- Email: [email protected]
Master equation versus random walk approaches to phenomena far from equilibrium
ANNALS
OF PHYSICS 193,
Abstracts
Quantum
Geometry
252-253
(1%‘)
of Papers
of Strings
with Boundaries.
to Appear
HUGH
LUCKOCK.
in Future
Issues
Department of Physics, University of
Newcastle upon Tyne, United Kingdom. The quantum mechanical transition amplitudes between given string configurations can be obtained by integrating over all world-sheet geometries bounded by these configurations. In the case of spinning strings, certain components of the fermion fields must also be fixed on the boundary. It follows that expressions for quantum anomalies and divergences will generally include boundary contributions which must vanish if the theory is to be finite. Using the semi-classical approximation and the heat-kernel expansion, it is shown that such contributions vanish for bosonic and spinning strings in arbitrary spacetimes of the critical dimensions. This extends the result of Alvarez, which applied only to bosonic strings in flat spacetime.
Master
Equation Versus Random Walk Approaches to Phenomena Farfrom Equilibrium. J. M. AKKERMANS. Netherlands Energy Research Foundation ECN, P.O. Box 1, NL-1755 ZG Petten, The Netherlands; E. BETAK. Institute of Physics EPRC SAS, CS-84228 Bratislava, Czechoslovakia.
We study the relation between (discrete time) random walk and (continuous time) master equation approaches to phenomena in non-equilibrium systems. The equivalence of these approaches is proved under very broad conditions. The obtained equivalence theorem includes generalized master equations that can be derived from quantum mechanics in an exact manner. Results are illustrated by and applied to examples from nuclear physics. A certain soluble model example, concerning the Z and N distributions of emergent fragments in heavy-ion collisions, is presented in order to re-interpret earlier results of Hiller et al. seemingly contradicting the equivalence theorem. It is furthermore shown that experimental observables in nuclear physics applications are sensitive only to the mean time between intranuclear collisions, and not to the nature of the distribution of waiting times between these events.
The
Model and the Chiral Anomaly. M. WAKAMATSU. Institute of Theoretical Physics, University of Regensburg, D-8400 Regensburg, Federal Republic of Germany.
Nambu-Jona-Lasinio
An approximate bosonization of the Nambu-Jona-Lasinio model is shown to lead to either form of two low energy effective Lagrangians: i.e., the massive Yang-Mills form or the hidden local symmetry form of Bando et al. The specific underlying quark Lagrangian restricts the freedom in obtaining the anomalous elfective action in one and the other scheme. This enables us to show the equivalence of the two schemes not only for the physics of the non-anomalous sector but also for the physics of the anomalous sector. Our model in either representation, however, breaks low energy theorems for some of the anomalous processes. In pursuit of its origin, we investigate the general structure of the hadronic currents in the present model, putting special emphasis upon the underlying Lagrangian at the quark level. As an interesting by-product of the present analysis, we gain a new insight into the dynamical meaning of the parameter a, which appears as a free parameter in the hidden symmetry model of Bando et al.
252 0003-4916/89 $7.50 Copyright 0 1989 by Academic Press. Inc. All rights of reproduction in any form reserved.
OF PHYSICS 193,
Abstracts
Quantum
Geometry
252-253
(1%‘)
of Papers
of Strings
with Boundaries.
to Appear
HUGH
LUCKOCK.
in Future
Issues
Department of Physics, University of
Newcastle upon Tyne, United Kingdom. The quantum mechanical transition amplitudes between given string configurations can be obtained by integrating over all world-sheet geometries bounded by these configurations. In the case of spinning strings, certain components of the fermion fields must also be fixed on the boundary. It follows that expressions for quantum anomalies and divergences will generally include boundary contributions which must vanish if the theory is to be finite. Using the semi-classical approximation and the heat-kernel expansion, it is shown that such contributions vanish for bosonic and spinning strings in arbitrary spacetimes of the critical dimensions. This extends the result of Alvarez, which applied only to bosonic strings in flat spacetime.
Master
Equation Versus Random Walk Approaches to Phenomena Farfrom Equilibrium. J. M. AKKERMANS. Netherlands Energy Research Foundation ECN, P.O. Box 1, NL-1755 ZG Petten, The Netherlands; E. BETAK. Institute of Physics EPRC SAS, CS-84228 Bratislava, Czechoslovakia.
We study the relation between (discrete time) random walk and (continuous time) master equation approaches to phenomena in non-equilibrium systems. The equivalence of these approaches is proved under very broad conditions. The obtained equivalence theorem includes generalized master equations that can be derived from quantum mechanics in an exact manner. Results are illustrated by and applied to examples from nuclear physics. A certain soluble model example, concerning the Z and N distributions of emergent fragments in heavy-ion collisions, is presented in order to re-interpret earlier results of Hiller et al. seemingly contradicting the equivalence theorem. It is furthermore shown that experimental observables in nuclear physics applications are sensitive only to the mean time between intranuclear collisions, and not to the nature of the distribution of waiting times between these events.
The
Model and the Chiral Anomaly. M. WAKAMATSU. Institute of Theoretical Physics, University of Regensburg, D-8400 Regensburg, Federal Republic of Germany.
Nambu-Jona-Lasinio
An approximate bosonization of the Nambu-Jona-Lasinio model is shown to lead to either form of two low energy effective Lagrangians: i.e., the massive Yang-Mills form or the hidden local symmetry form of Bando et al. The specific underlying quark Lagrangian restricts the freedom in obtaining the anomalous elfective action in one and the other scheme. This enables us to show the equivalence of the two schemes not only for the physics of the non-anomalous sector but also for the physics of the anomalous sector. Our model in either representation, however, breaks low energy theorems for some of the anomalous processes. In pursuit of its origin, we investigate the general structure of the hadronic currents in the present model, putting special emphasis upon the underlying Lagrangian at the quark level. As an interesting by-product of the present analysis, we gain a new insight into the dynamical meaning of the parameter a, which appears as a free parameter in the hidden symmetry model of Bando et al.
252 0003-4916/89 $7.50 Copyright 0 1989 by Academic Press. Inc. All rights of reproduction in any form reserved.