Rémi Robin
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View article: Unconditionally stable time discretization of Lindblad master equations in infinite dimension using quantum channels
Unconditionally stable time discretization of Lindblad master equations in infinite dimension using quantum channels Open
We examine the time discretization of Lindblad master equations in infinite-dimensional Hilbert spaces. Our study is motivated by the fact that, with unbounded Lindbladian, projecting the evolution onto a finite-dimensional subspace using …
View article: A posteriori error estimates for the Lindblad master equation
A posteriori error estimates for the Lindblad master equation Open
We are interested in the simulation of open quantum systems governed by the Lindblad master equation in an infinite-dimensional Hilbert space. To simulate the solution of this equation, the standard approach involves two sequential approxi…
View article: Shape Optimization of Harmonic Helicity in Toroidal Domains
Shape Optimization of Harmonic Helicity in Toroidal Domains Open
View article: Existence of surfaces optimizing geometric and PDE shape functionals under reach constraint
Existence of surfaces optimizing geometric and PDE shape functionals under reach constraint Open
This article deals with the existence of hypersurfaces minimizing general shape functionals under certain geometric constraints. We consider as admissible shapes orientable hypersurfaces satisfying a so-called reach condition, also known a…
View article: Shape optimization of harmonic helicity in toroidal domains
Shape optimization of harmonic helicity in toroidal domains Open
In this paper, we introduce a new shape functional defined for toroidal domains that we call harmonic helicity, and study its shape optimization. Given a toroidal domain, we consider its associated harmonic field. The latter is the magneti…
View article: Convergence of bipartite open quantum systems stabilized by reservoir engineering
Convergence of bipartite open quantum systems stabilized by reservoir engineering Open
We study a generic family of Lindblad master equations modeling bipartite open quantum systems, where one tries to stabilize a quantum system by carefully designing its interaction with another, dissipative, quantum system-a strategy known…
View article: Stability and decoherence rates of a GKP qubit protected by dissipation
Stability and decoherence rates of a GKP qubit protected by dissipation Open
We analyze an experimentally accessible Lindblad master equation for a quantum harmonic oscillator. It approximately stabilizes finite-energy periodic grid states called Gottesman-Kitaev-Preskill (GKP) states, that can be used to encode an…
View article: Small-time global null controllability of generalized Burgers’ equations
Small-time global null controllability of generalized Burgers’ equations Open
In this paper, we study the small-time global null controllability of the generalized Burgers’ equations y t + γ| y | γ -1 y x — y xx = u ( t ) on the segment [0, 1]. The scalar control u ( t ) is uniform in space and plays a role similar …
View article: Stability and decoherence rates of a GKP qubit protected by dissipation⋆
Stability and decoherence rates of a GKP qubit protected by dissipation⋆ Open
We analyze an experimentally accessible Lindblad master equation for a quantum harmonic oscillator. It approximately stabilizes finite-energy periodic grid states called Gottesman-Kitaev-Preskill (GKP) states, that can be used to encode an…
View article: Chattering phenomenon in quantum optimal control
Chattering phenomenon in quantum optimal control Open
We present a quantum optimal control problem which exhibits a chattering phenomenon. This is the first instance of such a process in quantum control. Using the Pontryagin Maximum Principle and a general procedure due to V F Borisov and M I…
View article: Contrôle et optimisation de systèmes physiques : applications à la mécanique quantique et au confinement magnétique dans les stellarators.
Contrôle et optimisation de systèmes physiques : applications à la mécanique quantique et au confinement magnétique dans les stellarators. Open
This PhD manuscript deals with the optimization and control of several physical systems. It is divided into three parts.The first part is devoted to stellarators. This type of nuclear fusion reactor poses many challenges related to optimiz…
View article: Small-time global null controllability of generalized Burgers' equations
Small-time global null controllability of generalized Burgers' equations Open
In this paper, we study the small-time global null controllability of the generalized Burgers' equations $y_t + γ|y|^{γ-1}y_x-y_{xx}=u(t)$ on the segment $[0,1]$. The scalar control $u(t)$ is uniform in space and plays a role similar to th…
View article: Existence of surfaces optimizing geometric and PDE shape functionals under reach constraint
Existence of surfaces optimizing geometric and PDE shape functionals under reach constraint Open
This article deals with the existence of hypersurfaces minimizing general shape functionals under certain geometric constraints. We consider as admissible shapes orientable hypersurfaces satisfying a so-called reach condition, also known a…
View article: Minimization of magnetic forces on stellarator coils
Minimization of magnetic forces on stellarator coils Open
Magnetic confinement devices for nuclear fusion can be large and expensive. Compact stellarators are promising candidates for cost-reduction, but introduce new difficulties: confinement in smaller volumes requires higher magnetic field, wh…
View article: Optimal shape of stellarators for magnetic confinement fusion
Optimal shape of stellarators for magnetic confinement fusion Open
View article: Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations
Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations Open
View article: Optimal shape of stellarators for magnetic confinement fusion
Optimal shape of stellarators for magnetic confinement fusion Open
We are interested in the design of stellarators, devices for the production of controlled nuclear fusion reactions alternative to tokamaks. The confinement of the plasma is entirely achieved by a helical magnetic field created by the compl…
View article: Projet SNCF maths-entreprises AMIES.
Projet SNCF maths-entreprises AMIES. Open
View article: A Two-Step Model of Human Entrainment: A Quantitative Study of Circadian Period and Phase of Entrainment
A Two-Step Model of Human Entrainment: A Quantitative Study of Circadian Period and Phase of Entrainment Open
View article: Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations
Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations Open
In the physics literature it is common to see the rotating wave approximation andthe adiabatic approximation used "in cascade" to justify the use of chirped pulses for two-level quantum systems driven by one external field, in particular w…
View article: On the compatibility of the adiabatic and rotating wave approximations for robust population transfer in qubits
On the compatibility of the adiabatic and rotating wave approximations for robust population transfer in qubits Open
In the physics literature it is common to see the rotating wave approximation and the adiabatic approximation used to justify the use of chirped pulses for two-level quantum systems driven by one external field, in particular when the re…
View article: Calibration of a magnetometer array using motion capture equipment
Calibration of a magnetometer array using motion capture equipment Open
This paper studies the problem of calibrating an array of single‐axis magnetometers in an unknown static inhomogeneous magnetic field using motion capture equipment. A proof of identifiability is given, practical identifiability of calibra…