Related papers: An Energy-based, always Index $\le1$ and Structura…
Minimization of energy functionals is based on a discretization by the finite element method and optimization by the trust-region method. A key tool is a local evaluation of the approximated gradients together with sparsity of the resulting…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
This paper presents a port-Hamiltonian formulation of hysteretic energy storage elements. First, we revisit the passivity property of backlash-driven storage elements by presenting a family of storage functions associated to the…
A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A…
The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping…
Irreversible Port Hamiltonian Systems are departure of Port Hamiltonian Systems as they are generated not only by a Hamiltonian function but also by an entropy function and defined with respect to a quasi-Poisson bracket which embeds the…
We present an efficient approach to the electron correlation problem that is well-suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. %which is based on orbital optimization of electron…
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…
We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid & Wihler, Math. Comp. 89 (2020), Calcolo 57 (2020)] satisfies an energy…
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled…
The mechanical model of a thin plate with boundary control and observation is presented as a port-Hamiltonian system (pHs), both in vectorial and tensorial forms: the Kirchhoff-Love model of a plate is described by using a Stokes-Dirac…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical study of the finite size $2$-spin spherical model using both…
A method for finding the exact analytical solutions for the bulk and edge energy levels and corresponding eigenstates for all commensurate Aubry-Andr\'e/Harper single-particle models under open boundary conditions is presented here, both…
Electrical circuits offer a unique platform to explore physical phenomena, from topology to non-Hermitian effects. Investigations of the fundamental properties of this metamaterial platform are crucial to distinguish observed/measured…
Future developments of lighter, more compact and powerful motors-driven by environmental and sustainability considerations in the transportation industry-involve higher stresses, currents and electromagnetic fields. Strong couplings between…
This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in…
When electron correlations are important it is often necessary to use numerical methods to solve the Hamiltonian for a finite system (cluster) "exactly". Unfortunately, such methods are restricted to small systems. We propose to combine the…
Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic case is well-established, very few…