Publications related to Hamiltonian field theory

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

Covariant formulation of relativistic mechanics

Miguel Alexandre Ribeiro Correia

Accretion disks surrounding compact objects, and other environmental factors, deviate satellites from geodetic motion. Unfortunately, setting up the equations of motion for such relativistic trajectories is not as simple as in Newtonian mechanics. The prin ...

American Physical Society2022

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Ignacio Pagonabarraga Mora, Elena Sesé Sansa

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques ind ...

AIP Publishing2022

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

Collective behavior and emerging patterns in dense dry aligning active matter

Elena Sesé Sansa

In this thesis, we study systems of active particles interacting via generic torques of different nature. We analyze the phase behavior of these systems, which results from the interplay between self-propulsion, excluded-volume and torques. We tackle the p ...

EPFL2022

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

Momentum space CFT correlators for Hamiltonian truncation

Matthew Thomas Walters

We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding ...

Springer Nature2020

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

Dynamical Reduced Basis Methods for Hamiltonian Systems

Cecilia Pagliantini

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the ric ...

Springer2021

Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

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 ...

2018

Geometric Model Order Reduction

Babak Maboudi Afkham

During the past decade, model order reduction (MOR) has been successfully applied to reduce the computational complexity of elliptic and parabolic systems of partial differential equations (PDEs). However, MOR of hyperbolic equations remains a challenge. S ...

EPFL2018

Symplectic Model-Reduction with a Weighted Inner Product

Jan Sickmann Hesthaven, Babak Maboudi Afkham

In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems, symplectic model redu ...

2018

A multisymplectic integrator for elastodynamic frictionless impact problems

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures, Alejandro Marcos Aragon, Mathieu Desbrun

We present a structure preserving numerical algorithm for the collision of elastic bodies. Our integrator is derived from a discrete version of the field-theoretic (multisymplectic) variational description of nonsmooth Lagrangian continuum mechanics, combi ...

Elsevier2017

Noether Theorems and Quantum Anomalies

Tudor Ratiu

A quantum anomaly is the breaking of symmetry with respect to some transformations after the quantization of a classical Hamiltonian or Lagrangian system. It is shown that both the Noether theorems (including their infinite-dimensional versions) and the ex ...

Springer Verlag2017

Structure preserving model reduction of parametric Hamiltonian systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

While reduced-order models (ROMs) are popular for approximately solving large systems of differential equations, the stability of reduced models over long-time integration remains an open question. We present a greedy approach for ROM generation of paramet ...

2017

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

Dynamic Optimization of Constrained Semi-Batch Processes Using Pontryagin’s Minimum Principle – An Effective Quasi-Newton Approach

Dominique Bonvin

This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirect methods exist. Direct methods are often the methods of choice, but they exhibit certain limitations related to the compromise ...

Elsevier2017

Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive delta-impurities symmetrically situated around the origin

Fabio Rinaldi

In this presentation, we wish to provide an overview of the spectral features for the self-adjoint Hamiltonian of the three-dimensional isotropic harmonic oscillator perturbed by either a single attractive delta-interaction centered at the origin or by a p ...

St Petersburg Natl Research Univ Information Technologies, Mech & Optics2016

Bloch theorem with revised boundary conditions applied to glide and screw symmetric, quasi-one-dimensional structures

Florian Paul Robert Maurin

Bloch theorem is useful for analyzing wave propagation in periodic systems. It has been widely used to determine the energy bands of various translationally-periodic crystals and with the advent of nanoscale structures like nanotubes, it has been extended ...

Elsevier2016

The Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

Fabio Rinaldi

In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive delta'-interaction, of strength beta, centred at 0 (the bottom of the confining parabolic potential), that was rigorou ...

Iop Publishing Ltd2016