Finite Temperature Time-Dependent Effective Theory For The Goldstone Field In A BCS-Type Superfluid

We extend to finite temperature the time-dependent effective theory for the Goldstone field (the phase of the pair field) $\theta$ which is appropriate for a superfluid containing one species of fermions with s-wave interactions, described by the BCS Lagrangian. We show that, when Landau damping is neglected, the effective theory can be written as a local time-dependent non-linear Schr\"{o}dinger Lagrangian (TDNLSL) which preserves the Galilean invariance of the zero temperature effective theory and is identified with the superfluid component. We then calculate the relevant Landau terms which are non-local and which destroy the Galilean invariance. We show that the retarded $\theta$-propagator (in momentum space) can be well represented by two poles in the lower-half frequency plane, describing damping with a predicted temperature, frequency and momentum dependence. It is argued that the real parts of the Landau terms can be approximately interpreted as contributing to the normal fluid component.Comment: 25 pages, 5 figures, references added, Introduction rewritte

The scientific heritage of Richard Henry Dalitz, FRS (1925-2006)

Professor Richard H. Dalitz passed away on January 13, 2006. He was almost 81 years old and his outstanding contributions are intimately connected to some of the major breakthroughs of the 20th century in particle and nuclear physics. These outstanding contributions go beyond the Dalitz Plot, Dalitz Pair and CDD poles that bear his name. He pioneered the theoretical study of strange baryon resonances, of baryon spectroscopy in the quark model, and of hypernuclei, to all of which he made lasting contributions. His formulation of the "$\theta-\tau$ puzzle" led to the discovery that parity is not a symmetry of the weak interactions. A brief scientific evaluation of Dalitz's major contributions to particle and nuclear physics is hereby presented, followed by the first comprehensive list of his scientific publications, as assembled from several sources. The list is divided into two categories: the first, main part comprises Dalitz's research papers and reviews, including topics in the history of particle physics, biographies and reminiscences; the second part lists book reviews, public lectures and obituaries authored by Dalitz, and books edited by him. This provides the first necessary step towards a more systematic research of the Dalitz heritage in modern physics. The present 2016 edition updates the original 2006 edition, published in Nucl. Phys. A 771 (2006) 2-7, doi:10.1016/j.nuclphysa.2006.03.007, and 8-25, doi:10.1016/j.nuclphysa.2006.03.008, by including for the first time a dozen or so of publications, found recently in a list submitted to the Royal Society by Dalitz in 2004, that escaped our attention in the original version.Comment: updates the original edition by including several publications, mostly in category III, that were unknown to us in 200

Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at the Calculational Details

In July 1925 Heisenberg published a paper [Z. Phys. 33, 879-893 (1925)] which ended the period of `the Old Quantum Theory' and ushered in the new era of Quantum Mechanics. This epoch-making paper is generally regarded as being difficult to follow, perhaps partly because Heisenberg provided few clues as to how he arrived at the results which he reported. Here we give details of calculations of the type which, we suggest, Heisenberg may have performed. We take as a specific example one of the anharmonic oscillator problems considered by Heisenberg, and use our reconstruction of his approach to solve it up to second order in perturbation theory. We emphasize that the results are precisely those obtained in standard quantum mechanics, and suggest that some discussion of the approach - based on the direct computation of transition amplitudes - could usefully be included in undergraduate courses in quantum mechanics.Comment: 24 pages, no figures, Latex, submitted to Am. J. Phy

Gauge Theories in Particle Physics: A Practical Introduction, Volume 2: Non-Abelian Gauge Theories

Volume 2 of this revised and updated edition provides an accessible and practical introduction to the two non-Abelian quantum gauge field theories of the Standard Model of particle physics: quantum chromodynamics (QCD) and the Glashow-Salam-Weinberg (GSW) electroweak theory.This volume covers much of the experimental progress made in the last ten

Gauge Theories in Particle Physics: A Practical Introduction, Volume 1

Volume 1 of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED).The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a uniq

Effective Lagrangians for BCS Superconductors at T=0

We show that the low frequency, long wavelength dynamics of the phase of the pair field for a BCS-type s-wave superconductor at T=0 is equivalent to that of a time-dependent non-linear Schr\"odinger Lagrangian (TDNLSL), when terms required by Galilean invariance are included. If the modulus of the pair field is also allowed to vary, the system is equivalent to two coupled TDNLSL's. We also refer the interested reader to our earlier paper, `Nonlinear Schrodinger equation for superconductors' [cond-mat/9312099], for a different line of derivationComment: Latex, 13 page

Phase fluctuations in superconductors: from Galilean invariant to quantum XY models

We analyze the corrections to the superfluid density due to phase fluctuations within both a continuum and a lattice model for $s$- and d-wave superconductors. We expand the phase-only action beyond the Gaussian level and compare our results with the quantum XY model both in the quantum and in the classical regime. We find new dynamic anharmonic vertices, absent in the quantum XY model, which are responsible for the vanishing of the correction to the superfluid density at zero temperature in a continuum (Galilean invariant) model. Moreover the phase-fluctuation effects are reduced with respect to the XY model by a factor at least of order $1/(k_F\xi_0)^2$.Comment: 4 pages; shorter version, accepted for publication on Phys. Rev. B Rapid Com

Effective action for Superconductors and BCS-Bose crossover

A standard perturbative expansion around the mean-field solution is used to derive the low-energy effective action for superconductors at T=0. Taking into account the density fluctuations at the outset we get the effective action where the density $\rho$ is the conjugated momentum to the phase $\theta$ of the order parameter. In the hydrodynamic regime, the dynamics of the superconductor is described by a time dependent non-linear Schr\"odinger equation (TDNLS) for the field $\Psi(x)=\sqrt{\rho/2} e^{i\theta}$. The evolution of the density fluctuations in the crossover from weak-coupling (BCS) to strong-coupling (Bose condensation of localized pairs) superconductivity is discussed for the attractive Hubbard model. In the bosonic limit, the TDNLS equation reduces to the the Gross-Pitaevskii equation for the order parameter, as in the standard description of superfluidity. The conditions under which a phase-only action can be derived in the presence of a long-range interaction to describe the physics of the superconductivity of ``bad metals'' are discussed.Comment: 13 pages, accepted for publication on Phys. Rev.