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Despite the successes of machine learning methods in physical sciences, prediction of the Hamiltonian, and thus electronic properties, is still unsatisfactory. Here, based on graph neural network architecture, we present an extendable…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…
The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…
Molecular quantum magnets adsorbed on surfaces exhibit rich spin and orbital excitations that can be probed by scanning tunneling microscopy with inelastic electron tunneling spectroscopy (STM-IETS). However, the quantitative extraction of…
Port-Hamiltonian systems have gained a lot of attention in recent years due to their inherent valuable properties in modeling and control. In this paper, we are interested in constructing linear port-Hamiltonian systems from time-domain…
We present a scalable Bayesian framework for the analysis of confocal fluorescence spectroscopy data, addressing key limitations in traditional fluorescence correlation spectroscopy methods. Our framework captures molecular motion,…
By analyzing ``exact'' theoretical results from solving the time-dependent Schr\"odinger equation of atoms in few-cycle laser pulses, we established the general conclusion that differential elastic scattering and photo-recombination cross…
We present a general framework for reconstructing effective Hamiltonians from known gravitational energy density profiles in curved spacetime. Starting from local thermal equilibrium and Liouville dynamics, we establish an inverse procedure…
We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the…
A time-dependent completely integrable Hamiltonian system is quantized with respect to time-dependent action-angle variables near an instantly compact regular invariant manifold. Its Hamiltonian depends only on action variables, and has a…
Conceiving a molecule as composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences, and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient…
Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations leaves us with a…
We show how the dynamics of a specific subset of states can be separated from the dynamic of the total quantum state via a time-dependent projector-based formalism of adiabatic elimination. Within our formalism, we assume explicit time…
Hamiltonian parameter estimation is crucial in condensed matter physics, but time and cost consuming in terms of resources used. With advances in observation techniques, high-resolution images with more detailed information are obtained,…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…