| Quantum Theory and Its Stochastic Limit 2002 Edition Contributor(s): Accardi, Luigi (Author), Lu, Yun Gang (Author), Volovich, Igor (Author) |
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ISBN: 3540419284 ISBN-13: 9783540419280 Publisher: Springer OUR PRICE: $161.49 Product Type: Hardcover - Other Formats Published: August 2002 Annotation: The subject of this book is a new mathematical technique, the stochastic limit, developed for solving nonlinear problems in quantum theory involving systems with infinitely many degrees of freedom (typically quantum fields or gases in the thermodynamic limit). This technique is condensed into some easily applied rules (called "stochastic golden rules"), which allow us to single out the dominating contributions to the dynamical evolution of systems in regimes involving long times and small effects. In the stochastic limit the original Hamiltonian theory is approximated using a new Hamiltonian theory which is singular. These singular Hamiltonians still define a unitary evolution, and the new equations give much more insight into the relevant physical phenomena than the original Hamiltonian equations. Especially, one can explicitly compute multi-time correlations (e.g. photon statistics) or coherent vectors, which are beyond the reach of typical asymptotic techniques. |
| Additional Information |
| BISAC Categories: - Science | Physics - Quantum Theory - Computers | Information Technology - Mathematics | Probability & Statistics - General |
| Dewey: 530.12 |
| LCCN: 2001049456 |
| Physical Information: 1.27" H x 6.46" W x 9.36" (1.84 lbs) 474 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Nowadays it is becoming clearer and clearer that, in the description of natural phenomena, the triadic scheme - microseopie, mesoscopic, macroscopic - is only a rough approximation and that there are many levels of description, probably an infinite hierarchy, in which the specific properties of a given level express some kind of cumulative or collective behaviour of properties or sys- tems corresponding to the lower levels. One of the most interesting challenges for contemporary natural sciences is the comprehension of the connections among these different levels of description of reality and the deduction of the laws of higher levels in this hierarchy from basic laws corresponding to lower levels. Since these cumulative or collective phenomena are, typically, nonlin- ear effects, the transition from this general program to concrete scientific achievements requires the developement of techniques which allow physical information to be extracted from nonlinear quantum systems. Explicitly in- tegrable examples of such systems are rare, and the most interesting physical phenomena are not captured by them. Even in the case of linear systems the fact that an explicit solution is formally available is often useless, since it is impossible to interpret interesting physical phenomena from it. |