Related papers: A Dynamical Lie-Algebraic Framework for Hamiltonia…

Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…

In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…

A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is…

A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…

Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…

We present a non-perturbative framework for deriving effective Hamiltonians that describe low-energy excitations in quantum many-body systems. The method combines block diagonalization based on the Cederbaum--Schirmer--Meyer transformation…

In this work, a unified Lie-algebraic formulation of catability is constructed for relativistic quantum systems with arbitrary spin within this framework. In this case, the analysis starts with constructing catability as a quantitative…

We study the kick dynamics of periodically driven quantum systems, and provide a timeindependent effective Hamiltonian with the analytical form to reasonably describe the effective dynamics in a long timescale. It is shown that the…

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…

Dynamics and uncertainty are essential features of real-life argumentation, and many recent studies have focused on integrating both aspects into Dung's well-known abstract Argumentation Frameworks (AFs). This paper proposes a combination…

Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It, therefore,…

This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and…

Engineering quantum bath networks through non-Hermitian subsystem Hamiltonians has recently emerged as a promising strategy for qubit cooling, state stabilization, and fault-tolerant quantum computation. However, scaling these systems while…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

Characterizing quantum processes is crucial for the execution of quantum algorithms on available quantum devices. A powerful framework for this purpose is the Quantum Model Learning Agent (QMLA) which characterizes a given system by…

Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…

Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…

A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…