A Q-operator for the twisted XXX model

Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary conditions are needed to ensure convergence of the Q-operator construction and derive a quantum Wronskian relation which implies two different sets of Bethe ansatz equations, one above the other below the "equator" of total spin zero. We discuss the limit to periodic boundary conditions at the end and explain how this construction might be useful in the context of correlation functions on the infinite lattice. We also identify a special subclass of solutions to the quantum Wronskian for chains up to a length of 10 sites and possibly higher.Comment: 19 page

PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields

The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to be quasi-Hermitian for special values of the boundary parameters. This is proved by explicit construction of a new inner product employing a "quasi-fermion" algebra in momentum space where creation and annihilation operators are not related via Hermitian conjugation. For a special example, when the boundary fields lie on the imaginary axis, we show the spectral equivalence of the quasi-Hermitian XX spin-chain with a non-local fermion model, where long range hopping of the particles occurs as the non-Hermitian boundary fields increase in strength. The corresponding Hamiltonian interpolates between the open XX and the quantum group invariant XXZ model at the free fermion point. For an even number of sites the former is known to be related to a CFT with central charge c=1, while the latter has been connected to a logarithmic CFT with central charge c=-2. We discuss the underlying algebraic structures and show that for an odd number of sites the superalgebra symmetry U(gl(1|1)) can be extended from the unit circle along the imaginary axis. We relate the vanishing of one of its central elements to the appearance of Jordan blocks in the Hamiltonian.Comment: 37 pages, 5 figure

Atmospheric neutrons

Contributions to fast neutron measurements in the atmosphere are outlined. The results of a calculation to determine the production, distribution and final disappearance of atmospheric neutrons over the entire spectrum are presented. An attempt is made to answer questions that relate to processes such as neutron escape from the atmosphere and C-14 production. In addition, since variations of secondary neutrons can be related to variations in the primary radiation, comment on the modulation of both radiation components is made

Quantum cohomology via vicious and osculating walkers

We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang–Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged u^(n)k -WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov’s toric Schur functions and can be interpreted as generating functions for Gromov–Witten invariants. We reveal an underlying quantum group structure in terms of Yang–Baxter algebras and use it to give a generating formula for toric Schur functions in terms of divided difference operators which appear in known representations of the nil-Hecke algebra

Baxter Q-operators of the XXZ chain and R-matrix factorization

We construct Baxter operators as generalized transfer matrices being traces of products of generic $R$ matrices. The latter are shown to factorize into simpler operators allowing for explicit expressions in terms of functions of a Weyl pair of basic operators. These explicit expressions are the basis for explicit expression for Baxter Q-operators and for investigating their properties.Comment: 19 pages LaTex, references adde

Interactive effects of joint angle, contraction state and method on estimates of Achilles tendon moment arms

The muscle-tendon moment arm is an important input parameter for musculoskeletal models. Moment arms change as a function of joint angle and contraction state and depend on the method being employed. The overall purpose was to gain insights into the interactive effects of joint angle, contraction state and method on the Achilles tendon moment arm using the center of rotation (COR) and the tendon excursion method (TE). Moment arms were obtained at rest (TErest, CORrest) and during a maximum voluntary contraction (CORMVC) at four angles. We found strong correlations between TErest and CORMVC for all angles (0.72 ≤ r ≤ 0.93) with Achilles tendon moment arms using CORMVC being 33 - 36% greater than those obtained from TErest. The relationship between Achilles tendon moment arms and angle was similar across both methods and both levels of muscular contraction. Finally, Achilles tendon moment arms for CORrest were 1 – 8% greater than for CORMVC. [NB rendition of scientific symbols is approximate in this display; please check full text for precise rendition]

Factorization of the transfer matrices for the quantum sl(2) spin chains and Baxter equation

It is shown that the transfer matrices of homogeneous sl(2) invariant spin chains with generic spin, both closed and open, are factorized into the product of two operators. The latter satisfy the Baxter equation that follows from the structure of the reducible representations of the sl(2) algebra.Comment: 14 pages, 9 figures, typos correcte

JOINT-SPECIFIC POWER PRODUCTION DURING SUBMAXIMAL AND MAXIMAL CYCLING

Cycle ergometry is commonly used to quantify muscular work and power, and to elicit perturbations to metabolic homeostasis for a broad range of physiological investigations. Separate authors have reported that knee extension dominates power production during submaximal cycling (SUBcyc; Ericson, 1988) and hip extension is the dominate action during maximal cycling (MAXcyc, Martin & Brown, 2009). Changes in joint-specific powers across broad ranges of net cycling powers within one group of cyclists have not been reported. Our purpose was to determine the extent to which ankle, knee, and hip joint actions produced power across a range of net cycling powers. Based on previous reports we hypothesized that relative contributions of knee extension power would decrease and relative knee flexion and hip extension powers would increase as net cycling power increase

Electronic origin of x-ray absorption peak shifts

Encoded in the transient x-ray absorption (XAS) and magnetic circular (MCD) response functions resides a wealth of information of the microscopic processes of ultrafast demagnetization. Employing state-of-the-art first-principles dynamical simulations we show that the experimentally observed energy shift of the L3 XAS peak in Ni, and the absence of a corresponding shift in the dichroic MCD response, can be explained in terms of laser-induced changes in band occupation. Strikingly, we predict that for the same ultrashort pump pulse applied to Co the opposite effect will occur: a substantial shift upward in energy of the MCD peaks will be accompanied by very small change in the position of XAS peaks, a fact we relate to the reduced d-band filling of Co that allows a greater energetic range above the Fermi energy into which charge can be excited. We also carefully elucidate the dependence of this effect on pump pulse parameters. These findings (i) establish an electronic origin for early-time peak shifts in transient XAS and MCD spectroscopy and (ii) illustrate the rich information that may be extracted from transient response functions of the underlying dynamical system