Shortcuts to Adiabaticity Assisted by Counterdiabatic Born-Oppenheimer Dynamics

Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time. Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales. We introduce Counterdiabatic Born-Oppenheimer Dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales. CBOD exploits the Born-Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each subsystem. We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison, and further apply it to a system of two-charged particles.Comment: 14 pages, 3 figures, published New Journal of Physic

QED2 as a testbed for interpolations between quenched and full QCD

Lattice QED2 with the Wilson formulation of fermions is used as a convenient model system to study artifacts of the quenched approximation on a finite lattice. The quenched functional integral is shown to be ill-defined in this system as a consequence of the appearance of exactly real modes for physical values of the fermion mass. The location and frequency of such modes is studied as a function of lattice spacing, lattice volume, topological charge and improved action parameters. The efficacy of the recently proposed modified quenched approximation is examined, as well as a new approach to the interpolation from the quenched to full dynamical theory employing a truncated form of the fermion determinant.Comment: Talk presented by A. Duncan at LATTICE97 (theoretical developments

Importance of including small body spin effects in the modelling of intermediate mass-ratio inspirals. II Accurate parameter extraction of strong sources using higher-order spin effects

We improve the numerical kludge waveform model introduced in [1] in two ways. We extend the equations of motion for spinning black hole binaries derived by Saijo et al. [2] using spin-orbit and spin-spin couplings taken from perturbative and post-Newtonian (PN) calculations at the highest order available. We also include first-order conservative self-force corrections for spin-orbit and spin-spin couplings, which are derived by comparison to PN results. We generate the inspiral evolution using fluxes that include the most recent calculations of small body spin corrections, spin-spin and spin-orbit couplings and higher-order fits to solutions of the Teukolsky equation. Using a simplified version of this model in [1], we found that small body spin effects could be measured through gravitational wave observations from intermediate-mass ratio inspirals (IMRIs) with mass ratio eta ~ 0.001, when both binary components are rapidly rotating. In this paper we study in detail how the spin of the small/big body affects parameter measurement using a variety of mass and spin combinations for typical IMRIs sources. We find that for IMRI events of a moderately rotating intermediate mass black hole (IMBH) of ten thousand solar masses, and a rapidly rotating central supermassive black hole (SMBH) of one million solar masses, gravitational wave observations made with LISA at a fixed signal-to-noise ratio (SNR) of 1000 will be able to determine the inspiralling IMBH mass, the central SMBH mass, the SMBH spin magnitude, and the IMBH spin magnitude to within fractional errors of ~0.001, 0.001, 0.0001, and 9%, respectively. LISA can also determine the location of the source in the sky and the SMBH spin orientation to within ~0.0001 steradians. We show that by including conservative corrections up to 2.5PN order, systematic errors no longer dominate over statistical errors for IMRIs with typical SNR ~1000.Comment: 21 pages, 7 figures. v2: three references added, edits in Sections II-V, including additional results in Section V to address comments by the referee. v3: mirrors version accepted to PR

The eta-prime propagator in quenched QCD

The calculation of the eta-prime hairpin diagram is carried out in the modified quenched approximation (MQA) in which the lattice artifact which causes exceptional configurations is removed by shifting observed poles at kappa<kappa_c in the quark propagators to the critical value of hop ping parameter. By this method, the eta-prime propagator can be accurately calculated even for very light quark mass. A determination of the topological susceptibility for quenched QCD is also obtained, using the fermionic method of Smit and Vink to calculate winding numbers.Comment: 3 pages, 3 postscript figure

Low Dirac Eigenmodes and the Topological and Chiral Structure of the QCD Vacuum

Several lattice calculations which probe the chiral and topological structure of QCD are discussed. The results focus attention on the low-lying eigenmodes of the Dirac operator in typical gauge field configurations.Comment: Talk presented at the DPF2000 Conferenc

Unquenched QCD with Light Quarks

We present recent results in unquenched lattice QCD with two degenerate light sea quarks using the truncated determinant approximation (TDA). In the TDA the infrared modes contributing to the quark determinant are computed exactly up to some cutoff in quark off-shellness (typically 2$\Lambda_{QCD}$). This approach allows simulations to be performed at much lighter quark masses than possible with conventional hybrid MonteCarlo techniques. Results for the static energy and topological charge distributions are presented using a large ensemble generated on very coarse (6$^4$) but physically large lattices. Preliminary results are also reported for the static energy and meson spectrum on 10$^3$x20 lattices (lattice scale $a^{-1}$=1.15 GeV) at quark masses corresponding to pions of mass $\leq$ 200 MeV. Using multiboson simulation to compute the ultraviolet part of the quark determinant the TDA approach becomes an exact with essentially no increase in computational effort. Some preliminary results using this fully unquenched algorithm are presented.Comment: LateX, 39 pages, 16 eps figures, 1 ps figur