Publications related to Schrödinger picture

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...

EPFL2024

Large-cage occupation and quantum dynamics of hydrogen molecules in sII clathrate hydrates

Richard Gaal, Livia Eleonora Bove Kado, Umbertoluca Ranieri

Hydrogen clathrate hydrates are ice-like crystalline substances in which hydrogen molecules are trapped inside polyhedral cages formed by the water molecules. Small cages can host only a single H-2 molecule, while each large cage can be occupied by up to f ...

Aip Publishing2024

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

A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid

Jiri Vanicek, Seonghoon Choi

One of the most accurate methods for solving the time-dependent Schrödinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid points, we let the grid ...

2019

The S-matrix bootstrap IV: multiple amplitudes

João Miguel Augusto Penedones Fernandes, Jonathan Campbell Toledo

We explore the space of consistent three-particle couplings in Z(2)-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity, analyticity and crossing symmetry of the two-to-two scattering amplitud ...

Springer Nature2019

On sums of eigenvalues of elliptic operators on manifolds

Joachim Stubbe

We use the averaged variational principle introduced in a recent article on graph spectra [10] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kroger's bound ...

European Mathematical Soc2017

Nonadiabatic effects in electronic and nuclear dynamics

Majed Chergui, Ursula Röthlisberger, Jiri Vanicek, Martin Peter Bircher, Tomas Zimmermann, Elisa Liberatore, Aurélien Kevin Fabrice Patoz, Nicholas John Browning

Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by th ...

2017

Geometric Integrators for Nonadiabatic Molecular Quantum Dynamics Induced by the Interaction with the Electromagnetic Field

Aurélien Kevin Fabrice Patoz

Understanding the elementary steps involved in a chemical reaction forms the cornerstone of physical chemistry research. One way to deepen this understanding is by studying chemical and physical processes using linear and nonlinear spectroscopic techniques ...

EPFL2017

Exact diagonalization of SU( N ) Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains using the full SU( N ) symmetry

Frédéric Mila, Pierre Marcel Nataf, Kianna Wan

We present a method for the exact diagonalization of the SU(N) Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global SU(N) group. This generalized scheme is applicable to chains consisting ...

2017

In vivo neurochemical measurements in cerebral tissues using a droplet-based monitoring system

Philippe Renaud, Guillaume Cédric Yves Petitpierre, Bernard Schneider, Arnaud Bertsch, Philippe Colin, Aurélien Thomas

Direct collection of extracellular fluid (ECF) plays a central role in the monitoring of neurological disorders. Current approaches using microdialysis catheters are however drastically limited in term of temporal resolution. Here we show a functional in v ...

Nature Publishing Group2017

Symmetries and optical transitions of hexagonal quantum dots in GaAs/AlGaAs nanowires

Marc-André Dupertuis

We investigate the properties of electronic states and optical transitions in hexagonal GaAs quantum dots within Al0.3Ga0.7As nanowires, grown in axial direction [111]. Such dots are particularly interesting due to their high degree of symmetry. A streamli ...

Amer Physical Soc2015

Spectral series of the Schrodinger operator with delta-potential on a three-dimensional spherically symmetric manifold

Tudor Ratiu

The spectral series of the Schrodinger operator with a delta-potential on a threedimensional compact spherically symmetric manifold in the semiclassical limit as h -> 0 are described. ...

Springer US2013

Symmetry Reduction Of Brownian Motion And Quantum Calogero-Moser Models

Simon Hochgerner

Let Q be a Riemannian G-manifold. This paper is concerned with the symmetry reduction of Brownian motion in Q and ramifications thereof in a Hamiltonian context. Specializing to the case of polar actions, we discuss various versions of the stochastic Hamil ...

World Scientific Publ Co Pte Ltd2013

Impact of saturation on the polariton renormalization in III-nitride based planar microcavities

Nicolas Grandjean, Jean-François Carlin, Raphaël Butté, Jacques Levrat, Eric Feltin, Georg Rossbach

It has been widely observed that an increasing carrier density in a strongly coupled semiconductor microcavity (MC) alters the dispersion of cavity polaritons, below and above the condensation threshold. The interacting nature of cavity polaritons stems fr ...

Amer Physical Soc2013

Measurement of Form-Factor-Independent Observables in the Decay B-0 -> K*(0)mu(+)mu(-)

Olivier Schneider, Aurelio Bay, Yiming Li, Guido Haefeli, Frédéric Blanc, Christoph Frei, Tatsuya Nakada, Julien Rouvinet, Barinjaka Rakotomiaramanana, Raluca Anca Muresan, Michel De Cian, Johan Luisier, Luca Pescatore, Anne Keune, Jian Wang, Yi Zhang, Lei Zhang, Jessica Prisciandaro, Mark Tobin, Minh Tâm Tran, Niko Neufeld, Matthew Needham, Marc-Olivier Bettler, Greig Alan Cowan, Maurizio Martinelli, Vladislav Balagura, Donal Patrick Hill, Cédric Potterat, Liang Sun, Pietro Marino, Jean Wicht, Ilya Komarov, Plamen Hristov Hopchev, Bastien Luca Muster, Frédéric Guillaume Dupertuis, Pierre Jaton, Joël Bressieux, Songmei Wu, Hans Dijkstra, Gerhard Raven, Peter Clarke, , , , , , ,

Trace Identities For Commutators, With Applications To The Distribution Of Eigenvalues

Joachim Stubbe

We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schrodinger operators and Schrodinger operators on immersed manifolds. In particular, we prove bounds on t ...

2011

Accelerating Calculations of Ultrafast Time-Resolved Electronic Spectra with Efficient Quantum Dynamics Methods

Jiri Vanicek, Miroslav Sulc, Marius Wehrle

We explore three specific approaches for speeding up the calculation of quantum time correlation functions needed for time-resolved electronic spectra. The first relies on finding a minimum set of sufficiently accurate electronic surfaces. The second incre ...

2011

A Framework for Numerical Simulations of Structure Formation

Claude Becker

In the absence of a full analytical treatment of nonlinear structure formation in the universe, numerical simulations provide the critical link between the properties of the underlying model and the features of the observed structures. Currently N-body sim ...

EPFL2011

Universal monotonicity of eigenvalue moments and sharp Lieb-Thirring inequalities

Joachim Stubbe

We show that phase space bounds on the eigenvalues of Schrodinger operators can be derived from universal bounds recently obtained by E. M. Harrell and the author via a monotonicity property with respect to coupling constants. In particular, we provide a n ...

2010

Universal Bounds And Semiclassical Estimates For Eigenvalues Of Abstract Schrodinger Operators

Joachim Stubbe

We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operato ...

2010