Random matrices, Virasoro algebras, and noncommutative KP

What is the connection of random matrices with integrable systems? Is this connection really useful? The answer to these questions leads to a new and unifying approach to the theory of random matrices. Introducing an appropriate time t-dependence in the probability distribution of the matrix ensemble, leads to vertex operator expressions for the n-point correlation functions (probabilities of n eigenvalues in infinitesimal intervals) and the corresponding Fredholm determinants (probabilities of no eigenvalue in a Borel subset E); the latter probability is a ratio of tau-functions for the KP-equation, whose numerator satisfy partial differential equations, which decouple into the sum of two parts: a Virasoro-like part depending on time only and a Vect(S^1)-part depending on the boundary points A_i of E. Upon setting t=0, and using the KP-hierarchy to eliminate t-derivatives, these PDE's lead to a hierarchy of non-linear PDE's, purely in terms of the A_i. These PDE's are nothing else but the KP hierarchy for which the t-partials, viewed as commuting operators, are replaced by non-commuting operators in the endpoints A_i of the E under consideration. When the boundary of E consists of one point and for the known kernels, one recovers the Painleve equations, found in prior work on the subject.Comment: 56 page

Femtoscopic results in Au+Au and p+p from PHENIX at RHIC

Ultra-relativistic gold-gold and proton-proton collisions are investigated in the experiments of the Relativistic Heavy Ion Collider (RHIC). In the last several years large amount of results were revealed about the matter created in these collisions. The latest PHENIX results for femtoscopy and correlations are reviewed in this paper. Bose-Einstein correlations of charged kaons in 200 GeV Au+Au collisions and of charged pions in 200 GeV p+p collisions are shown. They are both compatible with previous measurements of charged pions in gold-gold collisions, with respect to transverse mass or number of participants scaling.Comment: Talk given at the VI Workshop on Particle Correlations and Femtoscopy, Kiev, September 14-18, 2010. 6 pages, 4 figures. This work was supported by the OTKA grant NK73143 and M. Csanad's Bolyai scholarshi

No Eigenvalue in Finite Quantum Electrodynamics

We re-examine Quantum Electrodynamics (QED) with massless electron as a finite quantum field theory as advocated by Gell-Mann-Low, Baker-Johnson, Adler, Jackiw and others. We analyze the Dyson-Schwinger equation satisfied by the massless electron in finite QED and conclude that the theory admits no nontrivial eigenvalue for the fine structure constant.Comment: 13 pages, Late

One-dimensional quantum antiferromagnetism in the p−p-orbital CsO2_2 compound revealed by electron paramagnetic resonance

Recently it was proposed that the orbital ordering of $\pi_{x,y}^*$ molecular orbitals in the superoxide CsO$_2$ compound leads to the formation of spin-1/2 chains below the structural phase transition occuring at $T_{\rm{s1}}=61$~K on cooling. Here we report a detailed X-band electron paramagnetic resonance (EPR) study of this phase in CsO$_2$ powder. The EPR signal appears as a broad line below $T_{\rm{s1}}$, which is replaced by the antiferromagnetic resonance below the N\'{e}el temperature $T_{\rm N}=8.3$~K. The temperature dependence of the EPR linewidth between $T_{\rm{s1}}$ and $T_{\rm{N}}$ agrees with the predictions for the one-dimensional Heisenberg antiferromagnetic chain of $S=1/2$ spins in the presence of symmetric anisotropic exchange interaction. Complementary analysis of the EPR lineshape, linewidth and the signal intensity within the Tomonaga-Luttinger liquid (TLL) framework allows for a determination of the TLL exponent $K=0.48$. Present EPR data thus fully comply with the quantum antiferromagnetic state of spin-1/2 chains in the orbitally ordered phase of CsO$_2$, which is, therefore, a unique $p-$orbital system where such a state could be studied.Comment: 6 pages, 3 figure

Non-colliding Brownian Motions and the extended tacnode process

We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.Comment: 38 pages. In the revised version a few arguments have been expanded and many typos correcte

Buda-Lund hydro model for ellipsoidally symmetric fireballs and the elliptic flow at RHIC

The ellipsoidally symmetric extension of Buda-Lund hydrodynamic model is shown here to yield a natural description of the pseudorapidity dependence of the elliptic flow $v_2(\eta)$, as determined recently by the PHOBOS experiment for Au+Au collisions at $\sqrt{s_{NN}} = 130$ and 200 GeV. With the same set of parameters, the Buda-Lund model describes also the transverse momentum dependence of $v_2$ of identified particles at mid-rapidity. The results confirm the indication for quark deconfinement in Au+Au collisions at RHIC, obtained from a successful Buda-Lund hydro model fit to the single particle spectra and two-particle correlation data, as measured by the BRAHMS, PHOBOS, PHENIX and STAR collaborations.Comment: 16 pages, 2 figures, 1 table added, discussion extended and an important misprint in the caption of Fig. 1 is correcte

Spatial correlations of the 1D KPZ surface on a flat substrate

We study the spatial correlations of the one-dimensional KPZ surface for the flat initial condition. It is shown that the multi-point joint distribution for the height is given by a Fredholm determinant, with its kernel in the scaling limit explicitly obtained. This may also describe the dynamics of the largest eigenvalue in the GOE Dyson's Brownian motion model. Our analysis is based on a reformulation of the determinantal Green's function for the totally ASEP in terms of a vicious walk problem.Comment: 11 pages, 2 figure

Diagnosing Energy Loss: PHENIX Results on High-pT Hadron Spectra

Measurements of inclusive spectra of hadrons at large transverse momentum over a broad range of energy in different collision systems have been performed with the PHENIX experiment at RHIC. The data allow to study the energy and system size dependence of the suppression observed in RAA of high-pT hadrons at sqrt(s_NN)= 200 GeV. Due to the large energy range from sqrt(s_NN)= 22 GeV to 200 GeV, the results can be compared to results from CERN SPS at a similar energy. The large Au+Au dataset from the 2004 run of RHIC also allows to constrain theoretical models that describe the hot and dense matter produced in such collisions. Investigation of particle ratios such as eta/pi0 helps understanding the mechanisms of energy loss.Comment: 4 pages, 6 figures. To appear in the proceedings of the 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2006), Shanghai, China, November 14-20, 200

Pseudorapidity dependence of parton energy loss in relativistic heavy ion collisions

We analyze the recent data from the BRAHMS Collaboration on the pseudorapidity dependence of nuclear modification factors in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV by using the full three dimensional hydrodynamic simulations for the density effects on parton energy loss. We first compute the transverse spectra at $\eta=0$ and 2.2, and next take a ratio $R_{\eta}=R_{AA}(\eta=2.2)/R_{AA}(\eta=0)$, where $R_{AA}$ is a nuclear modification factor. It is shown that hydrodynamic components account for $R_{\eta}\simeq 1$ at low $p_\mathrm{T}$ and that quenched pQCD components lead $R_{\eta} < 1$ at high $p_\mathrm{T}$ which are consistent with the data. Strong suppression at $\eta=2.2$ is compatible with the parton energy loss in the final state.Comment: 5 pages, 4 figures; one figure adde