Publications related to Geometrical and mathematical aspects of the adiabatic theorem of quantum mechanics

On the finite-size Lyapunov exponent for the Schröedinger operator with skew-shift potential

It is known that a one-dimensional quantum particle is localized when subjected to an arbitrarily weak random potential. It is conjectured that localization also occurs for an arbitrarily weak potential generated from the nonlinear skew-shift dynamics: $v_ ...

2019

Weyl-type bounds for Steklov eigenvalues

Joachim Stubbe, Luigi Provenzano

We present upper and lower bounds for Steklov eigenvalues for domains in RN+1 with C-2 boundary compatible with the Weyl asymptotics. In particular, we obtain sharp upper bounds on Riesz-means and the trace of corresponding Steklov heat kernel. The key res ...

EUROPEAN MATHEMATICAL SOC2019

Pattern formation in thin liquid films: from coating-flow instabilities to microfluidic droplets

Gioele Mariano Nicolò Balestra

Nature and technical applications abound with thin viscous flows, ranging from the lava flow on volcanoes to the lubricating layer around confined bubbles in the microchannels of Lab-on-a-Chip devices. Countless are the examples where coating flows arise i ...

EPFL2018

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

Marius Christopher Lemm, Rui Han

We study the one-dimensional discrete Schrödinger operator with the skew-shift potential

2\lambda\cos\left(2\pi \left(\binom{j}{2} \omega+jy+x\right)\right)

. This potential is long conjectured to behave like a random one, i.e., it is expected to produce ...

2018

Criteria for the existence of a potential well

Charles Stuart

We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The deriv ...

Pergamon-Elsevier Science Ltd2017

Path integral approach to the quantum fidelity amplitude

Jiri Vanicek

The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and its applications, suc ...

Royal Soc2016

A generalized mountain-pass theorem: the existence of multiple critical points

Hans-Jörg Ruppen

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...

Springer Heidelberg2016

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Daniel Kressner, André Uschmajew

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...

Elsevier Science Inc2016

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

The motion of a deforming capsule through a corner

Lailai Zhu

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral m ...

Cambridge University Press2015

Geometrical and mathematical aspects of the adiabatic theorem of quantum mechanics

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On the finite-size Lyapunov exponent for the Schröedinger operator with skew-shift potential

Weyl-type bounds for Steklov eigenvalues

Pattern formation in thin liquid films: from coating-flow instabilities to microfluidic droplets

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

Criteria for the existence of a potential well

Path integral approach to the quantum fidelity amplitude

A generalized mountain-pass theorem: the existence of multiple critical points

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

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

The motion of a deforming capsule through a corner

Pattern formation in thin liquid films: from coating-flow instabilities to microfluidic droplets

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

Weyl-type bounds for Steklov eigenvalues

Path integral approach to the quantum fidelity amplitude

Criteria for the existence of a potential well

A generalized mountain-pass theorem: the existence of multiple critical points

On the finite-size Lyapunov exponent for the Schröedinger operator with skew-shift potential

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

The motion of a deforming capsule through a corner