14,092 research outputs found

    Slippery Wave Functions V2.01

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    Superfluids and superconductors are ordinary matter that show a very surprising behavior at low temperatures. As their temperature is reduced, materials of both kinds can abruptly fall into a state in which they will support a persistent, essentially immortal, flow of particles. Unlike anything in classical physics, these flows engender neither friction nor resistance. A major accomplishment of Twentieth Century physics was the development of an understanding of this very surprising behavior via the construction of partially microscopic and partially macroscopic quantum theories of superfluid helium and superconducting metals. Such theories come in two parts: a theory of the motion of particle-like excitations, called quasiparticles, and of the persistent flows itself via a huge coherent excitation, called a condensate. Two people, above all others, were responsible for the construction of the quasiparticle side of the theories of these very special low-temperature behaviors: Lev Landau and John Bardeen. Curiously enough they both partially ignored and partially downplayed the importance of the condensate. In both cases, this neglect of the actual superfluid or superconducting flow interfered with their ability to understand the implications of the theory they had created. They then had difficulty assessing the important advances that occurred immediately after their own great work. Some speculations are offered about the source of this unevenness in the judgments of these two leading scientists.Comment: 30 pages, 3 figure

    Reflections on Gibbs: From Statistical Physics to the Amistad

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    This note is based upon a talk given at a celebration in Austin Texas of the achievements of J. Willard Gibbs. J. Willard Gibbs, the younger, was the first American physical sciences theorist. He was one of the inventors of statistical physics. He introduced and developed the concepts of phase space, phase transitions, and thermodynamic surfaces in a remarkably correct and elegant manner. These three concepts form the basis of different areas of physics. The connection among these areas has been a subject of deep reflection from Gibbs' time to our own. This talk therefore tries to celebrate Gibbs by talking about modern ideas about how different parts of physics fit together. At the end of the talk, I shall get to a more personal note. Our own J. Willard Gibbs had all his achievements concentrated in science. His father, also J. Willard Gibbs, also a Professor at Yale, had one great achievement that remains unmatched in our day. I shall describe it.Comment: This work was originally given as a talk in 2003 in Austin, Texas. It has now been updated in a manner aimed at publicatio

    Relating Theories via Renormalization

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    The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is the outgrowth of one hundred and fifty years of scientific study of thermal physics and phase transitions. Different phases of matter show qualitatively different behavior separated by abrupt phase transitions. These qualitative differences seem to be present in experimentally observed condensed-matter systems. However, the "extended singularity theorem" in statistical mechanics shows that sharp changes can only occur in infinitely large systems. Abrupt changes from one phase to another are signaled by fluctuations that show correlation over infinitely long distances, and are measured by correlation functions that show algebraic decay as well as various kinds of singularities and infinities in thermodynamic derivatives and in measured system parameters. Renormalization methods were first developed in field theory to get around difficulties caused by apparent divergences at both small and large scales. The renormalization (semi-)group theory of phase transitions was put together by Kenneth G. Wilson in 1971 based upon ideas of scaling and universality developed earlier in the context of phase transitions and of couplings dependent upon spatial scale coming from field theory. Correlations among regions with fluctuations in their order underlie renormalization ideas. Wilson's theory is the first approach to phase transitions to agree with the extended singularity theorem. Some of the history of the study of these correlations and singularities is recounted, along with the history of renormalization and related concepts of scaling and universality. Applications are summarized.Comment: This note is partially a summary of a talk given at the workshop "Part and Whole" in Leiden during the period March 22-26, 201

    Theories of Matter: Infinities and Renormalization

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    This paper looks at the theory underlying the science of materials from the perspectives of physics, the history of science, and the philosophy of science. We are particularly concerned with the development of understanding of the thermodynamic phases of matter. The question is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) rise from a pot of heated water. The nature of the phases is brought into the sharpest focus in phase transitions: abrupt changes from one phase to another and hence changes from one behavior to another. This article starts with the development of mean field theory as a basis for a partial understanding of phase transition phenomena. It then goes on to the limitations of mean field theory and the development of very different supplementary understanding through the renormalization group concept. Throughout, the behavior at the phase transition is illuminated by an "extended singularity theorem", which says that a sharp phase transition only occurs in the presence of some sort of infinity in the statistical system. The usual infinity is in the system size. Apparently this result caused some confusion at a 1937 meeting celebrating van der Waals, since mean field theory does not respect this theorem. In contrast, renormalization theories can make use of the theorem. This possibility, in fact, accounts for some of the strengths of renormalization methods in dealing with phase transitions. The paper outlines the different ways phase transition phenomena reflect the effects of this theorem

    Amplification of coupling for Yukawa potentials

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    It is well known that Yukawa potentials permit bound states in the Schrodinger equation only if the ratio of the exchanged mass to bound mass is below a critical multiple of the coupling constant. However, arguments suggested by the Darwin term imply a more complex situation. By numerically studying the Dirac equation with a Yukawa potential we investigate this amplification effect.Comment: 7 pages, 2 figure

    Translations between Quaternion and Complex Quantum Mechanics

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    While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a {\em partial} set of {\em translations} may be made. We define these translations and use the rules to obtain rapid quaternion counterparts (some of which are new) of standard quantum mechanical results.Comment: 15 pages, LaTeX, ULTH-93-3
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