# Les 20 dernières publications du LPTMS

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## Archive ouverte HAL – When Random Walkers Help Solving Intriguing Integrals

### Satya Majumdar

^{1}Emmanuel Trizac^{1}#### Satya Majumdar, Emmanuel Trizac. When Random Walkers Help Solving Intriguing Integrals.

*Physical Review Letters*, American Physical Society, 2019, 123 (2), ⟨10.1103/PhysRevLett.123.020201⟩. ⟨hal-02291790⟩We revisit a family of integrals that delude intuition, and that recently appeared in mathematical literature in connection with computer algebra package verification. We show that the remarkable properties displayed by these integrals become transparent when formulated in the language of random walks. In turn, the random walk view naturally leads to a plethora of nontrivial generalizations, that are worked out. Related complex identities are also derived, without the need of explicit calculation. The crux of our treatment lies in a causality argument where a message that travels at finite speed signals the existence of a boundary.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material

### M. Isoard

^{1}A. M. Kamchatnov^{2}N. Pavloff^{1}#### M. Isoard, A. M. Kamchatnov, N. Pavloff. Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material.

*Physical Review A*, American Physical Society 2019, 99 (5), ⟨10.1103/PhysRevA.99.053819⟩. ⟨hal-02291908⟩We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described within a nondispersive approximation by means of Riemann's approach. For larger distances, wave breaking occurs, leading to the formation of dispersive shocks at both ends of the pulse. We describe this phenomenon within Whitham modulation theory, which yields an excellent agreement with numerical simulations. Our analytic approach makes it possible to extract the leading asymptotic behavior of the parameters of the shock.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute of Spectroscopy

## Archive ouverte HAL – Topological proximity effects in a Haldane graphene bilayer system

### Peng Cheng

^{1}Philipp W. KleinKirill Plekhanov^{2, 3}Klaus Sengstock^{4}Monika AidelsburgerChristof Weitenberg^{5}Karyn Le Hur^{2}Philipp KleinKaryn Le Hur^{2}#### Peng Cheng, Philipp W. Klein, Kirill Plekhanov, Klaus Sengstock, Monika Aidelsburger, et al.. Topological proximity effects in a Haldane graphene bilayer system.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 100 (8), ⟨10.1103/PhysRevB.100.081107⟩. ⟨hal-02291915⟩We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. We propose an alternative definition of the topological invariant on the Bloch sphere.

- 1. DALEMBERT - Institut Jean Le Rond d'Alembert
- 2. CPHT - Centre de Physique Théorique [Palaiseau]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Zentrum für Optische Quantentechnologien
- 5. MPQ - Max-Planck-Institut für Quantenoptik

## Archive ouverte HAL – The equilibrium landscape of the Heisenberg spin chain

### Enej IlievskiEoin Quinn

^{1}#### Enej Ilievski, Eoin Quinn. The equilibrium landscape of the Heisenberg spin chain.

*SciPost Physics*, SciPost Foundation, 2019, 7 (3), ⟨10.21468/SciPostPhys.7.3.033⟩. ⟨hal-02295879⟩We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical Y-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The algebraic area of closed lattice random walks

### Stephane Ouvry

^{1}Shuang Wu^{1}#### Stephane Ouvry, Shuang Wu. The algebraic area of closed lattice random walks.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, ⟨10.04098⟩. ⟨hal-02292208⟩We propose a formula for the enumeration of closed lattice random walks of length $n$ enclosing a given algebraic area. The information is contained in the Kreft coefficients which encode, in the commensurate case, the Hofstadter secular equation for a quantum particle hopping on a lattice coupled to a perpendicular magnetic field. The algebraic area enumeration is possible because it is split in $2^{n/2-1}$ pieces, each tractable in terms of explicit combinatorial expressions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Stress-dependent amplification of active forces in nonlinear elastic media

### Pierre Ronceray

^{1}Chase Broedersz^{2}Martin Lenz^{3}*Soft Matter*, Royal Society of Chemistry, 2019The production of mechanical stresses in living organisms largely relies on localized, force-generating active units embedded in filamentous matrices. Numerical simulations of discrete fiber networks with fixed boundaries have shown that buckling in the matrix dramatically amplifies the resulting active stresses. Here we extend this result to a bucklable continuum elastic medium subjected to an arbitrary external stress, and derive analytical expressions for the active, nonlinear constitutive relations characterizing the full active medium. Inserting these relations into popular "active gel" descriptions of living tissues and the cytoskeleton will enable investigations into nonlinear regimes previously inaccessible due to the phenomenological nature of these theories.

- 1. Princeton University
- 2. Arnold Sommerfeld Center for Theoretical Physics
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Statistical mechanics of asymmetric tethered membranes: Spiral and crumpled phases

### Tirthankar Banerjee

^{1}Niladri Sarkar^{2}John Toner^{2}Abhik Basu#### Tirthankar Banerjee, Niladri Sarkar, John Toner, Abhik Basu. Statistical mechanics of asymmetric tethered membranes: Spiral and crumpled phases.

*Physical Review E*, American Physical Society (APS), 2019, 99 (5), ⟨10.1103/PhysRevE.99.053004⟩. ⟨hal-02291841⟩We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends upon the local in-plane dilation of the tethered network. This in turn leads to long-ranged interactions between the local mean and Gaussian curvatures, which is not present in symmetric tethered membranes. This interplay between asymmetry and Gaussian curvature leads to a new {\em double-spiral} phase not found in symmetric tethered membranes. At temperature $T=0$, tethered membranes of arbitrarily large size are always rolled up tightly into a conjoined pair of Archimedes' spirals. At finite $T$ this spiral structure swells up significantly into algebraic spirals characterized by universal exponents which we calculate. These spirals have long range orientational order, and are the asymmetric analogs of statistically flat symmetric tethered membranes. We also find that sufficiently strong asymmetry can trigger a structural instability leading to crumpling of these membranes as well. This provides a new route to crumpling for asymmetric tethered membranes. We calculate the maximum linear extent $L_c$ beyond which the membrane crumples, and calculate the universal dependence of $L_c$ on the membrane parameters. By tuning the asymmetry parameter, $L_c$ can be continuously varied, implying a {\em scale-dependent} crumpling. Our theory can be tested on controlled experiments on lipids with artificial deposits of spectrin filaments, in-vitro experiments on %\sout{artificial deposition of spectrin filaments on} red blood cell membrane extracts, %\sout{after %depletion of adenosine-tri-phosphate molecules} and on graphene coated on one side.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. MPI-PKS - Max Planck Institute for the Physics of Complex Systems

## Archive ouverte HAL – Spontaneous rotation can stabilise ordered chiral active fluids

### Ananyo Maitra

^{1}Martin Lenz^{1}#### Ananyo Maitra, Martin Lenz. Spontaneous rotation can stabilise ordered chiral active fluids.

*Nature Communications*, Nature Publishing Group, 2019, 10 (1), ⟨10.1038/s41467-019-08914-7⟩. ⟨hal-02102862⟩Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases are by now well established, the effect of chirality on these phases is much less studied. In this paper, we present the first complete dynamical theory of orientationally ordered chiral particles in two-dimensional incompressible systems. We show that phase-coherent states of rotating chiral particles are remarkably stable in both momentum-conserved and non-conserved systems in contrast to their non-rotating counterparts. Furthermore, defect separation -- which drives chaotic flows in non-rotating active fluids -- is suppressed by intrinsic rotation of chiral active particles. We thus establish chirality as a source of dramatic stabilization in active systems, which could be key in interpreting the collective behaviours of some biological tissues, cytoskeletal systems and collections of bacteria.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Smoluchowski flux and lamb-lion problems for random walks and Lévy flights with a constant drift

### Satya Majumdar

^{1}Philippe Mounaix^{2}Gregory Schehr^{1}#### Satya Majumdar, Philippe Mounaix, Gregory Schehr. Smoluchowski flux and lamb-lion problems for random walks and Lévy flights with a constant drift.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (8), pp.083214. ⟨10.1088/1742-5468/ab35e5⟩. ⟨hal-02272076⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CPHT - Centre de Physique Théorique [Palaiseau]

## Archive ouverte HAL – Simply modified GKL density classifiers that reach consensus faster

### J. Ricardo G. Mendonça

^{1}#### J. Ricardo G. Mendonça. Simply modified GKL density classifiers that reach consensus faster.

*Modern Physics Letters A*, World Scientific Publishing, 2019, 383 (19), pp.2264-2266. ⟨10.1016/j.physleta.2019.04.033⟩. ⟨hal-02291810⟩The two-state Gacs-Kurdyumov-Levin (GKL) cellular automaton has been a staple model in the study of complex systems due to its ability to classify binary arrays of symbols according to their initial density. We show that a class of modified GKL models over extended neighborhoods, but still involving only three cells at a time, achieves comparable density classification performance but in some cases reach consensus more than twice as fast. Our results suggest the time to consensus (relative to the length of the CA) as a complementary measure of density classification performance.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Shortcut to stationary regimes: A simple experimental demonstration

### Stéphane Faure

^{1}Sergio Ciliberto^{2}Emmanuel Trizac^{3}David Guéry-Odelin^{1}*American Journal of Physics*, American Association of Physics Teachers, 2019, 87 (2), pp.125-129. 〈10.1119/1.5082933〉- 1. Atomes Froids (LCAR)
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks

### Jonathan Bares

^{1}Daniel Bonamy^{2}Alberto Rosso^{3}#### Jonathan Bares, Daniel Bonamy, Alberto Rosso. Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks.

*Physical Review E*, American Physical Society (APS), 2019, 100 (2), pp.023001. ⟨10.1103/PhysRevE.100.023001⟩. ⟨hal-02269109⟩Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.

- 1. Servex - Moyens expérimentaux
- 2. SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Run-and-tumble particle in one-dimensional confining potentials: Steady-state, relaxation, and first-passage properties

### Abhishek Dhar

^{1}Anupam Kundu^{1}Satya N. Majumdar^{2}Sanjib Sabhapandit^{3}Gregory Schehr^{2}#### Abhishek Dhar, Anupam Kundu, Satya N. Majumdar, Sanjib Sabhapandit, Gregory Schehr. Run-and-tumble particle in one-dimensional confining potentials: Steady-state, relaxation, and first-passage properties.

*Physical Review E*, American Physical Society (APS), 2019, 99 (3), ⟨10.1103/PhysRevE.99.032132⟩. ⟨hal-02102138⟩We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x) = \alpha \, |x|^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$ values. We show that the stationary probability density $P(x)$ has a rich behavior in the $(p, \alpha)$-plane. For $p>1$, the distribution has a finite support in $[x_-,x_+]$ and there is a critical line $\alpha_c(p)$ that separates an active-like phase for $\alpha > \alpha_c(p)$ where $P(x)$ diverges at $x_\pm$, from a passive-like phase for $\alpha < \alpha_c(p)$ where $P(x)$ vanishes at $x_\pm$. For $p<1$, the stationary density $P(x)$ collapses to a delta function at the origin, $P(x) = \delta(x)$. In the marginal case $p=1$, we show that, for $\alpha < \alpha_c$, the stationary density $P(x)$ is a symmetric exponential, while for $\alpha > \alpha_c$, it again is a delta function $P(x) = \delta(x)$. For the special cases $p=2$ and $p=1$, we obtain exactly the full time-dependent distribution $P(x,t)$, that allows us to study how the system relaxes to its stationary state. In addition, in these two cases, we also study analytically the full distribution of the first-passage time to the origin. Numerical simulations are in complete agreement with our analytical predictions.

- 1. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Raman Research Insitute

## Archive ouverte HAL – Rotating trapped fermions in two dimensions and the complex Ginibre ensemble: Exact results for the entanglement entropy and number variance

### Bertrand Lacroix-A-Chez-Toine

^{1}Satya N. Majumdar^{1}Grégory Schehr^{1}*Phys.Rev.A*, 2019, 99 (2), pp.021602. 〈10.1103/PhysRevA.99.021602〉We establish an exact mapping between the positions of N noninteracting fermions in a two-dimensional rotating harmonic trap in its ground state and the eigenvalues of the N×N complex Ginibre ensemble of random matrix theory (RMT). Using RMT techniques, we make precise predictions for the statistics of the positions of the fermions, both in the bulk as well as at the edge of the trapped Fermi gas. In addition, we compute exactly, for any finite N, the Rényi entanglement entropy and the number variance of a disk of radius r in the ground state. We show that while these two quantities are proportional to each other in the (extended) bulk, this is no longer the case very close to the trap center nor at the edge. Near the edge, and for large N, we provide exact expressions for the scaling functions associated with these two observables.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Rolled Up or Crumpled: Phases of Asymmetric Tethered Membranes

### Tirthankar Banerjee

^{1}Niladri Sarkar^{2}John Toner^{2}Abhik Basu#### Tirthankar Banerjee, Niladri Sarkar, John Toner, Abhik Basu. Rolled Up or Crumpled: Phases of Asymmetric Tethered Membranes.

*Physical Review Letters*, American Physical Society, 2019, 122 (21), ⟨10.1103/PhysRevLett.122.218002⟩. ⟨hal-02291826⟩We show that inversion-asymmetric tethered membranes exhibit a new double-spiral phase with long range orientational order not present in symmetric membranes. We calculate the universal algebraic spiral shapes of these membranes in this phase. Asymmetry can trigger the crumpling of these membranes as well. In-vitro experiments on lipid, red blood cell membrane extracts, and on graphene coated on one side, could test these predictions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. MPI-PKS - Max Planck Institute for the Physics of Complex Systems

## Archive ouverte HAL – Role of information backflow in the emergence of quantum Darwinism

### Nadia Milazzo

^{1}Salvatore LorenzoMauro Paternostro^{2}G. Massimo Palma#### Nadia Milazzo, Salvatore Lorenzo, Mauro Paternostro, G. Massimo Palma. Role of information backflow in the emergence of quantum Darwinism.

*Physical Review A*, American Physical Society 2019, 100 (1), ⟨10.1103/PhysRevA.100.012101⟩. ⟨hal-02291799⟩Quantum Darwinism attempts to explain the emergence of objective reality of the state of a quantum system in terms of redundant information about the system acquired by independent non interacting fragments of the environment. The consideration of interacting environmental elements gives rise to a rich phenomenology, including the occurrence of non-Markovian features, whose effects on objectification {\it a' la} quantum Darwinism needs to be fully understood. We study a model of local interaction between a simple quantum system and a multi-mode environment that allows for a clear investigation of the interplay between information trapping and propagation in the environment and the emergence of quantum Darwinism. We provide strong evidence of the correlation between non-Markovianity and quantum Darwinism in such a model, thus providing strong evidence of a potential link between such fundamental phenomena.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centre for Theoretical Atomic, Molecular and Optical Physics

## Archive ouverte HAL – Rigid Fuchsian systems in 2-dimensional conformal field theories

### Vladimir BelavinYoshishige HaraokaRaoul Santachiara

^{1}*Commun.Math.Phys.*, 2019, 365 (1), pp.17-60. 〈10.1007/s00220-018-3274-x〉We investigate Fuchsian equations arising in the context of 2-dimensional conformal field theory (CFT) and we apply the Katz theory of Fucshian rigid systems to solve some of these equations. We show that the Katz theory provides a precise mathematical framework to answer the question whether the fusion rules of degenerate primary fields are enough for determining the differential equations satisfied by their correlation functions. We focus on the case of ${\mathcal{W}_{3}}$ Toda CFT: we argue that the differential equations arising for four-point conformal blocks with one nth level semi-degenerate field and a fully-degenerate one in the fundamental sl$_{3}$ representation are associated to Fuchsian rigid systems. We show how to apply Katz theory to determine the explicit form of the differential equations, the integral expression of solutions and the monodromy group representation. The theory of twisted homology is also used in the analysis of the integral expression. The computation of the connection coefficients is done for the first time in the case of a Katz system with multiplicities, thus extending the work done by Oshima in the multiplicity free case. This approach allows us to construct the corresponding fusion matrices and to perform the whole bootstrap program: new explicit factorization of ${\mathcal{W}_{3}}$ correlation functions as well as shift relations between structure constants for general Toda theories are also provided.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Quantum Hall skyrmions at ν = 0 , ± 1 in monolayer graphene

### Thierry Jolicoeur

^{1}Bradraj Pandey^{1}#### Thierry Jolicoeur, Bradraj Pandey. Quantum Hall skyrmions at ν = 0 , ± 1 in monolayer graphene.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 100 (11), ⟨10.1103/PhysRevB.100.115422⟩. ⟨hal-02291775⟩Monolayer graphene under a strong perpendicular field exhibit quantum Hall ferromagnetism with spontaneously broken spin and valley symmetry. The approximate SU(4) spin/valley symmetry is broken by small lattice scale effects in the central Landau level corresponding to filling factors $\nu=0,\pm 1$. Notably the ground state at $\nu=0$ is believed to be a canted antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component of the magnetic field parallel to the layer and the strength of small anisotropies. We study the skyrmions for the filling factors $\nu=\pm 1,0$ by using exact diagonalizations on the spherical geometry. If we neglect anisotropies we confirm the validity of the standard skyrmion picture generalized to four degrees of freedom. For filling factor $\nu=- 1$ the hole skyrmion is an infinite-size valley skyrmion with full spin polarization because it does not feel the anisotropies. The electron skyrmion is also always of infinite size. In the F phase it is always fully polarized while in the AF phase it undergoes continuous magnetization under increasing Zeeman energy. In the case of $\nu=0$ the skyrmion is always maximally localized in space both in F and AF phase. In the F phase it is fully polarized while in the AF it has also progressive magnetization with Zeeman energy. The magnetization process is unrelated to the spatial profile of the skyrmions contrary to the SU(2) case. In all cases the skyrmion physics is dominated by the competition between anisotropies and Zeeman effect but not directly by the Coulomb interactions, breaking universal scaling with the ratio Zeeman to Coulomb energy.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Quadratic Mean Field Games

### Denis Ullmo

^{1}Igor Swiecicki^{2, 1}Thierry Gobron^{2}#### Denis Ullmo, Igor Swiecicki, Thierry Gobron. Quadratic Mean Field Games.

*Physics Reports*, Elsevier, 2019. ⟨hal-02291869⟩Mean field games were introduced independently by J-M. Lasry and P-L. Lions, and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new approach to optimization problems with a large number of interacting agents. The description of such models split in two parts, one describing the evolution of the density of players in some parameter space, the other the value of a cost functional each player tries to minimize for himself, anticipating on the rational behavior of the others. Quadratic Mean Field Games form a particular class among these systems, in which the dynamics of each player is governed by a controlled Langevin equation with an associated cost functional quadratic in the control parameter. In such cases, there exists a deep relationship with the non-linear Schr\"odinger equation in imaginary time, connexion which lead to effective approximation schemes as well as a better understanding of the behavior of Mean Field Games. The aim of this paper is to serve as an introduction to Quadratic Mean Field Games and their connexion with the non-linear Schr\"odinger equation, providing to physicists a good entry point into this new and exciting field.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTM - Laboratoire de Physique Théorique et Modélisation

## Archive ouverte HAL – Properties of additive functionals of Brownian motion with resetting

### Frank Den Hollander

^{1}Satya N. Majumdar^{2}Janusz M. Meylahn^{1}Hugo Touchette^{3}#### Frank Den Hollander, Satya N. Majumdar, Janusz M. Meylahn, Hugo Touchette. Properties of additive functionals of Brownian motion with resetting.

*Journal of Physics A: Mathematical and General*, IOP Publishing, 2019. ⟨hal-02102127⟩We study the distribution of additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate and placed back to a given reset position. Our goal is two-fold: (1) For general functionals, we derive a large deviation principle in the presence of resetting and identify the large deviation rate function in terms of a variational formula involving large deviation rate functions without resetting. (2) For three examples of functionals (positive occupation time, area and absolute area), we investigate the effect of resetting by computing distributions and moments, using a formula that links the generating function with resetting to the generating function without resetting.

- 1. Leiden University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institute of Theoretical Physics