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

Symmetries in Quantum Mechanics and Statistical Physics

This book collects contributions to the Special Issue entitled "Symmetries in Quantum Mechanics and Statistical Physics" of the journal Symmetry. These contributions focus on recent advancements in the study of PT–invariance of non-Hermitian Hamiltonians, the supersymmetric quantum mechanics of relativistic and non-relativisitc systems, duality transformations for power–law potentials and conformal transformations. New aspects on the spreading of wave packets are also discussed

Besov estimates in the high-frequency Helmholtz equation, for a non-trapping and C2 potential

AbstractWe study the high-frequency Helmholtz equation, for a potential having C2 smoothness, and satisfying the non-trapping condition. We prove optimal Morrey–Campanato estimates that are both homogeneous in space and uniform in the frequency parameter. The homogeneity of the obtained bounds, together with the weak assumptions we require on the potential, constitute the main new result in the present text. Our result extends previous bounds obtained by Perthame and Vega, in that we do not assume the potential satisfies the virial condition, a strong form of non-trapping

How good is damped molecular dynamics as a method to simulate radiation damage in metals?

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