Related papers: A bivariational, stable and convergent hierarchy f…
The coupled cluster iteration scheme is analysed as a multivariate discrete-time map using nonlinear dynamics and synergetics. The nonlinearly coupled set of equations to determine the cluster amplitudes are driven by a fraction of the…
Dynamics of a cluster of chaotic oscillators on a network are studied using coupled maps. By introducing the association schemes, we obtain coupling strength in the adjacency matrices form, which satisfies Markov matrices property. We…
We show how conformal invariance predicts the functional form of two-point correlators in one-dimensional periodic quantum systems. Numerical evidence for this functional form in a wide class of models --- including long-ranged ones --- is…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex…
The response of a cold atom gas with contact interactions to a smoothly varying external harmonic confinement in the non-adiabatic regime is studied. The time variation of the angular frequency is varied such that the system is, for…
We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central to our discussion is the notion of mutual gravitational energy, which gives rise to the self-energy inner product on mass densities. We consider a…
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
Inspired by the ideas and techniques used in the study of cluster algebras we construct a new class of algebras, called bistellar cluster algebras, from closed oriented triangulated even-dimensional manifolds by performing…
Molecular dynamics simulations were employed to investigate the phase separation process of a two-dimensional active Brownian dumbbell model. We evaluated the time dependence of the typical size of the dense component using the scaling…
Gravitational clustering of a random distribution of point masses is dominated by the effective short-range interactions due to large-scale isotropy. We introduce a one-dimensional cellular automaton to reproduce this effect in the most…
Time series clustering is essential in scientific applications, yet methods for functional time series, collections of infinite-dimensional curves treated as random elements in a Hilbert space, remain underdeveloped. This work presents…
We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…
In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used $ab~initio$ methods, which is critically limited by its non-unitary nature. The unitary modification as an ideal solution to the problem is,…
In a Newtonian system with localized interactions the whole set of particles is naturally decomposed into dynamical clusters, defined as finite groups of particles having an influence on each other's trajectory during a given interval of…