Thermodynamics of the 3-State Potts Spin Chain

We demonstrate the relation of the infrared anomaly of conformal field theory with entropy considerations of finite temperature thermodynamics for the 3-state Potts chain. We compute the free energy and compute the low temperature specific heat for both the ferromagnetic and anti-ferromagnetic spin chains, and find the central charges for both.Comment: 18 pages, LaTex. Preprint # ITP-SB-92-60. References added and first section expande

Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites

We calculate the bulk contribution for the doubly degenerated largest eigenvalue of the transfer matrix of the eight vertex model with an odd number of lattice sites N in the disordered regime using the generic equation for roots proposed by Fabricius and McCoy. We show as expected that in the thermodynamic limit the result coincides with the one in the N even case.Comment: 11 pages LaTeX New introduction, Method change

The Importance of being Odd

In this letter I consider mainly a finite XXZ spin chain with periodic boundary conditions and \bf{odd} \rm number of sites. This system is described by the Hamiltonian $H_{xxz}=-\sum_{j=1}^{N}\{\sigma_j^{x}\sigma_{j+1}^{x} +\sigma_j^{y}\sigma_{j+1}^{y} +\Delta \sigma_j^z\sigma_{j+1}^z\}$. As it turned out, its ground state energy is exactly proportional to the number of sites $E=-3N/2$ for a special value of the asymmetry parameter $\Delta=-1/2$. The trigonometric polynomial $q(u)$, zeroes of which being the parameters of the ground state Bethe eigenvector is explicitly constructed. This polynomial of degree $n=(N-1)/2$ satisfy the Baxter T-Q equation. Using the second independent solution of this equation corresponding to the same eigenvalue of the transfer matrix, it is possible to find a derivative of the ground state energy w.r.t. the asymmetry parameter. This derivative is closely connected with the correlation function $=-1/2+3/2N^2$. In its turn this correlation function is related to an average number of spin strings for the ground state of the system under consideration: $= {3/8}(N-1/N)$. I would like to stress once more that all these simple formulas are \bf wrong \rm in the case of even number of sites. Exactly this case is usually considered.Comment: 9 pages, based on the talk given at NATO Advanced Research Workshop "Dynamical Symmetries in Integrable Two-dimensional Quantum Field Theories and Lattice Models", 25-30 September 2000, Kyiv, Ukraine. New references are added plus some minor correction

XXZXXZ model as effective Hamiltonian for generalized Hubbard models with broken η\eta-symmetry

We consider the limit of strong Coulomb attraction for generalized Hubbard models with $\eta$-symmetry. In this limit these models are equivalent to the ferromagnetic spin-1/2 Heisenberg quantum spin chain. In order to study the behaviour of the superconducting phase in the electronic model under perturbations which break the $\eta$-symmetry we investigate the ground state of the ferromagnetic non-critical $XXZ$-chain in the sector with fixed magnetization. It turns out to be a large bound state of $N$ magnons. We find that the perturbations considered here lead to the disappearance of the off-diagonal longe-range order.Comment: Results of previous version are generalized, new title, references added. 10 pages, Latex, no figure

Bethe Ansatz Equations for the Broken ZNZ_{N}-Symmetric Model

We obtain the Bethe Ansatz equations for the broken ${\bf Z}_{N}$-symmetric model by constructing a functional relation of the transfer matrix of $L$-operators. This model is an elliptic off-critical extension of the Fateev-Zamolodchikov model. We calculate the free energy of this model on the basis of the string hypothesis.Comment: 43 pages, latex, 11 figure

Optimal Control of One-Qubit Gates

We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy spent in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions.Comment: 5 page

Predictive value of hematological and phenotypical parameters on postchemotherapy leukocyte recovery

Background: Grade IV chemotherapy toxicity is defined as absolute neutrophil count <500/μL. The nadir is considered as the lowest neutrophil number following chemotherapy, and generally is not expected before the 7th day from the start of chemotherapy. The usual prophylactic dose of rHu-G-CSF (Filgrastim) is 300 μg/day, starting 24-48 h after chemotherapy until hematological recovery. However, individual patient response is largely variable, so that rHu-G-CSF doses can be different. The aim of this study was to verify if peripheral blood automated flow cytochemistry and flow cytometry analysis may be helpful in predicting the individual response and saving rHu-G-CSF. Methods: During Grade IV neutropenia, blood counts from 30 cancer patients were analyzed daily by ADVIA 120 automated flow cytochemistry analyzer and by Facscalibur flow cytometer till the nadir. "Large unstained cells" (LUCs), myeloperoxidase index (MPXI), blasts, and various cell subpopulations in the peripheral blood were studied. At nadir rHu-G-CSF was started and 81 chemotherapy cycles were analyzed. Cycles were stratified according to their number and to two dose-levels of rHuG-CSF needed to recovery (300-600 vs. 900-1200 μg) and analyzed in relation to mean values of MPXI and mean absolute number of LUCs in the nadir phase. The linear regressions of LUCs % over time in relation to two dose-levels of rHu-G-CSF and uni-multivariate analysis of lymphocyte subpopulations, CD34+ cells, MPXI, and blasts were also performed. Results: In the nadir phase, the increase of MPXI above the upper limit of normality (>10; median 27.7), characterized a slow hematological recovery. MPXI levels were directly related to the cycle number and inversely related to the absolute number of LUCs and CD34 +/CD45+ cells. A faster hematological recovery was associated with a higher LUC increase per day (0.56% vs. 0.25%), higher blast (median 36.7/μL vs. 19.5/μL) and CD34+/CD45+ cell (median 2.2/μL vs. 0.82/μL) counts. Conclusions: Our study showed that some biological indicators such as MPXI, LUCs, blasts, and CD34 +/CD45+ cells may be of clinical relevance in predicting individual hematological response to rHu-G-CSF. Special attention should be paid when nadir MPXI exceeds the upper limit of normality because the hematological recovery may be delayed. © 2009 Clinical Cytometry Society

Low-Temperature Expansions and Correlation Functions of the Z_3-Chiral Potts Model

Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z_3-chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z_n-spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z_3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.Comment: 17 pages (Plain TeX), BONN-HE-93-1

Degrees of controllability for quantum systems and applications to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio