On the c-theorem in more than two dimensions

Several pieces of evidence have been recently brought up in favour of the c-theorem in four and higher dimensions, but a solid proof is still lacking. We present two basic results which could be useful for this search: i) the values of the putative c-number for free field theories in any even dimension, which illustrate some properties of this number; ii) the general form of three-point function of the stress tensor in four dimensions, which shows some physical consequences of the c-number and of the other trace-anomaly numbers.Comment: Latex, 7 pages, 1 tabl

Performance of Reynolds Averaged Navier-Stokes Models in Predicting Separated Flows: Study of the Hump Flow Model Problem

Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump

Composite Fermion Wavefunctions Derived by Conformal Field Theory

The Jain theory of hierarchical Hall states is reconsidered in the light of recent analyses that have found exact relations between projected Jain wavefunctions and conformal field theory correlators. We show that the underlying conformal theory is precisely given by the W-infinity minimal models introduced earlier. This theory involves a reduction of the multicomponent Abelian theory that is similar to the projection to the lowest Landau level in the Jain approach. The projection yields quasihole excitations obeying non-Abelian fractional statistics. The analysis closely parallels the bosonic conformal theory description of the Pfaffian and Read-Rezayi states.Comment: 4 pages, 1 figur

Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux

Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the Z_k parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov-Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a non-trivial contribution coming from the neutral sector. We emphasize the crucial role of the non-holomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.Comment: 14 pages, RevTeX4, 7 figures (eps

Torus Knot and Minimal Model

We reveal an intimate connection between the quantum knot invariant for torus knot T(s,t) and the character of the minimal model M(s,t), where s and t are relatively prime integers. We show that Kashaev's invariant, i.e., the N-colored Jones polynomial at the N-th root of unity, coincides with the Eichler integral of the character.Comment: 10 page

A Comment on the Zamolodchikov c-Function and the Black String Entropy

Using the spectral representation approach to the Zamolodchikov's c-function and the Maldacena conjecture for the D1-branes, we compute the entropy of type IIB strings. An agreement, up to a numerical constant which cannot be determined using this approach, with the Bekenstein-Hawking entropy is found.Comment: 7 pages, LaTe

On parity functions in conformal field theories

We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie algebras, for which we give two efficient formulas. We investigate the consequences of these for the modular invariance problem.Comment: 18 pages, no figure, LaTeX2

Ring Vibrations to Sense Anionic Ibuprofen in Aqueous Solution as Revealed by Resonance Raman

We unravel the potentialities of resonance Raman spectroscopy to detect ibuprofen in diluted aqueous solutions. In particular, we exploit a fully polarizable quantum mechanics/molecular mechanics (QM/MM) methodology based on fluctuating charges coupled to molecular dynamics (MD) in order to take into account the dynamical aspects of the solvation phenomenon. Our findings, which are discussed in light of a natural bond orbital (NBO) analysis, reveal that a selective enhancement of the Raman signal due to the normal mode associated with the C–C stretching in the ring, νC=C, can be achieved by properly tuning the incident wavelength, thus facilitating the recognition of ibuprofen in water samples

Bulk Versus Edge in the Quantum Hall Effect

The manifestation of the bulk quantum Hall effect on edge is the chiral anomaly. The chiral anomaly {\it is} the underlying principle of the ``edge approach'' of quantum Hall effect. In that approach, \sxy should not be taken as the conductance derived from the space-local current-current correlation function of the pure one-dimensional edge problem.Comment: 4 pages, RevTex, 1 postscript figur

The W_N minimal model classification

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten theories at level (p-N,q-N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W_3(p,q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W_3(p,p+1), were classified. For all N our correspondence yields for free an extensive list of W_N(p,q) modular invariants. The W_3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3)xSU(3) modular invariants, and find there a new infinite series of exceptionals.Comment: 25 page