Related papers: Time-Dependent Lagrangian Biomechanics
We formulate equations of motion and conservation laws for a quantum many-body system in a co-moving Lagrangian reference frame. It is shown that generalized inertia forces in the co-moving frame are described by Green's deformation tensor…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
A time dependent generalization of the Ginzburg -Landau Lagrangian is proposed. It contains two terms determining the time dependence and the four arbitrary scalar functions. Relevant equations, which coincide with equations following from…
We illustrate how the different kinds of constraints acting on an impulsive mechanical system can be clearly described in the geometric setup given by the configuration space--time bundle $\pi_t:\mathcal{M} \to \mathbb{E}$ and its first jet…
In this essay, we wish to propose a general principle: \it{the equation of motion or dynamics of a fundamental force should not be prescribed but instead be entirely driven by geometry of the appropriate spacetime manifold, and the equation…
We consider a spin-boson Hamiltonian which is generalized such that the Hamiltonians for the system ($\hat{H}_{\cal S}$) and the interaction with the environment ($\hat{H}_{\rm int}$) do not commute with each other. Considering a…
We develop Hamiltonian mechanics on Aristotelian manifolds, which lack local boost symmetry and admit absolute time and space structures. We construct invariant phase space dynamics, define free Hamiltonians, and establish a generalized…
Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we…
In this paper, we derive an accelerated continuous-time formulation of Adam by modeling it as a second-order integro-differential dynamical system. We relate this inertial nonlocal model to an existing first-order nonlocal Adam flow through…
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
We introduce a framework for resolving electron-hole dynamics within wavefunction-based multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory. Central to this framework is a time-domain generalization of the extended Koopmans'…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
In this work, we analyze the evolution of the phase-space structures of KCN molecular system as a function of the vibrational energy using Lagrangian descriptors. For low energies, the motion is mostly regular around the absolute minimum of…
I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a…
The time dependence of deviations from the Gaussian state in a freely cooling homogeneous system of smooth inelastically colliding spheres is investigated by kinetic theory. We determine the full time dependence of the coefficients of an…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…
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 study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…