The Bethe ansatz equations for reflecting magnons

We derive the Bethe ansatz equations on the half line for particles interacting through factorized S-matrices invariant relative to the centrally extended su(2|2) Lie superalgebra and su(1|2) open boundaries. These equations may be of relevance for the study of the spectrum of open strings on AdS₅×S⁵ background attached to Y=0 giant graviton branes. A one-dimensional spin chain Hamiltonian associated to this system is also derived.     

Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

We present analytically the exact solutions of the Schrödinger equation in the N-dimensional spaces for the pseudoharmonic oscillator potential by means of the ansatz method. The energy eigenvalues of the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained. A realization of the ladder operators for the wavefunctions is studied and we deduced that these operators satisfy the commutation relations of the generators of the dynamical group SU(1,1). Some expectation values for 〈r ^?2〉, 〈r ²〉, 〈T〉, 〈V〉, 〈H〉, 〈p ²〉 and the virial theorem for the pseudoharmonic oscillator potential in an arbitrary number of dimensions are obtained by means of the Hellmann–Feynman theorems. Each solution obtained is dimensions and parameters dependent.     

Two-Term Dilogarithm Identities Related to Conformal Field Theory

We study 2 × 2 matrices A such that the corresponding thermodynamic Bethe ansatz (TBA) equations yield in the form of the effective central charge of a minimal Virasoro model. Certain properties of such matrices and the corresponding solutions of the TBA equations are established. Several continuous families and a discrete set of admissible matrices A are found. The corresponding two-term dilogarithm identities (some of which appear to be new) are obtained. Most of them are proven or shown to be equivalent to previously known identities.     

Shannon information entropy for a hyperbolic double‐well potential

We use the ansatz method to obtain the symmetric and antisymmetric solutions of a hyperbolic double‐well potential by solving the Heun differential equation. The Shannon entropy is studied. The position S_x and momentum S_p information entropies for the low‐lying two states N = 1, 2 are calculated. Some interesting features of the information entropy densities ρ_s(x) and ρ_s(p) as well as the probability density ρ(x) are demonstrated. We find that ρ(x) is equal or greater than 1 at positions for the allowed potential‐depth values of U₀ = 595.84 (symmetric case) and U₀ = 1092.8 (antisymmetric case). This arises from the fact that most of the density is less than 1, the curve has to rise higher than 1 to have a total area of 1 as required for all probability distributions. We find that the position information entropy S_x decreases with the potential strength but the momentum entropy S_p is contrary to the S_x. The Bialynicki‐Birula–Mycielski inequality is also tested and found to hold for these cases. © 2015 Wiley Periodicals, Inc.     

Projection method and a universal weight function for the quantum affine algebra

We calculate the projection of the product of the Drinfeld currents on the intersection of the different Borel subalgebras in the current realization of the quantum affine algebra . This projection yields a universal weight function and has the structure of nested Bethe vectors. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 286–303, February, 2007.     

Exact solution of an integrable quantum spin chain with competing interactions

We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky-Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T-Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.     

Integrability of N-Component Bariev Model Under Open Boundary Conditions

N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.     

Universal Large-Deviation Function of the Kardar–Parisi–Zhang Equation in One Dimension

Using the Bethe ansatz, we calculate the whole large-deviation function of the displacement of particles in the asymmetric simple exclusion process (ASEP) on a ring. When the size of the ring is large, the central part of this large deviation function takes a scaling form independent of the density of particles. We suggest that this scaling function found for the ASEP is universal and should be characteristic of all the systems described by the Kardar–Parisi–Zhang equation in 1+1 dimension. Simulations done on two simple growth models are in reasonable agreement with this conjecture.     

Development and applications of a relaxation-inducing cluster expansion theory for treating strong relaxation and differential correlation effects

We present in this paper a multi-reference coupled cluster (MRCC) formulation for energy differences which treats orbital relaxation and correlation effects on the same footing, by invoking a novel cluster ansatz of the valence portion of the wave operator Ω_v. Unlike in the traditional normal-ordered exponential representation of Ω_v, our new relaxation-inducing ansatz, represented symbolically as E _r(S), allows contractions between the spectator lines and also certain other special contractions. By an extensive theoretical analysis, taking as an example the case of one-hole model space (the IP problem), we demonstrate that our ansatz incorporates in a manifestly spin-free form the orbital relaxation to all orders. The traditional Thouless-type of exponential transformation via one-body excitations can induce the same effect, as is done in the valence-specific or the quasi-valence-specific MRCC formalisms, but they have to be done in the spin-orbital basis – making the spin adaptation of the problem a complicated exercise. In contrast, we use a spin-free representation of the cluster operators right from start, but expand the rank of the cluster operators by involving spectator orbitals to distinguish the various spin possibilities. The combinatorial factors entering the contracted power series in E _r(S) are chosen in such a way that they correspond to what we would have obtained if we had used a Thouless-like transformation to induce the orbital relaxation. Our working equations generally have only finite powers of the cluster operators S, resulting in a very compact formulation of the relaxation problem. Pilot numerical applications for the IP computations of HF and H₂O in the core, the inner valence and the outer valence regions show very good performance of the method vis-a-vis those obtained using the traditional normal ordered ansatz for Ω_v. The improvement in the core IP value is particularly impressive, although even for the valence regions there is an overall improvement of the IP values. Received: 3 August 1998 / Accepted: 30 September 1998 / Published online: 15 February 1999