2,175 research outputs found
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
Improved Soundness for QMA with Multiple Provers
We present three contributions to the understanding of QMA with multiple
provers:
1) We give a tight soundness analysis of the protocol of [Blier and Tapp,
ICQNM '09], yielding a soundness gap Omega(1/N^2). Our improvement is achieved
without the use of an instance with a constant soundness gap (i.e., without
using a PCP).
2) We give a tight soundness analysis of the protocol of [Chen and Drucker,
ArXiV '10], thereby improving their result from a monolithic protocol where
Theta(sqrt(N)) provers are needed in order to have any soundness gap, to a
protocol with a smooth trade-off between the number of provers k and a
soundness gap Omega(k^2/N), as long as k>=Omega(log N). (And, when
k=Theta(sqrt(N)), we recover the original parameters of Chen and Drucker.)
3) We make progress towards an open question of [Aaronson et al., ToC '09]
about what kinds of NP-complete problems are amenable to sublinear
multiple-prover QMA protocols, by observing that a large class of such examples
can easily be derived from results already in the PCP literature - namely, at
least the languages recognized by a non-deterministic RAMs in quasilinear time.Comment: 24 pages; comments welcom
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
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