Hamiltonian mechanics ≈ Hamiltonian mechanics
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Hamiltonian Neural Networks Open
Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models t…
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Covariant phase space with boundaries Open
The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically t…
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Contact Hamiltonian Dynamics: The Concept and Its Use Open
We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical mechanics. Some relevant examples are provi…
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Structure and structure-preserving algorithms for plasma physics Open
Hamiltonian and action principle (HAP) formulations of plasma physics are reviewed for the purpose of explaining structure preserving numerical algorithms. Geometric structures associated with and emergent from HAP formulations are discuss…
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Generalized spin mapping for quantum-classical dynamics Open
We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. E. Runeson and J. O. Richardson, J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equ…
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Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control Open
In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better ge…
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Benchmarking Quasiclassical Mapping Hamiltonian Methods for Simulating Electronically Nonadiabatic Molecular Dynamics Open
Quasi-classical mapping Hamiltonian methods have recently emerged as a promising approach for simulating electronically nonadiabatic molecular dynamics. The classical-like dynamics of the overall system within these methods makes them comp…
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Machine Learning: Deepest Learning as Statistical Data Assimilation Problems Open
We formulate an equivalence between machine learning and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in a feedforward artificial network setti…
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Physics-enhanced neural networks learn order and chaos Open
Artificial neural networks are universal function approximators. They can forecast dynamics, but they may need impractically many neurons to do so, especially if the dynamics is chaotic. We use neural networks that incorporate Hamiltonian …
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Open system trajectories specify fluctuating work but not heat Open
Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated. Y…
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Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics Open
Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent …
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Communication: Note on detailed balance in symmetrical quasi-classical models for electronically non-adiabatic dynamics Open
It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the…
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Entropic Dynamics Open
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints ap…
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Hamiltonian Nullspace Shuttles Open
We present a method to explore the effective nullspace of nonlinear inverse problems without Monte Carlo sampling. This is based on the construction of an artificial Hamiltonian system where a model is treated as a high‐dimensional particl…
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Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control Open
In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN i…
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Explicit symplectic algorithms based on generating functions for charged particle dynamics Open
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term acc…
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Accessing Many-Body Localized States through the Generalized Gibbs Ensemble Open
We show how the thermodynamic properties of large many-body localized systems can be studied using quantum Monte Carlo simulations. We devise a heuristic way of constructing local integrals of motion of high quality, which are added to the…
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Energy management of hybrid vehicles with state constraints: A penalty and implicit Hamiltonian minimization approach Open
When designing hybrid vehicles, the energy management is formulated as an optimal control problem. The Pontryagin's minimum principle represents a powerful methodology capable of solving the energy management offline. Moreover, the Pontrya…
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Characterizing breathing dynamics of magnetic skyrmions and antiskyrmions within the Hamiltonian formalism Open
We derive an effective Hamiltonian system describing the low energy dynamics\nof circular magnetic skyrmions and antiskyrmions. Using scaling and symmetry\narguments we model (anti-)skyrmion dynamics through a finite set of coupled,\ncanon…
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Reducing the two-body problem in scalar-tensor theories to the motion of a test particle: A scalar-tensor effective-one-body approach Open
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Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium Open
An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relat…
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Learning Hamiltonian dynamics with reservoir computing Open
Reconstructing the Kolmogorov-Arnold-Moser (KAM) dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the s…
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Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics Open
We show that a novel, general phase space mapping Hamiltonian for nonadiabatic systems, which is reminiscent of the renowned Meyer-Miller mapping Hamiltonian, involves a commutator variable matrix rather than the conventional zero-point-en…
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Performance evaluation of the symmetrical quasi-classical dynamics method based on Meyer-Miller mapping Hamiltonian in the treatment of site-exciton models Open
The symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC) shows the great potential in the treatment of the nonadiabatic dynamics of complex systems. We performed the comprehensive benchmark cal…
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Exact dynamics of two ultra-cold bosons confined in a one-dimensional double-well potential Open
The dynamics of two ultra-cold bosons confined in a one-dimensional double-well potential is studied. We compare the exact dynamics governed by a full two-body Hamiltonian with the dynamics obtained in a two-mode model approximation. We sh…
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Phase space analysis of the dynamics on a potential energy surface with an entrance channel and two potential wells Open
In this paper, we unveil the geometrical template of phase space structures that governs transport in a Hamiltonian system described by a potential energy surface with an entrance/exit channel and two wells separated by an index-1 saddle. …
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Long-term dynamics driven by resonant wave–particle interactions: from Hamiltonian resonance theory to phase space mapping Open
In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant traject…
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Hamiltonian Generative Networks Open
The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful prope…
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Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control Open
Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions.Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning.This motivates…
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The Entropic Dynamics Approach to Quantum Mechanics Open
Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codifie…