds of p atoms are also discussed in the framework of this model and the one of black and white p atoms.     

On the Haar measure of the quantumSU(N) group

We prove that the Haar state associated to the compact matrix quantum groupSU (N) is faithful for ]–1,1[,0, and anyN2.     

On the geometrization of electrodynamics

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion of spacetime. This conjecture is made feasible by the natural separation of the connection ^v into gravitational and electromagnetic parts ^v and ^v , respectively, related to the metric and to the torsion. When ^v is neglected in front of ^v , the affine geodesics are shown to become the equations of motion of charged particles with Lorentz force, for an appropriate choice of . Since ^v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when ^{v v} ).In addition to the factor q/m, the velocity of the test particle appears in . This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor.     

Time-energy uncertainty and relativistic canonical commutation relations in quantum spacetime

It is shown that the time operatorQ ⁰ appearing in the realization of the RCCR's [Q,P^v]=–jhg^v, on Minkowski quantum spacetime is a self adjoint operator on Hilbert space of square integrable functions over _m =×v _m , where is a timelike hyperplane. This result leads to time-energy uncertainty relations that match their space-momentum counterparts. The operators Q appearing in Born's metric operator in quantum spacetime emerge as internal spacetime operators for exciton states, and the condition that the metric operator should possess a ground exciton state assumes the significance of achieving minimal spacetime4-momentum uncertainty in fundamental standards for spacetime measurements.Supported in part by NSERC research grant No. A5206.     

Muon-pair formation in the collision of polarized hadrons

The angular dependence of the differential cross section of muon-pair formation in hadron-hadron collisions a₁+a₂+^–+X is investigated in general form, attention being directed mainly toward those contributions to the differential cross section which are determined by the vector polarization of the incident hadron a₁. The specific mechanism of processes a₁ + a₂ ⁺ + ^– +X is not given in detail here, but use is made of such general properties as the conservation of electromagnetic hadron current and the invariance of the electromagnetic interaction of hadrons with respect to spatial reflections.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 88–91, July, 1982.     

Towards slow μ− production via muon catalyzed fusion

Slow ^– production via dd-CF using a two-layer arrangement is investigated. To determine its feasibility, experimental measurements are now in progress using the muonic X-ray detection method. The following experimental steps are being considered: (1) measurement of the number of ^– stopped inside a solid H₂/D₂ layer by detecting p K X-rays, (2) hot d emission detection by placing a secondary target at a distance of 10–30 mm from the layer and by detecting specific delayed X-rays, (3) measurement of the disappearance of d emission as the added D₂ layer is increased, (4) dd-CF measurement by detecting fusion protons, and (5) slow ^– emission detection. Results of the initial test experiment are presented.     

Low temperature nuclear orientation of149, 151Gd in gadolinium

^{149, 151}Gd fused in gadolinium metal have been oriented at low temperature. The main results are: ¦ (¹⁴⁹Gd,7/2^–¦=0.97(6)_N, ¦(¹⁵¹Gd,7/2^–¦= 0.77(6)_N and I(¹⁴⁹Eu,939 keV)=7/2. Some M1/E2 and E2/M3 mixing ratios in Eu daughter nuclei are also established.     

X-ray measurement on muon to alpha sticking in muon catalyzed d-t fusion; present and future

Among a series of X-ray experiments on the muon catalyzed fusion (CF) carried out by using pulsed muons at UTMSL/KEK, a direct knowledge of -sticking probability ( _s) in CF of high density D-T mixture with high T concentration has been obtained by measuring a characteristic muonic X-ray from the () atoms (central energy of 8.2 keV with a correct Doppler broadening). Combining with the recent X-ray measurements in (d) to³He and⁴He impurities, new insight is now obtained for the detailed background structure in the X-ray spectrum, suggesting the future direction for the X-ray measurements.