Preface 1. Recollection of an independent thinker Joel A. Snow 2. A look back: early applications of maximum entropy estimation to quantum statistical mechanics D. J. Scalapino 3. The Jaynes-Cummings revival B. W. Shore and P. L. Knight 4. The Jaynes-Cummings model and the one-atom-master H. Walther 5. The Jaynes-Cummings model is alive and well P. Meystre 6. Self-consistent radiation reaction in quantum optics - Jaynes' influence and a new example in cavity QED J. H. Eberly 7. Enhancing the index of refraction in a nonabsorbing medium: phaseonium versus a mixture of two-level atoms M. O. Scully, T. W. Hansch, M. Fleischhauer, C. H. Keitel and Shi-Yao Zhu 8. Ed Jaynes' steak dinner problem II Michael D. Crisp 9. Source theory of vacuum field effects Peter W. Milonni 10. The natural line shape Edwin A. Power 11. An operational approach to Schrodinger's cat L. Mandel 12. The classical limit of an atom C. R. Stroud, Jr. 13. Mutual radiation reaction in spontaneous emission Richard J. Cook 14. A model of neutron star dynamics F. W. Cummings 15. The kinematic origin of complex wave function David Hestenes 16. On radar target identification C. Ray Smith 17. On the difference in means G. Larry Bretthorst 18. Bayesian analysis, model selection and prediction Arnold Zellner and Chung-ki Min 19. Bayesian numerical analysis John Skilling 20. Quantum statistical inference R. N. Silver 21. Application of the maximum entropy principle to nonlinear systems far from equilibrium H. Haken 22. Nonequilibrium statistical mechanics Baldwin Robertson 23. A backward look to the future E. T. James Appendix. Vita and bibliography of Edwin T. Jaynes Index.
Preface 1. Recollection of an independent thinker Joel A. Snow 2. A look back: early applications of maximum entropy estimation to quantum statistical mechanics D. J. Scalapino 3. The Jaynes-Cummings revival B. W. Shore and P. L. Knight 4. The Jaynes-Cummings model and the one-atom-master H. Walther 5. The Jaynes-Cummings model is alive and well P. Meystre 6. Self-consistent radiation reaction in quantum optics - Jaynes' influence and a new example in cavity QED J. H. Eberly 7. Enhancing the index of refraction in a nonabsorbing medium: phaseonium versus a mixture of two-level atoms M. O. Scully, T. W. Hansch, M. Fleischhauer, C. H. Keitel and Shi-Yao Zhu 8. Ed Jaynes' steak dinner problem II Michael D. Crisp 9. Source theory of vacuum field effects Peter W. Milonni 10. The natural line shape Edwin A. Power 11. An operational approach to Schrodinger's cat L. Mandel 12. The classical limit of an atom C. R. Stroud, Jr. 13. Mutual radiation reaction in spontaneous emission Richard J. Cook 14. A model of neutron star dynamics F. W. Cummings 15. The kinematic origin of complex wave function David Hestenes 16. On radar target identification C. Ray Smith 17. On the difference in means G. Larry Bretthorst 18. Bayesian analysis, model selection and prediction Arnold Zellner and Chung-ki Min 19. Bayesian numerical analysis John Skilling 20. Quantum statistical inference R. N. Silver 21. Application of the maximum entropy principle to nonlinear systems far from equilibrium H. Haken 22. Nonequilibrium statistical mechanics Baldwin Robertson 23. A backward look to the future E. T. James Appendix. Vita and bibliography of Edwin T. Jaynes Index.
The pioneering work of Edwin T. Jaynes in the field of statistical physics, quantum optics, and probability theory has had a significant and lasting effect on the study of many physical problems, ranging from fundamental theoretical questions through to practical applications such as optical image restoration. Physics and Probability is a collection of papers in these areas by some of his many colleagues and former students, based largely on lectures given at a symposium celebrating Jaynes' contributions, on the occasion of his seventieth birthday and retirement as Wayman Crow Professor of Physics at Washington University. The collection contains several authoritative overviews of current research on maximum entropy and quantum optics, where Jaynes' work has been particularly influential, as well as reports on a number of related topics. In the concluding paper, Jaynes looks back over his career, and gives encouragement and sound advice to young scientists. All those engaged in research on any of the topics discussed in these papers will find this a useful and fascinating collection, and a fitting tribute to an outstanding and innovative scientist.
Edwin T Jaynes, the well known American scientist and educator, has made seminal contributions to several branches of physics and probability theory. This volume commemorates his extraordinarily diverse career in a collection of essays on topics ranging from the kinematics of complex wavefunctions to radar target identification. The book contains 23 papers written by former students, distinguished colleagues and by Jaynes himself, based on lectures presented at a symposium celebrating Jaynes' 70th birthday and official retirement.
Preface Part I. Quantum Mechanics: 1. On the low density of Boson models: Langevin equation L. Accardi and L. Y. Gang 2. Schrodinger operators with potentials supported by null sets S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, W. Karwowski and T. Lindstrom 3. Landau Hamiltonians on symmetric spaces J. E. Avron and A. Pnueli 4. Renormalization group analysis and quasicrystals J. Bellissard 5. The measurement problem in the stochastic formulation of quantum mechanics Ph. Blanchard, M. Cini and M. Serva 6. Schrodinger operators at threshold D. Bolle 7. Spectral analysis and scattering theory for Schrodinger operators with an interaction supported by a regular curve J. F. Brasche and A. Teta 8. Lattice models of solids V. V. Evstratov and B. S. Pavlov 9. Schrodinger operators on unusual manifolds P. Exner and P. Seba 10. High energy resolvent estimates for Schrodinger operators A. Jensen 11. Point interactions as solvable models W. Kirsch 12. Stochastic model of quantum mechanics V. P. Maslov Part II. Quantum Field Theory: 13. Maximality of infinite dimensional Dirichlet forms and Hoegh-Krohn's model of quantum fields S. Albeverio and S. Kusuoka 14. Global Markov property in quantum field theory and statistical mechanics: a review on results and problems S. Albeverio and B. Zegarlinski 15. Hypercontractivity: a bibliographic review E. B. Davies, L. B. Gross and B. Simon 16. Progress and problems in algebraic quantum field theory S. Doplicher 17. Hoegh-Krohn's model of quantum fields and the absolute continuity of measures S. Kusuoka 18. Baryon states in lattice QCD R. A. Minlos and E. A. Zhinzhina 19. The energy of a Weyl soliton R. F. Streater Part III. Statistical Physics: 20. Morphology and classification of galaxies: a stochastic model S. Albeverio, Ph. Blanchard, D. Gandolfo, R. Hoegh-Krohn and M. Mebkhout 21. Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction R. L. Dobrushin and S. B. Shlosman 22. Verification of the global Markov property for strongly coupled trigonometric interactions R. Gielerak 23. Decomposition of Ising models and the Mayer expansion C. M. Newman and G. A. Baker, Jr 24. Towards time-dynamics for bosonic systems in quantum statistical mechanics A. G. Shuhov, Yu. M. Suhov and A. V. Teslenko 25. Towards time-dynamics for bosonic systems in quantum statistical mechanics, 2 A. G. Shuhov and Yu. M. Suhov.
Abstract A short personal and historical account of the field of radiation interacting with (two-level) atoms is given. Subsequent to 1963, developments and extensions have been extensive and fruitful. One of the most fortunate changes in my life came in late 1957. I was looking for a thesis advisor, after two years of graduate course-work at Stanford. I chanced to see a notice of an upcoming lecture by a professor named Edwin T Jaynes. I could not understand from the announcement what he intended to talk about, but I was searching; I went to find out. That decision was a very lucky one. Ed was talking about a subject that inspired him then, and had been for many years, namely his concept of 'Max-Ent'. 'Maximum-Entropy' is a subject now close to my heart also. Ed's very-clear, well-thought-out papers, spread over many subsequent years, are transforming the field of probability (albeit too gradually) to the 'subjective' outlook of Bayes. (A recent book 'Maximum Entropy and Ecology' [1] will probably convert many nay-sayers to 'Max-Ent'.) I went into Ed's office (late 1957) and asked if I could work with him on a thesis. Did he have a problem for me? Yes, he did. Somewhat to my surprise, he asked me to look into the 'maser problem', involving a comparison of the semi-classical theory of radiation to a proper quantum treatment. To make a two-year story short, Ed's guidance was expert. (I imagine that if another of Ed's students (e.g. Joe Eberly) had come into his office fifteen minutes before me, the 'Jaynes–Cummings' (J–C) model would now perhaps be called otherwise, e.g., the 'J–E' model). In the two-year time frame (∼1958–60), Ed had a number of other PhD dissertation students whom I knew; these included Joe Eberly, Doug Scalapino, Baldwin Robertson, Larry Davis and Mike Duggan. My thesis work under Ed reminds me of a story about Michelangelo and his famous 'Pieta'. Michelangelo was an old man about then, so he hired a young craftsman to do much of the physical work: 'chip here, carve there, cut off here, eliminate this, etc'. When the beautiful Pieta was finished, the young man was heard to say, 'I didn't realize before this that I was so talented'. Experiments by Clauser in 1972 on Bell's inequalities (e.g. [2]) showed them to be correct, and indicated that semi-classical alternatives to quantum electrodynamics were not viable. Working with Stuart Freedman, these were the first experimental tests of the predictions of Bell's theorem, the first observation of quantum entanglement, as well as the first experimental observation of a violation of a Bell inequality. The perturbation formulation of quantum radiation theory has long been rife with vexing infinities. Ed always insisted that only experiment can end an argument, so he and his students had been sensibly exploring semi-classical theory. This was not only because of the serious failings of standard QED, but more importantly because of the fact that (an improved) semi-classical theory was able to predict both spontaneous emission, with the correct Einstein coefficients, and the Lamb shift. These two effects have long been thought only possible in the quantum radiation domain (cf [3]). Ed readily accepted losing his bet with Franken about what experiment had to say about the Lamb shift. What is clear is that this bet of $50 with Peter Franken stimulated so much subsequent research that this bet played an important role in generally furthering the field of quantum optics. How did 'J–C' come to be published as it did in the IEEE [4]? Ed was not well known for the extravagant use of words, rather for paucity, clarity and economy. After about two years of working with Ed, he said to me one day, 'You have enough, write it up'. He also said 'We should publish'. (This was around early 1960). About this same time, I was contacted by someone from a new research lab just starting in Newport Beach, California (called 'Aeroneutronic', a division of Ford), asking if I would come to work there. I thought it sounded about right as an approximately two–three year position: repay some debts and look around at other possibilities (especially academe?). I left around June 1960 to take up this position in the research lab in Newport Beach. At about this same time (∼late 1959), Ed was moving to his new 'chair' at Washington University in St Louis. I proceeded as quickly as I could to put together a thesis after arriving in Newport Beach; I wrote about what I had done, as best as I could in my naiveté about such undertakings. I wrote of the work I had done under Ed's kind and patient guidance for the two years in Palo Alto. I soon remembered that Ed had done a recent Stanford Microwave Lab report on our project; his writing was so much better than mine that I thought it witless to put out something as 'uneven' as I had written by then. At just this time that I was cobbling together a thesis, a consultant at Aeroneutronic, Jay Singer of UC Berkeley EE department, approached me in the hall, (no tele-commuting then!) asking if I might have something to contribute to a special issue of a journal of the IEEE he was editing, on the subject of 'Quantum Electronics'. (Comment: One of the earliest predecessors to the MRI, Jay Singer was then measuring the blood flow in rat tails and human arms; he holds two key MRI patents). I said I thought I did have something. The journal sounded appropriate, so I soon handed my 'thesis' to Jay, put Ed's name first (of course, since it consisted so largely of his words from the Microwave Lab report, but also since Ed was my 'guru'), ...and that was that...done [4]. From my perspective, it seemed to subsequently sink to the bottom of the sea, not to be seen by me again for many years until the elegant Walther–Rempe–Klein (WRK) experiments of 1987 on long-time coherent radiative behavior appeared [5]. They confirmed the long-time quantum-theoretical results of Eberly, Narozhny and Sanchez-Mondragon [6]. Bob Buley and I, while at Aeroneutronic, had published in the field of lasers [7], based on the J–C model. We found very strange, puzzling 'chaotic' output of a 'Q-switched' laser. When computer time-steps were changed, the chaos didn't disappear. It was about then (∼June 1963) that both Bob and I headed elsewhere: I to the early-forming UC Riverside Physics Department as Assistant Professor, and Bob to a company in Santa Barbara. Our work on the mysterious 'chaotic' laser effect then ended (the term 'chaos' was not yet in the physics lexicon); Bob was the computer expert, our non-linear laser problem demanded rigorous numerical computations, and I was not savvy with the (then) 'refrigerator-sized' computers at UCR. P W Milonni has greatly extended this work (cf [8]). Mike Tavis, my graduate student at UCR around 1965, extended the J–C model to N atoms [9]. (We have more recently collaborated in a further study of this and other extensions of J–C.) The silence and zero feedback from the 'J–C', Buley and 'T–C' papers for so many years following 1965 was a bit deafening, so I thought it would be best that I go mostly onto other topics. One day in about 1989, I got a tap on the shoulder from a colleague at UCR: 'I saw your name in the title of a paper'. ('Huh?'). An astonishing number of exciting and important new topics have emerged since the 1987 WRK experiment, providing an ever-branching tree of both new theory and experiment. It is tempting to entitle this piece as 'Get your name in print: Diagonalize a 2 × 2'. References [1] Harte J 2011 Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics (Oxford Series in Ecology and Evolution) (Oxford: Oxford University Press) [2] Freedman S J and Clauser J F 1972 Experimental test of local hidden-variable theories Phys. Rev. Lett. 28 938 [3] Stroud C R Jr and Jaynes E T 1970 Long-term solutions in semiclassical radiation theory Phys. Rev. A 1 106 [4] Jaynes E T and Cummings F W 1963 Comparison of quantum and semiclassical radiation theories with application to the beam maser Proc. IEEE 51 89 [5] Rempe G, Walther H and Klein N 1987 Observation of quantum collapse and revival in a one-atom maser Phys. Rev. Lett. 58 353 [6] Eberly J H, Narozhny N B and Sanchez-Mondragon J J 1980 Periodic spontaneous collapse and revival in a simple quantum Phys. Rev. Lett. 44 1323 [7] Buley E R and Cummings F W 1964 Dynamics of a system of N atoms interacting with a radiation field Phys. Rev. 134 A1454 [8] Milonni P W, Shin M-L and Ackerhalt J R 1987 Chaos in Laser–Matter Interactions (Singapore: World Scientific) [9] Tavis M and Cummings F W 1968 Exact solution for an N -molecule—radiation-field Hamiltonian Phys. Rev. 170 379
Volume 1: Introduction P. Humphreys. Part I: Probability. Some Contributions to Formal Theory of Probability K. Popper, D. Miller. Elementary Non-Archimedean Representations of Probability for Decision Theory and Games P.J. Hammond. Random Sequences and Hypotheses Tests R. Chuaqui. Changing Probability Judgements I. Levi. Upper and Lower Probability T.L. Fine. Some Connections between Epistemic Logic and the Theory of Nonadditive Probability P. Mongin. On the Properties of Conditional Independence W. Spohn. Qualitative Probabilities Revisited Z. Domotor. The Monks' Vote: a Dialogue on Unidimensional Probabilistic Geometry J.-C. Falmagne. Part II: Probabilistic Causality. Probabilistic Causation without Probability P.W. Holland. Causal Tendency, Necessitivity and Sufficientivity: an Updated Review I.J. Good. Practical Causal Generalizations E.W. Adams. In Place of Regression C. Glymour, P. Spirtes, R. Scheines. Testing Probabilistic Causality D. Costantini. Psychologistic Aspects of Suppes' Definition of Causality P. Legrenzi, M. Sonino. Name Index. Subject Index. Volume 2: Part III: Philosophy of Physics. Probability and Quantum Theory B. Loewer. Schrodinger's Version of EPR, and its Problems A. Fine. Classical Field Magnitudes J. Vuillemin. Quantity, Representation and Geometry B. Mundy. Numerical Experimentation P. Humphreys. Part IV: Theory Structure. Theories and Theoretical Models R. Wojcicki. Suppes Predicates and the Construction of Unsolvable Problems in the Axiomatized Sciences N.C.A. da Costa, F.A. Doria. Structural Explanation J.D. Sneed. Part V: Measurement Theory. Fifteen Problems concerning the Representational Theory of Measurement R.D. Luce, L. Narens. The Meaningfulness of Ordinal Comparisons for General Order Relational Systems F.S. Roberts, Z.S. Rosenbaum. Theories as Nets: the Case of Combinatorial Measurement Theory C.U. Moulines, J.A. Diez. Name Index. Subject Index. Volume 3: Part VI: Philosophy of Language and Logic. Patrick Suppes' Contribution to the Philosophy of Language D. Follesdal. Open Problems in Relational Grammar M. Bottner. A Variable-Free Logic for Anaphora W.C. Purdy. Is Snow White? J. Moravcsik. Can there be Reasons for Putting Limitations on Classical Logic? P. Weingartner. Quantum Logic as a Logic of Identification J. Hintikka, I. Halonen. Logic and Probability in Quantum Mechanics M.L. dalla Chiara, R. Giuntini. Part VII: Learning Theory, Action Theory, and Robotics. From Stimulus-Sampling to Array-Similarity Theory W.K. Estes. Action as Seeing to it that Something is the Case R. Tuomela, G. Sandu. Command Satisfaction and the Acquisition of Habits C. Crangle. Part VIII: General Philosophy of Science. Some Observations on Patrick Suppes' Philosophy of Science M.C. Galavotti. Epilogue. Postscript P. Suppes. Chronological and Topical Bibliography of Patrick Suppes' Publications. Name Index. Subject Index.
We propose a variation of the Jaynes-Cummings Model (JCM), which consists of a Two-Level Atom (TLA) within a cross cavity configuration. This new geometry is a suitable tool to understand the origin of new QED features that the original JCM does not reveal, showing revivals in cases where they are not expected to appear. Full Text: PDF References E.T. Jaynes, F.W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser", Proc. IEEE 51, 1 (1963). CrossRef M. Wilkens, P. Meystre, "Nonlinear atomic homodyne detection: A technique to detect macroscopic superpositions in a micromaser", Phys. Rev. A 43, 7 (1991). CrossRef I.V. Jyotsna, G.S. Agarwal, "The Jaynes-Cummings model with continuous external pumping", Opt. Commun. 99, 344 (1993). CrossRef M.S. Abdalla, M. Abdel-Aty, A.-S.F. Obada, "Quantum entropy of isotropic coupled oscillators interacting with a single atom", Opt. Comm. 211, 225 (2001). CrossRef M.A. Marchiolli, R.J. Missori, "Qualitative aspects of entanglement in the Jaynes?Cummings model with an external quantum field", J. Phys. A: Math. Gen. 36, 49 (2003). CrossRef J.C. García-Melgarejo, Ph.D. Thesis. INAOE (2015). J.R. Ackerhalt, K. Rzazewski, "Heisenberg-picture operator perturbation theory", Phys. Rev. A 12, 6 (1975) CrossRef J.H. Eberly, N.B. Narozhny, J.J. Sanchez-Mondragon, "Periodic Spontaneous Collapse and Revival in a Simple Quantum Model", Phys. Rev. Lett. 44, 20 (1980). CrossRef N.B. Narozhny, J.J. Sanchez-Mondragon, J.H. Eberly, "Coherence versus incoherence: Collapse and revival in a simple quantum model", Phys. Rev. A 23, 1 (1981). CrossRef L. Allen, J.H. Eberly, Optical resonance and two-level atoms (New York, Wiley 1975). A. Joshi, R.R. Puri, "Effects of the Binomial Field Distribution on Collapse and Revival Phenomena in the Jaynes-Cummings Model", J. Modern Optics 34, 11 (1987). CrossRef