Time-Dependent Superfluid Local Density Approximation

The time-dependent superfluid local density approximation (TDSLDA) is an extension of the Hohenberg-Kohn density functional theory (DFT) to time-dependent phenomena in superfluid fermionic systems. Unlike linear response theory, which is only valid for weak external fields, the (TDSLDA) approach allows one to study non-linear excitations in fermionic superfluids, including large amplitude collective modes, and the response to strong external probes. Even in the case of weak external fields, the (TDSLDA) approach is technically easier to implement. We will illustrate the implementation of the (TDSLDA) for the unitary Fermi gas, where dimensional arguments and Galilean invariance simplify the form of the functional, and ab initio input from (QMC) simulations fix the coefficients to quite high precision.Comment: 6 pages, 1 figure. Unedited version of chapter to appear in Quantum Gases: Finite Temperature and Non-Equilibrium Dynamics (Vol. 1 Cold Atoms Series). N.P. Proukakis, S.A. Gardiner, M.J. Davis and M.H. Szymanska, eds. Imperial College Press, London, 2013 (in press). See http://www.icpress.co.uk/physics/p817.htm

Use of the Discrete Variable Representation Basis in Nuclear Physics

The discrete variable representation (DVR) basis is nearly optimal for numerically representing wave functions in nuclear physics: Suitable problems enjoy exponential convergence, yet the Hamiltonian remains sparse. We show that one can often use smaller basis sets than with the traditional harmonic oscillator basis, and still benefit from the simple analytic properties of the DVR bases which requires no overlap integrals, simply permit using various Jacobi coordinates, and admit straightforward analyses of the ultraviolet and infrared convergence properties.Comment: Published version: New figure demonstrating convergence for 3- and 4-body problem

The Unitary Fermi Gas: From Monte Carlo to Density Functionals

In this chapter, we describe three related studies of the universal physics of two-component unitary Fermi gases with resonant short-ranged interactions. First we discuss an ab initio auxiliary field quantum Monte Carlo technique for calculating thermodynamic properties of the unitary gas from first principles. We then describe in detail a Density Functional Theory (DFT) fit to these thermodynamic properties: the Superfluid Local Density Approximation (SLDA) and its Asymmetric (ASLDA) generalization. We present several applications, including vortex structure, trapped systems, and a supersolid Larkin-Ovchinnikov (FFLO/LOFF) state. Finally, we discuss the time-dependent extension to the density functional (TDDFT) which can describe quantum dynamics in these systems, including non-adiabatic evolution, superfluid to normal transitions and other modes not accessible in traditional frameworks such as a Landau-Ginzburg, Gross-Pitaevskii, or quantum hydrodynamics.Comment: 73 pages, 20 figures. Chapter 9 in "The BCS-BEC Crossover and the Unitary Fermi Gas" edited by W. Zwerger (Springer, 2012). Updated to match published versio