Related papers: Variational approximations to homoclinic snaking i…
It is well known that the dynamics of a Hamiltonian system depends crucially on whether or not it possesses nonlinear resonances. In the generic case, the set of nonlinear resonances consists of independent clusters of resonantly…
A hybrid asymptotic-numerical theory is developed to analyze the effect of different types of localized heterogeneities on the existence, linear stability, and slow dynamics of localized spot patterns for the two-component Schnakenberg…
Partial solvability plays an important role in the context of statistical mechanics, since it has turned out to be closely related to the emergence of quantum many-body scar states, i.e., exceptional energy eigenstates which do not obey the…
In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the…
We study the dynamics of pairs of connected masses in the plane, when nonholonomic (knife-edge) constraints are realized by forces of viscous friction, in particular its relation to constrained dynamics, and its approximation by the method…
Recent advance in quantum simulations of interacting photons using superconducting circuits offers opportunities for investigating the Bose-Hubbard model in various geometries with hopping coefficients and self-interactions tuned to both…
A method is proposed to improve the accuracy of approximate techniques for strongly correlated electrons that use reduced Hilbert spaces. As a first step, the method involves a change of basis that incorporates exactly part of the short…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
Nonlinear stripe patterns occur in many different systems, from the small scales of biological cells to geological scales as cloud patterns. They all share the universal property of being stable at different wavenumbers $q$, i.e., they are…
We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, devising an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are…
A problem of practical significance is the analysis of large, spatially distributed data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show that the spatial correlations between variables can…
An analytical model that describes the interactive buckling of a thin-walled I-section strut under pure compression based on variational principles is presented. A formulation combining the Rayleigh--Ritz method and continuous displacement…
We have devised a variational sinc collocation method (VSCM) which can be used to obtain accurate numerical solutions to many strong-coupling problems. Sinc functions with an optimal grid spacing are used to solve the linear and non-linear…
We study solvable spin chains where either fields or couplings vary linearly in space and create a sandwich-like structure of the ground state. We find that the entanglement entropy between two halves of a chain varies logarithmically with…
Classical Hamiltonian spin systems are continuous dynamical systems on the symplectic phase space $(S^2)^n$. In this paper we investigate the underlying geometry of a time discretization scheme for classical Hamiltonian spin systems called…
A prominent spatiotemporal failure mode of frictional systems is self-healing slip pulses, which are propagating solitonic structures that feature a characteristic length. Here, we numerically derive a family of steady state slip pulse…
We consider the problem of simultaneous variable selection and constant coefficient identification in high-dimensional varying coefficient models based on B-spline basis expansion. Both objectives can be considered as some type of model…
The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement.…
The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal a surprising asymptotic conical structure in critical sample…
We provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes…