Multi-Periodic Coherent States and the WKB-Exactness

We construct the path integral formula in terms of ``multi-periodic'' coherent state as an extension of the Nielsen-Rohrlich formula for spin. We make an exact calculation of the formula and show that, when a parameter corresponding to the magnitude of spin becomes large, the leading order term of the expansion coincides with the exact result. We also give an explicit correspondence between the trace formula in the multi-periodic coherent state and the one in the ``generalized'' coherent state.Comment: 28 pages, late

Multi-Periodic Coherent States and the WKB-Exactness II ``Non-compact Case and Classical theories Revisited''

We show that the WKB approximation gives the exact result in the trace formula of ``$CQ^N$'', which is the non-compact counterpart of $CP^N$, in terms of the ``multi-periodic'' coherent state. We revisit the symplectic 2-forms on $CP^N$ and $CQ^N$ and, especially, construct that on $CQ^N$ with the unitary form. We also revisit the exact calculation of the classical patition functions of them.Comment: LaTeX, 29 page

Asymptotic form of two-point correlation function of the XXZ spin chain

Correlation functions of the XXZ spin chain in the critical regime is studied at zero-temperature. They are exactly represented in the Fredholm determinant form and are related with an operator-valued Riemann-Hilbert problem. Analyzing this problem we prove that a two-point correlation function consisting of sufficiently separated spin operators is expressed by power-functions of the distance between those operators.Comment: 9 pages, LaTeX2e (+ amssymb, amsthm); Proof of Lemma 1 is revise

Melting the Color Glass Condensate at the LHC

The charged particle multiplicity in central AA collisions and the production of heavy flavors in pA collisions at the LHC is predicted in the CGC framework.Comment: Presented at the Workshop on Heavy Ion Collisions at the LHC: Last Call for Predictions, Geneva, Switzerland, 14 May - 8 Jun 2007; 2 pages, 3 figure

Heavy flavor production in pA collisions

Heavy quark production in high-energy proton-nucleus (pA) collisions is described in the framework of the Color Glass Condensate. kT factorization is broken even at leading order albeit a more general factorization in pA holds at this order in terms of 2, 3 and 4 point correlators of Wilson lines in the nuclear target. The x-evolution of these correlators is computed in the large A and large N mean field limit of the Balitsky-Kovchegov equation. We show results for heavy quark production at RHIC and LHC energies.Comment: Talk given at QM2006. 4

Exact solution of Riemann--Hilbert problem for a correlation function of the XY spin chain

A correlation function of the XY spin chain is studied at zero temperature. This is called the Emptiness Formation Probability (EFP) and is expressed by the Fredholm determinant in the thermodynamic limit. We formulate the associated Riemann--Hilbert problem and solve it exactly. The EFP is shown to decay in Gaussian.Comment: 7 pages, to be published in J. Phys. Soc. Jp

Formal Relation among Various Hermitian and non-Hermitian Effective Interactions

A general definition of the model-space effective interaction is given. The energy-independent effective hamiltonians derived in a time-independent way are classified systematically.Comment: To appear in IJMPE; Proceedings of "Blueprints for the Nucleus," Istanbul, Turkey, May 200

An analytic study towards instabilities of the glasma

Strong longitudinal color flux fields will be created in the initial stage of high-energy nuclear collisions. We investigate analytically time evolution of such boost-invariant color fields from Abelian-like initial conditions, and next examine stability of the boost-invariant configurations against rapidity dependent fluctuations. We find that the magnetic background field has an instability induced by the lowest Landau level whose amplitude grows exponentially. For the electric background field there is no apparent instability although pair creations due to the Schwinger mechanism should be involved.Comment: 4p, 3figs; poster contribution to QM200