Concept
Hamiltonian mechanics
Related publications (117)
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 Soc2024Variational 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 Pk2024Leveraging 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 and momentum parameter that allows u ...
2024Adaptive 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 SOC2023Towards 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 ...
SPRINGER2023Quantum 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 QUANTENWISSENSCHAF2023High-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 ...
2023Rank-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 A2022State-to-state surface scattering of methane studied by bolometric infrared laser tagging detection
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 ...
EPFL2022Einstein's quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism
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