- Email: [email protected]
On the statistical theory of localized entropy flow
ABSTRACTS
363
the usual Ritz-Schrcdinger or Hylleraas-Bethe-Salpeter procedures which choose the functionals so that their extremum values are identically equal to certain energy eigenvalueg. As examples variational principles for the second-order Hartree-Fock energy and the second-order energy of an uncorrelated system in an electric field are derived. On the Statistical Theory of Localized Entropy Flow. F. PCHL~GL AND A. STAHL, Institut fiir Theoretische Physik der Technischen Hochschule Aachen, Aachen, Germany. The implications are analyzed which follow for the statistical description of a system shere entropy is conserved and localized as an entropy density. The possible type of the equations of motion is derived. Entropy flow is shown to be incompressible if the system is dynamically uniform. Conserved Vector Currents and Invariance Prcperties in Lagrangian Field Theory. D. HORN, Department of Physics, Tel-Aviv University, Tel-Aviv, Israel. It is shown that conserved vector currents in a local Lagrangian theory must stem from the invariance of the Lagrangian under general gauge transformations. Thus there exists a unique way of obtaining conserved vector current)s, namely, using the generalized Noether theorem. Vortex Lines and the X-Transition. EERO BYCKLING, NORDITA, Copenhagen, DenmarkVortex line contribution to the specific heat of liquid He II is expressed in terms of a lattice line model. A connection between the partition function of the model and that of the Ising lattice is found and applied to calculate properties of the model. The system has a phase transition, at which the concentration of lines and their average length increase suddenly and c,, has a logarithmic singularity. The possible connection with the X-transition is discussed. Permutation Symmetry and a Derivation of Unitary Symmetry. J. SCHECHTER, Y. UEDA, AND S. OKUBO, Department of Physics and Astronomy, University of Rochester, nocheater, New York. linear combinations Assuming the existence of three basic fields @I , #2 , (~3 with their & , $2 , $3 given by $,, = ~~=I a,‘.4, for some up”, we shall prove the following: The total Hamiltonian, H is invariant under the three dimensional unitary group U(3) if H is invariant under permutations of 9, , bz , d3 and if H preserves the particle numbers associated with the h-fields (CL = 1, 2, 3). This holds in general except for a very special form of a,’ in which case we obtain instead a broken U(3) symmetry. A New
Method for the Estimation of the Primary Energy of Cosmic Ray Jets. M. L. SHEN AND F. KAPLON, Department of Physics and Astronomy, University of Rochester, Rochester, New York. Methods of determining the primary energy of cosmic ray jets are reviewed and the corrections which have been developed to improve the basic assumptions are discussed to clarify the limit of this applicability. To avoid the disadvantages inherent in the usual methods, a new method has been developed for determining the primary energy of cosmic ray jets based mainly on the constancy of transverse momentum of the charged secondary shower particles and which is free of the usual assumptions employed. Nuclear interactions induced by 28.5 Be\: protons and 17 BeV r--mesons in emulsion have been analyzed to test the validity of this method and the results are compared with those obtained by using Cnstagnoli’s method and the IS,!,-method; the agreement is much better with the new AI.
363
the usual Ritz-Schrcdinger or Hylleraas-Bethe-Salpeter procedures which choose the functionals so that their extremum values are identically equal to certain energy eigenvalueg. As examples variational principles for the second-order Hartree-Fock energy and the second-order energy of an uncorrelated system in an electric field are derived. On the Statistical Theory of Localized Entropy Flow. F. PCHL~GL AND A. STAHL, Institut fiir Theoretische Physik der Technischen Hochschule Aachen, Aachen, Germany. The implications are analyzed which follow for the statistical description of a system shere entropy is conserved and localized as an entropy density. The possible type of the equations of motion is derived. Entropy flow is shown to be incompressible if the system is dynamically uniform. Conserved Vector Currents and Invariance Prcperties in Lagrangian Field Theory. D. HORN, Department of Physics, Tel-Aviv University, Tel-Aviv, Israel. It is shown that conserved vector currents in a local Lagrangian theory must stem from the invariance of the Lagrangian under general gauge transformations. Thus there exists a unique way of obtaining conserved vector current)s, namely, using the generalized Noether theorem. Vortex Lines and the X-Transition. EERO BYCKLING, NORDITA, Copenhagen, DenmarkVortex line contribution to the specific heat of liquid He II is expressed in terms of a lattice line model. A connection between the partition function of the model and that of the Ising lattice is found and applied to calculate properties of the model. The system has a phase transition, at which the concentration of lines and their average length increase suddenly and c,, has a logarithmic singularity. The possible connection with the X-transition is discussed. Permutation Symmetry and a Derivation of Unitary Symmetry. J. SCHECHTER, Y. UEDA, AND S. OKUBO, Department of Physics and Astronomy, University of Rochester, nocheater, New York. linear combinations Assuming the existence of three basic fields @I , #2 , (~3 with their & , $2 , $3 given by $,, = ~~=I a,‘.4, for some up”, we shall prove the following: The total Hamiltonian, H is invariant under the three dimensional unitary group U(3) if H is invariant under permutations of 9, , bz , d3 and if H preserves the particle numbers associated with the h-fields (CL = 1, 2, 3). This holds in general except for a very special form of a,’ in which case we obtain instead a broken U(3) symmetry. A New
Method for the Estimation of the Primary Energy of Cosmic Ray Jets. M. L. SHEN AND F. KAPLON, Department of Physics and Astronomy, University of Rochester, Rochester, New York. Methods of determining the primary energy of cosmic ray jets are reviewed and the corrections which have been developed to improve the basic assumptions are discussed to clarify the limit of this applicability. To avoid the disadvantages inherent in the usual methods, a new method has been developed for determining the primary energy of cosmic ray jets based mainly on the constancy of transverse momentum of the charged secondary shower particles and which is free of the usual assumptions employed. Nuclear interactions induced by 28.5 Be\: protons and 17 BeV r--mesons in emulsion have been analyzed to test the validity of this method and the results are compared with those obtained by using Cnstagnoli’s method and the IS,!,-method; the agreement is much better with the new AI.