The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

Effects of Chemical Potential on Hadron Masses in the Phase Transition Region

We study the response of hadron masses with respect to chemical potential at $\mu=0$. Our preliminary results of the pion channel show that $\partial m/\partial \mu$ in the confinement phase is significantly larger than that in the deconfinement phase, which is consistent with the chiral restoration.Comment: LATTICE99 (finite temperature and density), 3 pages, 3 figure

Responses of hadrons to chemical potential at finite temperature

We present a framework to compute the responses of hadron masses to the chemical potential in lattice QCD simulations. As a first trial, the screening mass of the pseudoscalar meson and its first and second responses are evaluated. We present results on a $16\times 8^2\times 4$ lattice with two flavors of staggered quarks below and above $T_c$. The responses to both the isoscalar and isovector chemical potentials are obtained. They show different behavior in the low and the high temperature phases, which may be explained as a consequence of chiral symmetry breaking and restoration, respectively.Comment: 10 pages, 11 figure

Resonant enhanced diffusion in time dependent flow

Explicit examples of scalar enhanced diffusion due to resonances between different transport mechanisms are presented. Their signature is provided by the sharp and narrow peaks observed in the effective diffusivity coefficients and, in the absence of molecular diffusion, by anomalous transport. For the time-dependent flow considered here, resonances arise between their oscillations in time and either molecular diffusion or a mean flow. The effective diffusivities are calculated using multiscale techniques.Comment: 18 latex pages, 11 figure

Heavy Hadron Spectroscopy

I review recent theoretical advances in heavy hadron spectroscopy.Comment: Plenary talk at the XXXIII International Conference on High Energy Physics (ICHEP 06), Moscow, Russia, July 26 - August 2, 2006; 11 page

Time-dependent quantum many-body theory of identical bosons in a double well: Early time ballistic interferences of fragmented and number entangled states

A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body wave functions within a restricted two state Fock space basis that includes the full effects of the condensate's mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, by construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states.Comment: 16 pages, 5 figure

Magnetic Fields in Quasar Cores II

Multi-frequency polarimetry with the Very Long Baseline Array (VLBA) telescope has revealed absolute Faraday Rotation Measures (RMs) in excess of 1000 rad/m/m in the central regions of 7 out of 8 strong quasars studied (e.g., 3C 273, 3C 279, 3C 395). Beyond a projected distance of ~20 pc, however, the jets are found to have |RM| < 100 rad/m/m. Such sharp RM gradients cannot be produced by cluster or galactic-scale magnetic fields, but rather must be the result of magnetic fields organized over the central 1-100 pc. The RMs of the sources studied to date and the polarization properties of BL Lacs, quasars and galaxies are shown to be consistent so far with the predictions of unified schemes. The direct detection of high RMs in these quasar cores can explain the low fractional core polarizations usually observed in quasars at centimeter wavelengths as the result of irregularities in the Faraday screen on scales smaller than the telescope beam. Variability in the RM of the core is reported for 3C 279 between observations taken 1.5 years apart, indicating that the Faraday screen changes on that timescale, or that the projected superluminal motion of the inner jet components samples a new location in the screen with time. Either way, these changes in the Faraday screen may explain the dramatic variability in core polarization properties displayed by quasars.Comment: Accepted to the ApJ. 27 pages, 9 figures including figure 6 in colo

Pion Propagation near the QCD Chiral Phase Transition

We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass. This fact is attributed to the decrease of the pion velocity near the phase transition.Comment: 8 pages (single column), RevTeX; added references, version to be published in PR

One-Flavour Hybrid Monte Carlo with Wilson Fermions

The Wilson fermion determinant can be written as product of the determinants of two hermitian positive definite matrices. This formulation allows to simulate non-degenerate quark flavors by means of the hybrid Monte Carlo algorithm. A major numerical difficulty is the occurrence of nested inversions. We construct a Uzawa iteration scheme which treats the nested system within one iterative process.Comment: 11 pages, to appear in proceedings of the workshop "Numerical Challenges in Lattice QCD", Springer Verla