Publications related to Hamiltonian mechanics

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Amer Mathematical Soc2024

Variational quantum time evolution without the quantum geometric tensor

Giuseppe Carleo, Riccardo Rossi, Julien Sebastian Gacon, Jannes Willy E. Nys, Stefan Woerner

Realand imaginary -time quantum state evolutions are crucial in physics and chemistry for exploring quantum dynamics, preparing ground states, and computing thermodynamic observables. On near -term devices, variational quantum time evolution is a promising ...

College Pk2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation

Jan Sickmann Hesthaven, Nicolò Ripamonti, Cecilia Pagliantini

. High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of para ...

AMER MATHEMATICAL SOC2023

Towards a nonperturbative construction of the S-matrix

Francesco Riva, Matthew Thomas Walters, Brian Quinn Henning

We present a nonperturbative recipe for directly computing the S-matrix in strongly-coupled QFTs. The method makes use of spectral data obtained in a Hamiltonian framework and can be applied to a wide range of theories, including potentially QCD. We demons ...

SPRINGER2023

Quantum circuits for solving local fermion-to-qubit map- pings

Giuseppe Carleo, Jannes Willy E. Nys

Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the lo-cality of the operators comes at the ex-pense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the l ...

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2023

High-order geometric integrators for the variational Gaussian approximation

Jiri Vanicek, Roya Moghaddasi Fereidani

Among the single-trajectory Gaussian-based methods for solving the time-dependent Schrödinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller’s original thawed Gaussian approximation, it is symplectic, conse ...

2023

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Jan Sickmann Hesthaven, Nicolò Ripamonti, Cecilia Pagliantini

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the ...

EDP SCIENCES S A2022

State-to-state surface scattering of methane studied by bolometric infrared laser tagging detection

Bo-Jung Chen

State-to-state molecule/surface scattering experiments prepare the incident molecules in a specific quantum state and measure the quantum state distribution of the scattered molecules. The comparison of state resolved experiments with theory can serve as s ...

EPFL2022

Einstein's quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism

Fabrizio Minganti

The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbeinlike formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones, rendering th ...

AMER PHYSICAL SOC2022

Hamiltonian mechanics

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WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Variational quantum time evolution without the quantum geometric tensor

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation

Towards a nonperturbative construction of the S-matrix

Quantum circuits for solving local fermion-to-qubit map- pings

High-order geometric integrators for the variational Gaussian approximation

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

State-to-state surface scattering of methane studied by bolometric infrared laser tagging detection

Einstein's quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism

High-order geometric integrators for the variational Gaussian approximation

Towards a nonperturbative construction of the S-matrix

Einstein's quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism

State-to-state surface scattering of methane studied by bolometric infrared laser tagging detection

Variational quantum time evolution without the quantum geometric tensor

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Quantum circuits for solving local fermion-to-qubit map- pings

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation