Related papers: Boxed Skew Plane Partition and Integrable Phase Mo…

To every product of $2\times2$ matrices, there corresponds a one-dimensional Schr\"{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and…

Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all plane partitions whose solid Young diagrams…

We define a finite Markov chain, called generalized crested product, which naturally appears as a generalization of the first crested product of Markov chains. A complete spectral analysis is developed and the $k$-step transition…

In this paper we use our previously developed projective phase space generator for the calculation of the hadronic production of a vector boson with one additional jet at Next-to-Leading Order. The projective phase space generator allows us…

In this work we use the algebraic Bethe ansatz to derive the general scalar product in the six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the…

In this paper we study generalized J-inner matrix valued functions which appear as resolvent matrices in various indefinite interpolation problems. Reproducing kernel indefinite inner product spaces associated with a generalized J-inner…

We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…

The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in…

The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…

We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,\alpha)$, has a standard $q$-expansion…

We review the problem of BPS state counting described by the generalized quiver matrix model of ADHM type. In four dimensions the generating function of the counting gives the Nekrasov partition function and we obtain generalization in…

We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…

We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…

We give a product formula for the number of shifted plane partitions of shifted double staircase shape with bounded entries. This is the first new example of a family of shapes with a plane partition product formula in many years. The proof…

We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.

In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced…

We give an explicit form of the symplectic groupoid that integrates the semiclassical standard Podles sphere. We show that Sheu's groupoid, whose convolution C*-algebra quantizes the sphere, appears as the groupoid of the Bohr-Sommerfeld…

The influence of immobile filler particles (spheres, fibers, platelets) on polymer blend phase separation is investigated computationally using a generalization of the Cahn-Hilliard-Cook (CHC) model. Simulation shows that the selective…

We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from (a x b x c) to ((a-1) x (b+1) x c) or ((a+1) x (b-1) x c). Algorithmic realization of…

We calculate parton and generalized parton distributions in Minkowski space using a scalar propagator with a pair of complex conjugate poles. Correct spectral and support properties are obtained only after careful analytic continuation from…