Abstract This paper contains the skeleton of one lecture, and of two raporteur's interventions, made at the Sanibel Symposium in February–March, 1979. The task asked of this lecturer was to present an outline of the program of nonequilibrium statistical mechanics, and to indicate some of the recent developments in our understanding of this program. Section I lists a few of the principal physical ingredients of the theory. The possible implementation of certain aspects of the program is demonstrated in Sec. II with the help of three exactly soluble models. Finally in Sec. III we extrapolate from these particular examples in two directions: the stochastic aspect of statistical mechanics, and some remarks on the theory of the quantum measurement process. The presence, at the Symposium, of several distinguished lecturers who presented their own original, and most interesting, contributions hopefully made appear less outrageous—at least at the time—the severe omissions due to the personal choices this particular speaker had to make to keep within the time limitations inherent to such a gathering. It is now hoped that, even when taken out of the full context of the Symposium, the rearranged text which follows might nevertheless help focusing attention on some of the important problems remaining to be solved. It is a pleasure to acknowledge here the stimulating hospitality of the Symposium Scientific Director, Professor P.‐O. Löwdin.
Abstract This paper contains the skeleton of one lecture, and of two raporteur's interventions, made at the Sanibel Symposium in February–March, 1979. The task asked of this lecturer was to present an outline of the program of nonequilibrium statistical mechanics, and to indicate some of the recent developments in our understanding of this program. Section I lists a few of the principal physical ingredients of the theory. The possible implementation of certain aspects of the program is demonstrated in Sec. II with the help of three exactly soluble models. Finally in Sec. III we extrapolate from these particular examples in two directions: the stochastic aspect of statistical mechanics, and some remarks on the theory of the quantum measurement process. The presence, at the Symposium, of several distinguished lecturers who presented their own original, and most interesting, contributions hopefully made appear less outrageous—at least at the time—the severe omissions due to the personal choices this particular speaker had to make to keep within the time limitations inherent to such a gathering. It is now hoped that, even when taken out of the full context of the Symposium, the rearranged text which follows might nevertheless help focusing attention on some of the important problems remaining to be solved. It is a pleasure to acknowledge here the stimulating hospitality of the Symposium Scientific Director, Professor P.‐O. Löwdin.
Intrinsic theory of irreversibility In connection with the previous chapter on Wigner–Weisskopf, quantum irreversibility, Gamov states and the Lax–Phillips theory of decay, we shall examine the recent program in statistical mechanics carried forward by Ilya Prigogine and his colleagues since his early book in 1962 (Prigogine, 1962). This discussion is somewhat out of the focus of the present book, since the work to be discussed has principally been devoted to isolated quantum systems, not those in interaction with “reservoirs.” In addition, Prigogine's work is very classical in its content. We shall not attempt the task of reviewing the many changes that have taken place between 1962 and the present. Fine texts describing some of this work are those of Balescu (1963, 1975). A recent critical overview of the “modern view” is in the unpublished thesis of B. C. Bishop of the University of Texas Philosophy Department (Bishop, 1999). In many ways this is related to the use of Gel'fand triplets (Gel'fand and Vilenkin, 1968), mentioned in Chapter 17.6, to describe irreversible quantum states, i.e. Gamov states. See Chapter 17, the book of Bohm and Gadella (1989) and also the more recent review article by Bohm and colleagues (Bohm et al. , 1997). The object in statistical mechanics is to extend the range of the Liouville operator (classical and quantum) such that its eigenvalues are complex and intrinsically irreversible. Statistical mechanics has always been focused on many particle systems and the appearance of a continuum spectrum in the thermodynamic limit, already used in many places in this book. In the classical case Antoniou and Tasaki carried out the adaptation of the Gel'fand triplet approach to the Liouville operator, but this is, apparently, not possible quantum mechanically (Antoniou and Tasaki, 1993). Thus, another route must be taken in what Prigogine has termed, for emphasis, “large Poincaré systems” which have a continuum spectrum (Prigogine, 1997).
I. Prigogine has proposed, and the writings of N. S. Krylov to some extent suggest, a novel and unorthodox solution to foundational problems in statistical mechanics. In particular, the view claims to offer new insight into two interconnected problems: underst and ing the role of probability in physics, and that of reconciling the irreversibility of physical processes with the temporal symmetry (time reversal invariance) of dynamical theories. The approach in question advocates a conception of the state of a system which incorporates features of the quantum mechanical state concept in a context, classical statistical mechanics, where quantum considerations are generally considered to be irrelevant. I examine the plausibility of this new approach by offering an analysis of the various notions of state employed in modern physics. In the first chapter, I analyze the conceptual connections between dynamical laws and the nature of a system's state. I argue that laws and states are correlative. In constructing dynamical theories one does not start with a fixed or pre-determined state concept. Neither is one given the laws of the theory from which the conception of state is derived. Rather, we get the law/state structure as a "package." In light of this general analysis, I next examine the notion of state employed in the quantum theory. Here I consider a variety of conceptions of quantum states and assess their ability to answer the "paradoxes" of quantum theory. I pay particular attention to the role of probability and related restrictions on the realization of certain states. The new approach to statistical mechanics proposes to exploit similar restrictions on states in order to resolve the irreversibility problem. But is this unorthodox approach viable? In the final four chapters, I offer a detailed critique of this approach, examining the plausibility of the radical reworking of the state concept. I argue that while some important progress can be made, certain old puzzles remain, and new and difficult ones arise--ones which raise serious doubts about the ultimate success of this particular approach. I conclude, however, by arguing that such radical proposals are not unmotivated; and that novel and unorthodox proposals concerning the foundations of statistical mechanics must be taken seriously.
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics. Special emphasis is put on new adiabatic theorems for steady states close to and far from equilibrium, and on investigating cyclic thermodynamic processes using an extension of Floquet theory.
Delivered at Trieste on the occasion of the 25th Anniversary of the International Centre for Theoretical Physics, 2 November 1989 The video of this lecture is available here . Please see the PDF for the transcript of the lecture. General remarks by Angelo Bassi and GianCarlo Ghirardi During the autumn of 1989 the International Centre for Theoretical Physics, Trieste, celebrated the 25th anniversary of its creation. Among the many prestigious speakers, who delivered extremely interesting lectures on that occasion, was the late John Stewart Bell. All lectures have been recorded on tape. We succeeded in getting a copy of John's lecture. In the lecture, many of the arguments that John had lucidly stressed in his writings appear once more, but there are also extremely interesting new remarks which, to our knowledge, have not been presented elsewhere. In particular he decided, as pointed out by the very choice of the title of his lecture, to call attention to the fact that the theory presents two types of difficulties, which Dirac classified as first and second class. The former are those connected with the so-called macro-objectification problem, the latter with the divergences characterizing relativistic quantum field theories. Bell describes the precise position of Dirac on these problems and he stresses appropriately how, contrary to Dirac's hopes, the steps which have led to a partial overcoming of the second class difficulties have not helped in any way whatsoever to overcome those of the first class. He then proceeds to analyse the origin and development of the Dynamical Reduction Program and draws attention to the problems that still affect it, in particular that of a consistent relativistic generalization. When the two meetings Are there quantum jumps? and On the present status of Quantum Mechanics were organized in Trieste and Losinj (Croatia), on 5–10 September 2005, it occurred to us that this lecture, which has never been published, might represent an extremely interesting historical record for all the participants who certainly shared with us a great admiration for this outstanding scientist and deep thinker. Accordingly, with the permission of the Abdus Salam International Centre for Theoretical Physics, and with thanks to the financial support of the Consorzio per la Fisica of the Trieste University, we have produced from the original record a DVD which has been given to all participants although, unfortunately, the video tape of the event was not particularly good. Taking into account that the participants to the meetings represented only a very small subset of those scientists who might be interested in hearing what John Bell said in probably his last lecture, we considered that it would be useful for the scientific community interested in foundational problems to publish the text of this lecture in order to make it accessible to everybody. The lecture was preceded by a presentation by the Chairman, Alain Aspect, which we have also included. Due to the aforementioned low quality of the recording it has not been easy to pass from the tape to the text we are presenting below, and we have to thank, for her precious collaboration, Dr Julia Filingeri who did most of the work, as well as Mrs Anne Gatti from ICTP, Professors Detlef Düurr and Sheldon Goldstein, and the staff of IOP Publishing who contributed in an essential way in deciphering some particularly difficult passages. Obviously, we take full responsibility for any possible inappropriate rendering of the original talk. We thank the Abdus Salam International Centre for Theoretical Physics for authorizing IOP Publishing to publish this important document. Some final remarks are in order. Firstly, we have put in square brackets parenthetical remarks that John made while reading sentences from his transparencies. We have also indicated by parenthetical ellipsis (...) very short parts of the speech (usually one word) which we have not been able to decipher. We have included a picture (figure 1) shown by him, taking it from the tape image which is of rather poor quality (we apologize for this) and three figures taken from his transparencies. Moreover, to help the reader in grasping the various points John Stewart Bell brilliantly raised in his talk we have divided the paper into six sections whose titles have been chosen by us to summarize the most crucial points of his argument. Presentation by the Chairman, Alain Aspect It is a great pleasure and an honour to introduce Professor Bell. When looking to my old papers I discovered that this 25th anniversary of the ICTP also coincides with the famous paper in which appeared, for the first time, inequalities that are now known as Bell's inequalities so it's a very good opportunity to have a talk by John Bell here. Many of us have been strongly influenced by this work of John Bell because he has shown us that quantum mechanics is much more difficult to understand that we thought it was. I am sure that today he will again raise some questions which are very embarrassing but that we have definitely to face.
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0 th, 1 st and 2 nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics. Special emphasis is put on new adiabatic theorems for steady states close to and far from equilibrium, and on investigating cyclic thermodynamic processes using an extension of Floquet theory. This work is based on the author’s doctoral thesis, ETH-Diss 16187.
Quantum mechanics is the most ground-breaking and fascinating theoretical concept developed in physics during the past century. Much of our present understanding of the microscopic world and its extension into the macroscopic world, including modern technical applications, is based upon quantum mechanics. We have experienced a remarkable development of information and communication technology during the past two decades, to a large extent depending upon successful fabrication of smaller and smaller components and circuits. However, we are finally approaching the physical limits of component miniaturization as we enter a microscopic world ruled by quantum mechanics. Present technology is mainly based upon classical physics such as mechanics and electromagnetism. We now face a similar paradigm shift as was experienced two hundred years ago, at the time of the industrial revolution. Engineered construction of systems is currently increasingly based on quantum physics instead of classical physics, and quantum information is replacing much of classical communication. Quantum computing is one of the most exciting sub-fields of this revolution. Individual quantum systems can be used to store and process information. They are called quantum bits, or qubits for short. A quantum computer could eventually be constructed by combining a number of qubits that act coherently. Important computations can be performed much more quickly than by classical computers. However, while we control and measure a qubit, it must be sufficiently isolated from its environment to avoid noise that causes decoherence at the same time. Currently, low temperature is generally needed to obtain sufficiently long decoherence times. Single qubits of many different kinds can be built and manipulated; some research groups have managed to successfully couple qubits and perform rudimentary logic operations. However, the fundamental problems, such as decoherence, entanglement, quantum measurements and error correction, have yet to be solved. It has been predicted that quantum computers will be able to perform certain complicated computations or simulations in minutes or hours instead of years as with present computers. So far there exist very few useful quantum algorithms; however there is hope that the development of these will be stimulated once there is a breakthrough in hardware. Remarkable progress has been made in quantum engineering and quantum measurements, but a large scale quantum computer is still far off. Quantum communication and cryptography are much closer to the market than a quantum computer. The development of quantum information has meant a large push in the field of quantum physics, that previously could only be studied in the microscopic world. Artificial atoms, realized by circuit technology and mimicking the properties of 'natural' atoms, are one example of the new possibilities opened up by quantum engineering. Several different types of qubits have been suggested. Some are based upon microscopic entities, like atoms and ions in traps, or nuclear spins in molecules. They can have long coherence times (i.e. a long period allowing many operations, of the order of 10 000, to be performed before the state needs to be refreshed) but they are difficult to integrate into large systems. Other qubits are based upon solid state components that facilitate integration and coupling between qubits, but they suffer from interactions with the environment and their coherent states have a limited lifetime. Advanced experiments have been performed with superconducting Josephson junctions and many breakthroughs have been reported in the last few years. They have an advantage in the inherent coherence of superconducting Cooper pairs over macroscopic distances. We chose to focus the Nobel Symposium on Qubits for Future Quantum Information on superconducting qubits to allow for depth in discussions, but at the same time to allow comparison with other types of qubits that may prevail in the long run. The purpose of the symposium was to bring together leading researchers in adjoining fields. Often, microscopic qubits are considered at conferences within atomic, molecular and optical physics, while macroscopic ones belong to the solid state community. At the symposium, we experienced objective comparisons between different types of qubits—pros and cons as well as prospects. One example was the topic of quantum electrodynamics of superconducting circuits where qubits are coupled to a high- Q microwave resonator. This breakthrough technology was covered in several talks and was compared, in detail, with the corresponding case of light coupled to atoms in a cavity. A highlight was the presentation of how arbitrary photon states can be created in a cavity and the measurement of the corresponding Wigner functions. A Nobel Symposium provides an excellent opportunity to bring together a group of outstanding scientists for a stimulating exchange of ideas and results. The present symposium took place in Gothenburg, 25–28 May 2009. In order to allow local researchers and students to get a feeling of what is happening in the field, the first day of the symposium was held at the Chalmers campus. The remaining three days were spent at the mansion built by William Chalmers, the benefactor behind Chalmers University of Technology. Thirty-three speakers gave popular lectures open to the general public, overviews of different types of qubits, quantum phenomena, and quantum computing requirements, as well as specialized contributions in six sessions, and ten posters were displayed. The list of participants, program, abstracts and summaries of presentations is given at www.chalmers.se/mc2/EN/nobel-symposium-2009 . In order to encourage constructive interactions and discussions, ample time was given to extensive critical discussions and to individual meetings in relaxing and stimulating environments. Questions and discussions followed all talks but longer, more extensive, discussions of about one hour ended each session. These discussions were initiated by a special questioner (a kind of 'devil's advocate'). Receptions were given by the President of Chalmers and by the City of Gothenburg. The participants also sailed with SS Bohuslän in the archipelago outside the city. The symposium was sponsored by the Nobel Foundation through its Nobel Symposium Committee and was organized by Thilo Bauch, Tord Claeson, Per Delsing, Ann-Marie Frykestig, Eva Hellberg, Göran Johansson, Göoran Wendin, and Chris Wilson. Special thanks are given to the program committee: John Clarke, Daniel Estève, Steve Girvin, Anne l'Huillier, Anthony Leggett, and Mikko Paalanen. The editor of the proceedings is Göran Johansson.