- Email: [email protected]
Kinetic theory of classical liquids. III. Numerical results on the transverse current correlation in liquid argon
ABSTRACTS
OF PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
529
Liouville Dynamics for Optimal Stochastic Phase-Space Representations of Quantum Mechanics. EDUARD PRUGOVEEKI, Department of Mathematics, University of Toronto, Toronto, Canada M5S 1Al. It is shown that the space B(r,) of r,-distribution functions p(q,p) (Husimi transforms) can be described without reference to any conventional representation of the density operator p. A Liouvilletype differential equation governing the free time-evolution of pt(q, p) is derived and solved explicitly; the time dependence of this solution supports the thesis that p(q, p) is a bona fide probability density observable with optimally accurate apparatus for the simultaneous measurement of position and momentum. Liouville-type equations are derived also for the case when local interactions described by analytic potentials are present. Probability currents corresponding to p(q, p) are defined and it is shown that they obey a continuity equation at space-time points. Reduced r,-distribution functions are defined and it is shown that they obey a BBGKY hierarchy of equations. A Brownian-motion experimental test of the underlying theory of measurement is suggested. Kinetic Theory of CIassical Liquids. I. Basic Theory. L. SJ&REN AND A. SJBLANDER, Institute of Theoretical Physics, Chalmers University of Technology, Fack, S-402 20 Gateborg 5, Sweden. A somewhat new approach to a kinetic theory of classical liquids is presented, and it is used to calculate the dynamical structure factor S(qw). It gives correctly the zeroth, second, and fourth frequency moments of S(qw), and it goes correctly over to the free particle value for large q. For small q and w it goes over to proper hydrodynamics, including the coupling to heat diffusion. Results of numerical calculations on liquid argon are presented and they show very good agreement with available neutron scattering and molecular dynamics data.
Kinetic Theory of Classical Liquids. II. Numerical Results on the Density Fluctuations in Liquid Argon. L. SJ%REN, Institute of Theoretical Physics, Chalmers University of Technology, Fack, S-402 20 GGteborg 5, Sweden. Based on a general theory given in an earlier paper, we present results of extensive calculations of the dynamical structure factor S(qw) for liquid argon. Detailed comparison is made with experimental and molecular dynamics data. Good agreement is found except for the smallest wavevectors, where temperature fluctuations are important. Kinetic Theory of Classical Liquids. III. Numerical Results on the Transverse Current Correlation in Liquid Argon. L. SJ~REN, Institute of Theoretical Physics, Chalmers University of Technology, Fack, S-402 20 Gijteborg 5, Sweden. Based on a theory developed in an earlier paper, we present results of calculations of the transverse current correlation function for liquid argon. Detailed comparison is made with molecular dynamics data. The agreement is satisfactory, considering that no adjustable parameters enter. From the results we draw useful conclusions concerning the approximations in the theory. Assumptions of the Singularity Theorems and the Rejuvenarion of Universes. JAMES ALISTAIR DONALD, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia. If rebound from gravitational collapse is possible then collapse is capable of rejuvenating universes and creating new ones. For this reason the assumptions required by the singularity theorems are examined critically. These assumptions are found to be questionable.
OF PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
529
Liouville Dynamics for Optimal Stochastic Phase-Space Representations of Quantum Mechanics. EDUARD PRUGOVEEKI, Department of Mathematics, University of Toronto, Toronto, Canada M5S 1Al. It is shown that the space B(r,) of r,-distribution functions p(q,p) (Husimi transforms) can be described without reference to any conventional representation of the density operator p. A Liouvilletype differential equation governing the free time-evolution of pt(q, p) is derived and solved explicitly; the time dependence of this solution supports the thesis that p(q, p) is a bona fide probability density observable with optimally accurate apparatus for the simultaneous measurement of position and momentum. Liouville-type equations are derived also for the case when local interactions described by analytic potentials are present. Probability currents corresponding to p(q, p) are defined and it is shown that they obey a continuity equation at space-time points. Reduced r,-distribution functions are defined and it is shown that they obey a BBGKY hierarchy of equations. A Brownian-motion experimental test of the underlying theory of measurement is suggested. Kinetic Theory of CIassical Liquids. I. Basic Theory. L. SJ&REN AND A. SJBLANDER, Institute of Theoretical Physics, Chalmers University of Technology, Fack, S-402 20 Gateborg 5, Sweden. A somewhat new approach to a kinetic theory of classical liquids is presented, and it is used to calculate the dynamical structure factor S(qw). It gives correctly the zeroth, second, and fourth frequency moments of S(qw), and it goes correctly over to the free particle value for large q. For small q and w it goes over to proper hydrodynamics, including the coupling to heat diffusion. Results of numerical calculations on liquid argon are presented and they show very good agreement with available neutron scattering and molecular dynamics data.
Kinetic Theory of Classical Liquids. II. Numerical Results on the Density Fluctuations in Liquid Argon. L. SJ%REN, Institute of Theoretical Physics, Chalmers University of Technology, Fack, S-402 20 GGteborg 5, Sweden. Based on a general theory given in an earlier paper, we present results of extensive calculations of the dynamical structure factor S(qw) for liquid argon. Detailed comparison is made with experimental and molecular dynamics data. Good agreement is found except for the smallest wavevectors, where temperature fluctuations are important. Kinetic Theory of Classical Liquids. III. Numerical Results on the Transverse Current Correlation in Liquid Argon. L. SJ~REN, Institute of Theoretical Physics, Chalmers University of Technology, Fack, S-402 20 Gijteborg 5, Sweden. Based on a theory developed in an earlier paper, we present results of calculations of the transverse current correlation function for liquid argon. Detailed comparison is made with molecular dynamics data. The agreement is satisfactory, considering that no adjustable parameters enter. From the results we draw useful conclusions concerning the approximations in the theory. Assumptions of the Singularity Theorems and the Rejuvenarion of Universes. JAMES ALISTAIR DONALD, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia. If rebound from gravitational collapse is possible then collapse is capable of rejuvenating universes and creating new ones. For this reason the assumptions required by the singularity theorems are examined critically. These assumptions are found to be questionable.