We find explicit expressions for two first finite size corrections to the distribution of Bethe roots, the asymptotics of energy and high conserved charges in the sl(2) quantum Heisenberg spin chain of length J in the thermodynamical limit J → ∞ for low lying states with energies E ∼ 1/J . This limit was recently studied in the context of integrability in perturbative N = 4 super-Yang-Mills the...

AIDAN SUDBURY MONASH UNIVERSITY Abstract. When gas molecules bind to a surface they may do so in such a way that the adsorption of one molecule inhibits the arrival of others. Two models which have frequently been studied are the “dimer model” and the “blocking model”, and rather complete solutions for these are known on fixed tree structures or Bethe lattices. In this paper comparisons are mad...

We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem which is then further mapped to a modified directed polymer problem on a Cayley tree. We employ the techniques of traveling fronts to solve the polymer problem and translate back to derive exact asymptotic properties in t...

We study quantum mechanical systems with " spin "-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the integrability of N-body systems with δ-interactions and point spin couplings. Bethe ansatz solutions, bound states and scattering matrices are explicitly gi...

Assuming all interactions to be instantaneous and the exact fermion propagator S to be approximately given by iS−1(p)= A(p2) p/−B(p2), i.e., with its scalar functions A and B depending only on p, a three-dimensional reduction of the homogeneous Bethe–Salpeter equation retaining, in contrast to the Salpeter equation, the exact propagators (crucial for, e.g., a proper incorporation of dynamical c...

We construct the fusion operators in the generalized τ -model using the fused L-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe ansatz discussion is conducted on two special classes of τ (2) which include the superintegrable chiral Potts model. We then perform the parallel discussion on the XXZ spin chain at roots of unity, and demonstrate that the s...

Many-body Green's function perturbation theories, such as the GW and Bethe-Salpeter formalisms, are starting to be routinely applied to study charged and neutral electronic excitations in molecular organic systems relevant to applications in photovoltaics, photochemistry or biology. In parallel, density functional theory and its time-dependent extensions significantly progressed along the line ...

The relationship between the pionium lifetime and the ππ scattering lengths is established, including the sizable electromagnetic corrections. The bound state formalism that is used is that of constraint theory which provides a covariant three-dimensional reduction of the Bethe–Salpeter equation. The framework of generalized chiral perturbation theory allows then an analysis of the lifetime val...

We study the generalized supersymmetric t−J model with boundaries in three different gradings: FFB, BFF and FBF. Starting from the trigonometric R-matrix, and in the framework of the graded quantum inverse scattering method (QISM), we solve the eigenvalue problems for the supersymmetric t−J model. A detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the ...

We study the generalized supersymmetric t − J model with Kondo impurities in the boundaries. We first construct the higher spin operator K-matrix for the XXZ Heisenberg chain. Setting the boundary parameter to be a special value, we find a higher spin reflecting K-matrix for the supersymmetric t− J model. By using the Quantum Inverse Scattering Method, we obtain the eigenvalue and the correspon...