T. A. Brody

Bio: T. A. Brody is an academic researcher from National Autonomous University of Mexico. The author has contributed to research in topics: Hidden variable theory & Monte Carlo method. The author has an hindex of 7, co-authored 10 publications receiving 1955 citations.

Random matrix physics: Spectrum and strength fluctuations

Abstract: It now appears that the general nature of the deviations from uniformity in the spectrum of a complicated nucleus is essentially the same in all regions of the spectrum and over the entire Periodic Table. This behavior, moreover, is describable in terms of standard Hamiltonian ensembles which could be generated on the basis of simple information-theory concepts, and which give also a good account of fluctuation phenomena of other kinds and, apparently, in other many-body systems besides nuclei. The main departures from simple behavior are ascribable to the moderation of the level repulsion by effects due to symmetries and collectivities, for the description of which more complicated ensembles are called for. One purpose of this review is to give a self-contained account of the theory, using methods: sometimes approximate: which are consonant with the usual theory of stochastic processes. Another purpose is to give a proper foundation for the use of ensemble theory, to make clear the origin of the simplicities in the observable fluctuations, and to derive other general fluctuation results. In comparing theory and experiment, the authors give an analysis of much of the nuclear-energy-level data, as well as an extended discussion of observable effects in nuclear transitionsmore » and reactions and in the low-temperature thermodynamics of aggregates of small metallic particles.« less

The Philosophy Behind Physics

Abstract: I. The Philosophy of Physics.- 1. The Active Epistemology.- 2. Higher-Level Epistemic Cycles.- 3. Systems and Experiments.- 4. The Structure of Theories.- 5. Induction and the Scope of Theories.- 6. The Incommensurability of Theories.- 7. A Minimal Ontology for Scientific Research.- 8. The Determinisms of Physics.- II. The Theory of Probability.- 9. The Nature of Probability.- 10. The Ensemble Interpretation of Probability.- 11. The Philosophy of Ensemble Probability.- 12. On Errors and Approximations.- III. The Philosophy of Quantum Mechanics.- 13. Problems and Promises of the Ensemble Interpretation of Quantum Mechanics.- 14. Probability and the Way Out of the Great Quantum Muddle.- 15. Are Hidden Variables Possible?.- 16. The Bell Inequality I: Joint Measurability.- 17. The Bell Inequality II: Locality.- 18. The Irrelevance of the Bell Inequality.- 19. Measurement and State Representation.- 20. On Quantum Logic.- 21. Resistance to Change in the Sciences: The Case of Quantum Mechanics.- IV. General.- 22. Epistemological Implications of Artificial Intelligence.- 23. Artificial Intelligence: Possibilities and Realities, Hopes and Dangers.- 24. Philosophy and Physicists.- 25. The Axiomatic Approach in Physics.- List of Publications of T.A. Brody.- Name Index.

Random Matrix Theories in Quantum Physics: Common Concepts

Abstract: We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics

Abstract: This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the i...

Multimode molecular dynamics beyond the Born-Oppenheimer approximation

Abstract: Mise au point. Theorie des effets de couplage vibronique multimodes. Probleme a 2 etats. Couplage vibronique mettant en jeu des modes et des etats degeneres. Effets du couplage vibronique multimodes en spectroscopie. Comportement statistique des niveaux d'energie vibroniques. Intersections coniques et evolution temporelle de la fluorescence

From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics

Abstract: This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the implications of quantum chaos and ETH to thermodynamics. Basic thermodynamic relations are derived, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, and the Einstein and Onsager relations. In particular, it is shown that quantum chaos allows one to prove these relations for individual Hamiltonian eigenstates and thus extend them to arbitrary stationary statistical ensembles. We then show how one can use these relations to obtain nontrivial universal energy distributions in continuously driven systems. At the end of the review, we briefly discuss the relaxation dynamics and description after relaxation of integrable quantum systems, for which ETH is violated. We introduce the concept of the generalized Gibbs ensemble, and discuss its connection with ideas of prethermalization in weakly interacting systems.