References of "Dubertrand, Rémy"
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See detailAnalytical results for the quantum non-Markovianity of spin ensembles undergoing pure dephasing dynamics
Dubertrand, Rémy ULiege; Cesa, Alexandre ULiege; Martin, John ULiege

in Physical Review. A (2018), 97

We study analytically the non-Markovianity of a spin ensemble, with arbitrary number of spins and spin quantum number, undergoing a pure dephasing dynamics. The system is considered as a part of a larger ... [more ▼]

We study analytically the non-Markovianity of a spin ensemble, with arbitrary number of spins and spin quantum number, undergoing a pure dephasing dynamics. The system is considered as a part of a larger spin ensemble of any geometry with pairwise interactions. We derive exact formulas for the reduced dynamics of the system and for its non-Markovianity as assessed by the witness of Lorenzo et al. [Phys. Rev. A 88, 020102(R) (2013)]. The non-Markovianity is further investigated in the thermodynamic limit when the environment’s size goes to infinity. In this limit and for finite-size systems, we find that the Markovian’s character of the system’s dynamics crucially depends on the range of the interactions. We also show that, when the system and its environment are initially in a product state, the appearance of non-Markovianity is independent of the entanglement generation between the system and its environment. [less ▲]

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See detailAnalytical results for the non-Markovianity of quantum spin ensembles
Dubertrand, Rémy ULiege; Cesa, Alexandre ULiege; Martin, John ULiege

Conference (2018, March)

We study the non-Markovian character of spin ensembles. The ensemble is assumed to be isolated and a subset of spins is taken as the system, while the remaining part of the ensemble is taken as the ... [more ▼]

We study the non-Markovian character of spin ensembles. The ensemble is assumed to be isolated and a subset of spins is taken as the system, while the remaining part of the ensemble is taken as the environment. For a large class of interaction range, we derive analytical expressions for the non-Markovianity [1] following a recently introduced measure [2]. In particular, we investigate the thermodynamic limit and derive conditions to observe a Markovian dynamics or not. For a system of a single spin, it is explicitly shown that our results agree with the other known measures of non-Markovianity. We believe that our work can be used to investigate further the dynamics of fundamental models in condensed matter physics from the new perspective of (non-)Markovianity. [1] R. Dubertrand, A. Cesa, J. Martin, to be submitted [2] S. Lorenzo, F. Plastina, and M. Paternostro, Phys. Rev. A 88 (2013) [less ▲]

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See detailScaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality
Garcia-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand et al

in Physical Review Letters (2017), 118

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1 < K < 2, through large scale numerical simulations and finite-size scaling analysis. We find that ... [more ▼]

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1 < K < 2, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase from an unusual delocalized phase that is ergodic at large scales but strongly nonergodic at smaller scales. In the critical regime, multifractal wave functions are located on a few branches of the graph. Different scaling laws apply on both sides of the transition: a scaling with the linear size of the system on the localized side, and an unusual volumic scaling on the delocalized side. The critical scalings and exponents are independent of the branching parameter, which strongly supports the universality of our results. [less ▲]

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See detailScattering theory of walking droplets in the presence of obstacles
Dubertrand, Rémy ULiege; Hubert, Maxime ULiege; Schlagheck, Peter ULiege et al

in New Journal of Physics (2016), 18

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created ... [more ▼]

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a pilot wave for the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by {\it Couder et al} [Phys. Rev. Lett. {\bf 97}, 154101 (2006)] there have been many attempts to accurately reproduce the experimental results. We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to the Helmholtz equation with Neumann boundary conditions on the obstacle(s) and outgoing boundary conditions at infinity. For a single-slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It stands for a promising candidate to account for the presence of arbitrary boundaries in the walker's dynamics. [less ▲]

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See detailSpectral statistics of chaotic many-body systems
Dubertrand, Rémy ULiege; Muller, Sebastian

in New Journal of Physics (2016), 18

We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or ... [more ▼]

We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. [less ▲]

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See detailOrigin of emission from square-shaped organic microlasers
Bittner, Stefan; Lafargue, C.; Gozhyk, I. et al

in Europhysics Letters (2016), 113

The emission from open cavities with non-integrable features remains a challenging problem of practical as well as fundamental relevance. Square-shaped dielectric microcavities provide a favorable case ... [more ▼]

The emission from open cavities with non-integrable features remains a challenging problem of practical as well as fundamental relevance. Square-shaped dielectric microcavities provide a favorable case study with generic implications for other polygonal resonators. We report on a joint experimental and theoretical study of square-shaped organic microlasers exhibiting a far-field emission that is strongly concentrated in the directions parallel to the side walls of the cavity. A semiclassical model for the far-field distributions is developed that is in agreement with even fine features of the experimental findings. Comparison of the model calculations with the experimental data allows the precise identification of the lasing modes and their emission mechanisms, providing strong support for a physically intuitive ray-dynamical interpretation. Special attention is paid to the role of diffraction and the finite side length. [less ▲]

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See detailMultifractality of quantum wave functions in the presence of perturbations
Dubertrand, Rémy ULiege; Garcia-Mata, Ignacio; Georgeot, Bertrand et al

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2015), 92

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a ... [more ▼]

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model, and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong-enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems. [less ▲]

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See detailThe two scenarios for quantum multifractality breakdown
Georgeot, Bertrand; Dubertrand, Rémy ULiege; Garcia-Mata, Ignacio et al

Scientific conference (2014, June)

Several types of physical systems are characterized by quantum wave func- tions with multifractal properties. In the quantum chaos field, they cor- respond to pseudointegrable systems, with properties ... [more ▼]

Several types of physical systems are characterized by quantum wave func- tions with multifractal properties. In the quantum chaos field, they cor- respond to pseudointegrable systems, with properties intermediate between integrability and chaos. In condensed matter, they include electrons in a disordered potential at the Anderson metal-insulator transition. This multi- fractality leads to particular transport properties and appears in conjunction with specific types of spectral statistics. In parallel, progress in experimental techniques allows to observe finer and finer properties of the wavefunctions of quantum or wave systems, as well as to perform experiments with un- precedented control on the dynamics of the systems studied. In this context, this talk will discuss the robustness of multifractality in presence of footnote- size perturbations. We expose two scenarios for the breakdown of quantum multifractality under the effect of such perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three- dimensional Anderson model at the metal-insulator transition, and show that for different types of perturbation the destruction of multifractal properties always follows one of these two ways. Our results thus suggest that quantum multifractality breakdown is universal and obeys one of these two scenarios depending on the perturbation. We also discuss the experimental implica- tions. [less ▲]

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See detailTwo Scenarios for Quantum Multifractality Breakdown
Dubertrand, Rémy ULiege; Garcia-Mata, Ignacio; Georgeot, Bertrand et al

in Physical Review Letters (2014), 112

We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations ... [more ▼]

We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications. [less ▲]

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See detailRobustness of quantum multifractality
Georgeot, Bertrand; Dubertrand, Rémy ULiege; Garcia-Mata, Ignacio et al

Scientific conference (2014, March)

Several models where quantum wave functions display multifractal properties have been recently identified. In the quantum chaos field, they correspond to pseudointegrable systems, with properties ... [more ▼]

Several models where quantum wave functions display multifractal properties have been recently identified. In the quantum chaos field, they correspond to pseudointegrable systems, with properties intermediate between integrability and chaos. In condensed matter, they include electrons in a disordered potential at the Anderson metal-insulator transition. These multifractality properties lead to particular transport properties and appear in conjunction with specific types of spectral statistics. In parallel, progress in experimental techniques allow to observe finer and finer properties of the wavefunctions of quantum or wave systems, as well as to perform experiments with unprecedented control on the dynamics of the systems studied. In this context, this talk will discuss the robustness of multifractality in presence of small perturbations. We identify two distinct processes of multifractality destruction according to the type of perturbation, and specify a range of parameters where multifractality could indeed be observed in physical systems in presence of imperfections. [less ▲]

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See detailOrigin of the exponential decay of the Loschmidt echo in integrable systems
Dubertrand, Rémy ULiege; Goussev, A

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2014), 89

We address the time decay of the Loschmidt echo, measuring the sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using a semiclassical analysis, we ... [more ▼]

We address the time decay of the Loschmidt echo, measuring the sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using a semiclassical analysis, we show that the Loschmidt echo may exhibit a well-pronounced regime of exponential decay, similar to the one typically observed in quantum systems whose dynamics is chaotic in the classical limit. We derive an explicit formula for the exponential decay rate in terms of the spectral properties of the unperturbed and perturbed Hamilton operators and the initial state. In particular, we show that the decay rate, unlike in the case of the chaotic dynamics, is directly proportional to the strength of the Hamiltonian perturbation. Finally, we compare our analytical predictions against the results of a numerical computation of the Loschmidt echo for a quantum particle moving inside a one-dimensional box with Dirichlet-Robin boundary conditions, and find the two in good agreement. [less ▲]

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See detailMultifractality of quantum wave functions
Dubertrand, Rémy ULiege; Garcia-Mata, Ignacio; Georgeot, Bertrand et al

Poster (2013, September)

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See detailTrace formula for dielectric cavities. III. TE modes
Bogomolny, E; Dubertrand, Rémy ULiege

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2012), 86

The construction of the semiclassical trace formula for resonances with transverse electric polarization for two-dimensional dielectric cavities is discussed. Special attention is given to the derivation ... [more ▼]

The construction of the semiclassical trace formula for resonances with transverse electric polarization for two-dimensional dielectric cavities is discussed. Special attention is given to the derivation of the two first terms of Weyl’s series for the average number of such resonances. The formulas obtained agree well with numerical calculations for dielectric cavities of different shapes. [less ▲]

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See detailTrace formula for chaotic dielectric resonators tested with microwave experiments
Bittner, S; Dietz, B; Dubertrand, Rémy ULiege et al

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2012), 85

We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev ... [more ▼]

We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good qualitative agreement between the experimental data and the predictions of the trace formula. Deviations could be attributed to missing resonances in the measured spectra in accordance with previous experiments [Phys. Rev. E 81, 066215 (2010)]. The investigation of the numerical length pectrum showed good qualitative and reasonable quantitative agreement with the trace formula. It demonstrated, however, the need for higher-order corrections of the trace formula. The application of a curvature correction to the Fresnel reflection coefficients entering the trace formula yielded better agreement, but deviations remained, indicating the necessity of further investigations. [less ▲]

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See detailFidelity for kicked atoms with gravity near a quantum resonance
Dubertrand, Rémy ULiege; Guarneri, I; Wimberger, S

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2012), 85

Kicked atoms under a constant Stark or gravity field are investigated for experimental setups with cold and ultracold atoms. The parametric stability of the quantum dynamics is studied using the fidelity ... [more ▼]

Kicked atoms under a constant Stark or gravity field are investigated for experimental setups with cold and ultracold atoms. The parametric stability of the quantum dynamics is studied using the fidelity. In the case of a quantum resonance, it is shown that the behavior of the fidelity depends on arithmetic properties of the gravity parameter. Close to a quantum resonance, the long-time asymptotics of the fidelity is studied by means of a pseudoclassical approximation introduced by Fishman et al. [J. Stat. Phys. 110, 911 (2003)]. The long-time decay of fidelity arises from the tunneling out of pseudoclassical stable islands, and a simple ansatz is proposed which satisfactorily reproduces the main features observed in numerical simulations. [less ▲]

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See detailFidelity of the near-resonant quantum kicked rotor
Probst, B; Dubertrand, Rémy ULiege; Wimberger, S.

in Journal of Physics: A Mathematical and General (2011), 44

We present a perturbative result for the temporal evolution of the fidelity of the quantum kicked rotor, i.e. the overlap of the same initial state evolved with two slightly different kicking strengths ... [more ▼]

We present a perturbative result for the temporal evolution of the fidelity of the quantum kicked rotor, i.e. the overlap of the same initial state evolved with two slightly different kicking strengths, for kicking periods close to a principal quantum resonance. Based on a pendulum approximation, we describe the fidelity for rotational orbits in the pseudo-classical phase space of a corresponding classical map. Our results are compared to numerical simulations indicating the range of applicability of our analytical approximation. [less ▲]

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See detailTrace formula for dielectric cavities. II. Regular, pseudointegrable, and chaotic examples
Bogomolny, E; Djellali, N; Dubertrand, Rémy ULiege et al

in Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics (2011), 83

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [Phys. Rev. E 78, 056202 (2008)] the trace formula for ... [more ▼]

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [Phys. Rev. E 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudointegrable (pentagon), and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simulations, and experiments based on organic microlasers. [less ▲]

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See detailSpectral properties of a pseudo-integrable map: the general case
Bogomolny, E; Dubertrand, Rémy ULiege; Schmit, C.

in Nonlinearity (2009)

It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In Bogomolny and Schmit (2004 ... [more ▼]

It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In Bogomolny and Schmit (2004 Phys. Rev. Lett. 93 254102) statistical properties of a certain quantized pseudo-integrable map had been calculated analytically but only for a special sequence of matrix dimensions. The purpose of this paper is to obtain the spectral statistics of the same quantum map for all matrix dimensions. [less ▲]

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See detailNear integrable systems
Bogomolny, E.; Dennis, M. R.; Dubertrand, Rémy ULiege

in Journal of Physics: A Mathematical and General (2009)

A two-dimensional circular quantum billiard with unusual boundary conditions introduced by Berry and Dennis (2008 J. Phys. A: Math. Theor. 41 135203) is considered in detail. It is demonstrated that most ... [more ▼]

A two-dimensional circular quantum billiard with unusual boundary conditions introduced by Berry and Dennis (2008 J. Phys. A: Math. Theor. 41 135203) is considered in detail. It is demonstrated that most of its eigenfunctions are strongly localized and the corresponding eigenvalues are close to eigenvalues of the circular billiard with Neumann boundary conditions. Deviations from strong localization are also discussed. These results agree well with numerical calculations. [less ▲]

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See detailCircular dielectric cavity and its deformation
Dubertrand, Rémy ULiege; Bogomolny, E; Djellali, N et al

in Physical Review. A (2008), 77

The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in detail. The obtained formulas are checked on the example of cut disks. A good agreement is found ... [more ▼]

The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in detail. The obtained formulas are checked on the example of cut disks. A good agreement is found with direct numerical simulations and far-field experiments. [less ▲]

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