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We introduce a method for solving a self consistent electronic calculation within localized atomic orbitals, that allows us to converge to the complete basis set (CBS) limit in a stable, controlled, and systematic way. We compare our…
We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bose-gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-like Hamiltonian,…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
We propose a box and ball system with a periodic boundary condition (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent with the…
This paper presents algorithms for the included-sums and excluded-sums problems used by scientific computing applications such as the fast multipole method. These problems are defined in terms of a $d$-dimensional array of $N$ elements and…
A new integrable lattice system is introduced, and its integrable discretizations are obtained. A B\"acklund transformation between this new system and the Toda lattice, as well as between their discretizations, is established.
Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the…
We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)]. The approach is based on merging the matrix product state (MPS) formalism with the method…
A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical close to TC model [7] is presented.…
We quantise the reduced theory obtained by substituting the soliton solutions of affine Toda theory into its symplectic form. The semi-classical S-matrix is found to involve the classical Euler dilogarithm.
We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the Sklyanin bracket, and use it to derive a multi-Hamiltonian structure for a set of integrable systems that includes…
We present an algorithm to reduce the coloured box-ball system, a one dimensional integrable cellular automaton described by motions of several colour (kind) of balls, into a simpler monochrome system. This algorithm extracts the colour…
We introduce the notion of a \emph{braided dihedral set} (BDS) to describe set-theoretical solutions of the Yang-Baxter equation (YBE) that furnish representations of the infinite dihedral group on the Cartesian square of the underlying…
The numbers $f_\lambda$ of standard tableaux of shape $\lambda\vdash n$ satisfy 2 fundamental recursions: $f_\lambda = \sum f_{\lambda^-}$ and $(n + 1)f_\lambda=\sum f_{\lambda^+}$, where $\lambda^-$ and $\lambda^+$ run over all shapes…
By using an elementary matrix approach, based on the technique of discrete Toda equation, we construct subtraction-free rational and piecewise linear transformations associated with various combinatorial algorithms, including the RSK…
In this work we analyze a non--interacting one dimensional polymer Bose--Einstein condensate in an harmonic trap within the semiclassical approximation. We use an effective Hamiltonian coming from the polymer quantization that arises in…
A nonautonomous version of the ultradiscrete hungry Toda lattice with a finite lattice boundary condition is derived by applying reduction and ultradiscretization to a nonautonomous two-dimensional discrete Toda lattice. It is shown that…
Inspired by G. Frieden's recent work on the geometric R-matrix for affine type A crystal associated with rectangular shaped Young tableaux, we propose a method to construct a novel family of discrete integrable systems which can be regarded…
The algebraic and Hamiltonian structures of the multicomponent dispersionless Benney and Toda hierarchies are studied. This is achieved by using a modified set of variables for which there is a symmetry between the basic fields. This…
In this paper we continue our study of the geometric properties of full symmetric Toda systems from \cite{CSS14,CSS17,CSS19}. Namely we describe here a simple geometric construction of a commutative family of vector fields on compact…