14,092 research outputs found

### Slippery Wave Functions V2.01

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

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

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

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

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

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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