From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model

We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives the solution of the T-system, plays an important role. In addition, we also calculate the high temperature expansion of the specific heat and the magnetic susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added; typos corrected; to appear in J. Phys. A: Math. Ge

Excited state TBA and functional relations in spinless Fermion model

The excited state thermodynamic Bethe ansatz (TBA) equations for the spinless Fermion model are presented by the quantum transfer matrix (QTM) approach. We introduce a more general family called T-functions and explore functional relations among them (T-system) and their certain combinations (Y-system). {}From their analytical property, we derive a closed set of non-linear integral equations which characterize the correlation length of $$ at any finite temperatures. Solving these equations numerically, we explicitly determine the correlation length, which coincides with earlier results with high accuracy.Comment: 4 page

The investigation of time dependent flame structure by ionization probes

Ionization probes were used to measure mean ionization current and frequency spectra, auto-correlations and cross-correlations in jet flames with variation in the initial Reynolds numbers and equivalence ratios. Special attention was paid to the transitional region between the burner exit plane and the plane of onset of turbulence

Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures

The thermodynamics of solvable isotropic chains with arbitrary spins is addressed by the recently developed quantum transfer matrix (QTM) approach. The set of nonlinear equations which exactly characterize the free energy is derived by respecting the physical excitations at T=0, spinons and RSOS kinks. We argue the implication of the present formulation to spinon character formula of level k=2S SU(2) WZWN model .Comment: 25 pages, 8 Postscript figures, Latex 2e,uses graphicx, added figures and detailed discussion

Difference L operators related to q-characters

We introduce a factorized difference operator L(u) annihilated by the Frenkel-Reshetikhin screening operator for the quantum affine algebra U_q(C^{(1)}_n). We identify the coefficients of L(u) with the fundamental q-characters, and establish a number of formulas for their higher analogues. They include Jacobi-Trudi and Weyl type formulas, canceling tableau sums, Casorati determinant solution to the T-system, and so forth. Analogous operators for the orthogonal series U_q(B^{(1)}_n) and U_q(D^{(1)}_n) are also presented.Comment: 25 pages, LaTeX2e, no figur

Temperature dependent spatial oscillations in the correlations of the XXZ spin chain

We study the correlation $$ for the XXZ chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.Comment: 4 pages, REVTEX, 6 table

Analysis of Cumulant Moments in High Energy Hadron-Hadron Collisions by Truncated Multiplicity Distributions

Oscillatory behavior of cumulant moments obtained from the experimental data in $pp$ collisions and $\bar{p}p$ collisions are analyzed by the modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Both distributions well describe the cumulant moments obtained from the data. This fact shows sharp contrast to the result in $e^+e^-$ collisions, which is described by the the MNBD much better than by the NBD.Comment: 7 pages, Latex type, 7 figure

Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model

We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the ones from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIE). In particular, a subset of these NLIE forms a system of NLIE which contains only a finite number of unknown functions. For r=1, this subset of NLIE reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIE is clarified. Based on our new NLIE, we also calculate the high temperature expansion of the free energy.Comment: 24 pages, 4 figures, to appear in J. Phys. A: Math. Ge

Energy levels in polarization superlattices: a comparison of continuum strain models

A theoretical model for the energy levels in polarization superlattices is presented. The model includes the effect of strain on the local polarization-induced electric fields and the subsequent effect on the energy levels. Two continuum strain models are contrasted. One is the standard strain model derived from Hooke's law that is typically used to calculate energy levels in polarization superlattices and quantum wells. The other is a fully-coupled strain model derived from the thermodynamic equation of state for piezoelectric materials. The latter is more complete and applicable to strongly piezoelectric materials where corrections to the standard model are significant. The underlying theory has been applied to AlGaN/GaN superlattices and quantum wells. It is found that the fully-coupled strain model yields very different electric fields from the standard model. The calculated intersubband transition energies are shifted by approximately 5 -- 19 meV, depending on the structure. Thus from a device standpoint, the effect of applying the fully-coupled model produces a very measurable shift in the peak wavelength. This result has implications for the design of AlGaN/GaN optical switches.Comment: Revtex

Functional Relations in Stokes Multipliers and Solvable Models related to U_q(A^{(1)}_n)

Recently, Dorey and Tateo have investigated functional relations among Stokes multipliers for a Schr{\"o}dinger equation (second order differential equation) with a polynomial potential term in view of solvable models. Here we extend their studies to a restricted case of n+1-th order linear differential equations.Comment: 20 pages, some explanations improved, To appear in J. Phys.