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 ...

Amer Physical Soc2024

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 ...

Springer Nature2023

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

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

Structure-preserving approaches and data-driven closure modeling for model order reduction

Nicolò Ripamonti

In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...

EPFL2022

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

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

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

Time-evolution of local information: Thermalization dynamics of local observables

Loïc Jean Pierre Herviou

Quantum many-body dynamics generically result in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal st ...

SCIPOST FOUNDATION2022

Structure-Preserving Reduced Basis Methods For Poisson Systems

Jan Sickmann Hesthaven, Cecilia Pagliantini

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

AMER MATHEMATICAL SOC2021

Scattering Map for the Vlasov–Poisson System

Klaus Martin Widmayer

We construct (modified) scattering operators for the Vlasov–Poisson system in three dimensions, mapping small asymptotic dynamics as t→−∞ to asymptotic dynamics as t→+∞. The main novelty is the construction of modified wave operators, but we also obtain a ...

2023

A unified framework for Hamiltonian deep neural networks

Giancarlo Ferrari Trecate, Clara Lucía Galimberti, Liang Xu

Training deep neural networks (DNNs) can be difficult due to the occurrence of vanishing/explod- ing gradients during weight optimization. To avoid this problem, we propose a class of DNNs stemming from the time discretization of Hamiltonian systems. The t ...

2021

Invariance principles in the theory and computation of transport coefficients

Federico Grasselli

In this work, we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved quantities being transpo ...

2021

Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

2020

Reduction of the sign problem near T=0 in quantum Monte Carlo simulations

Frédéric Mila, Jonathan D'Emidio

Building on a recent investigation of the Shastry-Sutherland model [S. Wessel et al., Phys. Rev. B 98, 174432 (2018)], we develop a general strategy to eliminate the Monte Carlo sign problem near the zero-temperature limit in frustrated quantum spin models ...

2020

Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?

Jiri Vanicek, Seonghoon Choi

Choosing an appropriate representation of the molecular Hamiltonian is one of the challenges faced by simulations of the nonadiabatic quantum dynamics around a conical intersection. The adiabatic, exact quasidiabatic, and strictly diabatic representations ...

2020

Schwinger pair production from Pade-Borel reconstruction

Adrien Florio

In this work, we show how the knowledge of the first few terms of the Euler-Heisenberg Lagrangian's weak-field expansion in a magnetic field background is enough to reconstruct the pair-production rate in a strong electric field background. To this end, we ...

American Physical Society2020