An elegant solution of the n-body Toda problem

The solution of the classical open-chain n-body Toda problem is derived from an ansatz and is found to have a highly symmetric form. The proof requires an unusual identity involving Vandermonde determinants. The explicit transformation to action-angle variables is exhibited.Comment: LaTeX, 13 p

“I Have a [Fair Use] Dream”: Historic Copyrighted Works and the Recognition of Meaningful Rights for the Public

Dr. Martin Luther King wrote and delivered his famous “I Have a Dream” speech more than fifty years ago. When he obtained copyright protection on the speech in 1963, Dr. King (and later his estate) would have expected the copyright to last a maximum of fifty-six years. That fifty-six-year copyright has become a ninety-five-year copyright, thanks to lengthy duration extensions enacted by Congress in the mid-1970s and late 1990s. As a result, the copyright on the “I Have a Dream” speech will not expire until the end of 2058. Because the Estate of Martin Luther King, Jr., Inc. and its affili- ates have closely guarded the speech in a copyright enforcement and li- censing sense, the public seldom sees more than snippets of one of the most highly regarded speeches in history. Greater public exposure to the full speech would serve important purposes of the sort recognized by Congress in the fair use section of the Copyright Act. However, those interested in borrowing from or otherwise using the speech have tended to drop their plans or have obtained a costly license from the King Estate or one of the affiliated entities—even when the users may had have a plausible right under the fair use doctrine to borrow from or use the speech without ob- taining a license. With the copyright on the speech not expiring until the end of 2058, there is a danger that the snippets-only nature of the pub- lic’s exposure to the speech will remain the status quo for more than another four decades. Infringement cases that have not been settled by the parties have yielded judicial rulings on whether the “I Have a Dream” speech was properly copyrighted, but no case has been litigated extensively enough to permit a court to address the defendant’s fair use defense. This Article proposes a fair use analysis appropriate for use by courts in the event that a user of the “I Have a Dream” speech departs from the usual tendency to obtain a license in order to avoid litigation and, instead, rests its fate on the fair use doctrine. The proposed analysis gives a suitably expansive scope to the fair use doctrine for cases dealing with uses of the speech or similarly historic works, given the important public purposes that could be served by many such uses. The Article also develops a test for use in determining whether a work is sufficiently historic, for purposes of the fair use analysis proposed here

Must Realists Be Pessimists About Democracy? Responding to Epistemic and Oligarchic Challenges

In this paper we show how a realistic normative democratic theory can work within the constraints set by the most pessimistic empirical results about voting behaviour and elite capture of the policy process. After setting out the empirical evidence and discussing some extant responses by political theorists, we argue that the evidence produces a two-pronged challenge for democracy: an epistemic challenge concerning the quality and focus of decision-making and an oligarchic challenge concerning power concentration. To address the challenges we then put forward three main normative claims, each of which is compatible with the evidence. We start with a critique of the epistocratic position commonly thought to be supported by the evidence. We then introduce a qualified critique of referenda and other forms of plebiscite, and an outline of a tribune-based system of popular control over oligarchic influence on the policy process. Our discussion points towards a renewal of democracy in a plebeian but not plebiscitarian direction: Attention to the relative power of social classes matters more than formal dispersal of power through voting. We close with some methodological reflections about the compatibility between our normative claims and the realist program in political philosophy

Canonical Transformations in Quantum Mechanics

Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in principle, be realized quantum mechanically as a product of these transformations. It is found that the intertwining of two super-Hamiltonians is equivalent to there being a canonical transformation between them. A consequence is that the procedure for solving a differential equation can be viewed as a sequence of elementary canonical transformations trivializing the super-Hamiltonian associated to the equation. It is proposed that the quantum integrability of a system is equivalent to the existence of such a sequence.Comment: 27 pages, McGill 92-29 (revised version--several typos fixed in examples