Publications associées à Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

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

Cecilia Pagliantini, Jan Sickmann Hesthaven, Nicolò Ripamonti

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

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

Structure-Preserving Reduced Basis Methods For Poisson Systems

Cecilia Pagliantini, Jan Sickmann Hesthaven

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

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

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

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation

Jiri Vanicek, Seonghoon Choi

Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian ...

2019

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

Cecilia Pagliantini, Jan Sickmann Hesthaven

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

Babak Maboudi Afkham, Jan Sickmann Hesthaven

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

Structure preserving model reduction of parametric Hamiltonian systems

Babak Maboudi Afkham, Jan Sickmann Hesthaven

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

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

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

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

Analysis of adiabatic trapping for quasi-integrable area-preserving maps

Cedric Jean-François Hernalsteens, Massimo Giovannozzi

Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinea ...

American Physical Society2014

A class of Neumann type systems and its application

Jinbing Chen

A class of Neumann type systems are derived separating the spatial and temporal variables for the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation and the modified Korteweg-de Vries (mKdV) hierarchy. The Lax-Moser matrix of Neumann type s ...

International Press2012

Geometry of nonabelian charged fluids

Tudor Ratiu, François Gay-Balmaz

The goal of this paper is to derive the Hamiltonian structure of polarized and magnetized Euler-Maxwell fluids by reduction of the canonical symplectic form on phase space, and to generalize the dynamics to the nonabelian case. The Hamiltonian function we ...

2011

Looping probabilities of elastic chains: A path integral approach

John Maddocks, Ludovica Cotta-Ramusino

We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit ...

2010