K-theoretic boson-fermion correspondence and melting crystals

We study non-Hermitian integrable fermion and boson systems from the perspectives of Grothendieck polynomials. The models considered in this article are the five-vertex model as a fermion system and the non-Hermitian phase model as a boson system. Both of the models are characterized by the different solutions satisfying the same Yang-Baxter relation. From our previous works on the identification between the wavefunctions of the five-vertex model and Grothendieck polynomials, we introduce skew Grothendieck polynomials, and derive the addition theorem among them. Using these relations, we derive the wavefunctions of the non-Hermitian phase model as a determinant form which can also be expressed as the Grothendieck polynomials. Namely, we establish a K-theoretic boson-fermion correspondence at the level of wavefunctions. As a by-product, the partition function of the statistical mechanical model of a 3D melting crystal is exactly calculated by use of the scalar products of the wavefunctions of the phase model. The resultant expression can be regarded as a K-theoretic generalization of the MacMahon function describing the generating function of the plane partitions, which interpolates the generating functions of two-dimensional and three-dimensional Young diagrams.Comment: v4, 31 pages, 14 figure

Density matrix for the kink ground state of the ferromagnetic XXZ chain

The exact expression for the density matrix of the kink ground state of the ferromagnetic XXZ chain is obtained. Utilizing this, we exactly calculate various correlation functions such as the longitudinal and transverse spin-spin correlation functions, and the ferromagnetic and antiferromagnetic string formation probabilities. The asymptotic behaviors of these correlation functions are also analyzed. As a consequence, we find that the spin-spin correlation functions decay exponentially for large distances, while the string formation probabilities exhibit Gaussian decay for large strings. We also evaluate the entanglement entropy, which shows interesting behaviors due to the lack of the translational invariance of the state.Comment: 7 pages, 9 figure

Life cycle management of concrete structures based on sustainability indicators

A concrete structure should be sufficiently planned, designed, executed and maintained to ensure its requirements during the life cycle. However, structures suffering from serious deterioration in structural members and sometimes subsequent loss in sustainability have been often found due to various reasons. One of the reasons is lack of total management for the structure. To meet these facts, it is extremely important to pursue coordination of engineering work in the design, execution and maintenance stages. The life cycle management is an organized system to support engineers decision to realize sufficient sustainability of the structure in the design, execution, maintenance, and all related work during its life cycle. The life cycle management is implemented based according to the life cycle management scenario in which balance of several sustainability indicators should be considered with ensuring overall sustainability. The sustainability indicators will be determined from the social, environmental and economic points of view. The scenario should be regularly reviewed based on the PDCA cycle and be updated if necessary. This paper deals with the concept and framework of the life cycle management of concrete structures to ensure sustainability during the structural life