# Les 20 dernières publications du LPTMS

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## 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 – 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 – 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 – 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 – Phase transitions and pattern formation in ensembles of phase-amplitude solitons in quasi-one-dimensional electronic systems

### P. Karpov

^{1}S. Brazovskii^{2}*Physical Review E*, American Physical Society (APS), 2019, 99 (2), 〈10.1103/PhysRevE.99.022114〉Most common types of symmetry breaking in quasi-one-dimensional electronic systems possess a combined manifold of states degenerate with respect to both the phase $\theta$ and the amplitude $A$ sign of the order parameter $A\exp(i\theta)$. These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge densities. To understand statistical properties and the phase diagram in the course of cooling under the controlled parameters, we present here an analytical treatment supported by Monte Carlo simulations for a generic coarse-grained two-fields model of XY-Ising type. The degeneracies give rise to two coexisting types of topologically nontrivial configurations: phase vortices and amplitude kinks -- the solitons. In 2D, 3D states with long-range (or BKT type) orders, the topological confinement sets in at a temperature $T=T_1$ which binds together the kinks and unusual half-integer vortices. At a lower $T=T_2$, the solitons start to aggregate into walls formed as rods of amplitude kinks which are ultimately terminated by half-integer vortices. With lowering $T$, the walls multiply passing sequentially across the sample. The presented results indicate a possible physical realization of a peculiar system of half-integer vortices with rods of amplitude kinks connecting their cores. Its experimental realization becomes feasible in view of recent successes in real space observations and even manipulations of domain walls in correlated electronic systems.

- 1. MISIS - National University of Science and Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Optimal work in a harmonic trap with bounded stiffness

### Carlos A. Plata

^{1, 2}David Guéry-Odelin^{3}E. Trizac^{4}A. Prados^{1}*Physical Review E*, American Physical Society (APS), 2019, 99 (1), pp.012140. 〈10.1103/PhysRevE.99.012140〉We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness $\kappa$. We work out the optimal time dependence $\kappa(t)$ by minimising the work performed on the particle under the non-holonomic constraint $0\leq\kappa\leq\kappa_{\max}$, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analysed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time $t_{\text{f}}$ and the desired compression ratio $\kappa_{\text{f}}/\kappa_{\text{\i}}$, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimisation of heat engines.

- 1. Universidad de Sevilla
- 2. Dipartimento di Fisica e Astronomia "Galileo Galilei"
- 3. Atomes Froids (LCAR)
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method

### M. Isoard

^{1}A. M. Kamchatnov^{2}N. Pavloff^{1}*Physical Review E*, American Physical Society (APS), 2019, 〈10.07952〉We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton, but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.

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

## Archive ouverte HAL – From chiral anomaly to two-fluid hydrodynamics for electronic vortices

### S. Brazovskii

^{1}N. Kirova^{2}*Annals Phys.*, 2019, 403, pp.184-197. 〈10.1016/j.aop.2018.07.004〉Many recent experiments addressed manifestations of electronic crystals, particularly the charge density waves, in nano-junctions, under electric field effect, at high magnetic fields, together with real space visualizations by STM and micro X-ray diffraction. This activity returns the interest to stationary or transient states with static and dynamic topologically nontrivial configurations: electronic vortices as dislocations, instantons as phase slip centers, and ensembles of microscopic solitons. Describing and modeling these states and processes calls for an efficient phenomenological theory which should take into account the degenerate order parameter, various kinds of normal carriers and the electric field. Here we notice that the commonly employed time-depend Ginzburg–Landau approach suffers with violation of the charge conservation law resulting in unphysical generation of particles which is particularly strong for nucleating or moving electronic vortices. We present a consistent theory which exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The resulting equations clarify partitions of charges, currents and rigidity among subsystems of the condensate and normal carriers. On this basis we perform the numerical modeling of a spontaneously generated coherent sequence of phase slips – the spacetime vortices – serving for the conversion among the injected normal current and the collective one.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Archive ouverte HAL – Fiber plucking by molecular motors yields large emergent contractility in stiff biopolymer networks

### Pierre Ronceray

^{1}Chase P. Broedersz^{2}Martin Lenz^{3, 4}*Soft Matter*, Royal Society of Chemistry, 2019The mechanical properties of the cell depend crucially on the tension of its cytoskeleton, a biopolymer network that is put under stress by active motor proteins. While the fibrous nature of the network is known to strongly affect the transmission of these forces to the cellular scale, our understanding of this process remains incomplete. Here we investigate the transmission of forces through the network at the individual filament level, and show that active forces can be geometrically amplified as a transverse motor-generated force force "plucks" the fiber and induces a nonlinear tension. In stiff and densely connnected networks, this tension results in large network-wide tensile stresses that far exceed the expectation drawn from a linear elastic theory. This amplification mechanism competes with a recently characterized network-level amplification due to fiber buckling, suggesting that that fiber networks provide several distinct pathways for living systems to amplify their molecular forces.

- 1. Princeton Center for Theoretical Science
- 2. LMU - Ludwig-Maximilians-Universität München
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment

## Archive ouverte HAL – Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems

### Ada Altieri

^{1}Silvio Franz^{2}*Physical Review E*, American Physical Society (APS), 2019, 99 (1), 〈10.1103/PhysRevE.99.010401〉We discuss a resource-competition model, which takes the MacArthur's model as a platform, to unveil interesting connections with glassy features and jamming in high dimension. This model presents two qualitatively different phases: a "shielded" phase, where a collective and self-sustained behavior emerges, and a "vulnerable" phase, where a small perturbation can destabilize the system and contribute to population extinction. We first present our perspective based on a strong similarity with continuous constraint satisfaction problems in their convex regime. Then, we discuss the stability in terms of the computation of the leading eigenvalue of the Hessian matrix of the free energy in the replica space. This computation allows us to efficiently distinguish between the two aforementioned phases and to relate high-dimensional critical ecosystems to glassy phenomena in the low-temperature regime.

- 1. LPS - Laboratoire de Physique Statistique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Anyonic tight-binding models of parafermions and of fractionalized fermions

### Davide RossiniMatteo CarregaMarcello Calvanese StrinatiLeonardo Mazza

^{1}*Phys.Rev.B*, 2019, 99 (8), pp.085113. 〈10.1103/PhysRevB.99.085113〉Parafermions are emergent quasiparticles which generalize Majorana fermions and possess intriguing anyonic properties. The theoretical investigation of effective models hosting them is gaining considerable importance in view of present-day condensed-matter realizations where they have been predicted to appear. Here we study the simplest number-conserving model of particlelike Fock parafermions, namely a one-dimensional tight-binding model. By means of numerical simulations based on exact diagonalization and on the density-matrix renormalization group, we prove that this quadratic model is nonintegrable and displays bound states in the spectrum due to its peculiar anyonic properties. Moreover, we discuss its many-body physics, characterizing anyonic correlation functions and discussing the underlying Luttinger-liquid theory at low energies. In the case when Fock parafermions behave as fractionalized fermions, we are able to unveil interesting similarities with two counterpropagating edge modes of two neighboring Laughlin states at filling 1/3.

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

## Towards Quantum Simulation with Circular Rydberg Atoms

### Thanh Long Nguyen

^{1}Jean-Michel Raimond^{1}Clément Sayrin^{1}Rodrigo Cortinas^{1}Tigrane Cantat-Moltrecht^{1}Fédéric Assemat^{1}Igor Dotsenko^{1}Sébastien Gleyzes^{1}Serge Haroche^{1}Guillaume Roux^{2}Thierry Jolicoeur^{2}Michel Brune^{1}*Physical Review X*, American Physical Society, 2018, 8 (1), 〈10.1103/PhysRevX.8.011032〉The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation.

- 1. LKB [Collège de France] - Laboratoire Kastler Brossel
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Topological Zak Phase in Strongly-Coupled LC Circuits

### Tal Goren

^{1}Kirill Plekhanov^{1, 2}Félicien Appas^{1}Karyn Le Hur^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\cal Z}_2$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sub-lattice symmetry, represented by an anti-unitary transformation. We present a methos to measure the winding of the topological Zak phase across the Brillouin zone by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems. We study the robustness of edge modes towards disorder.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The impact of the injection protocol on an impurity’s stationary state

### Oleksandr Gamayun

^{1, 2}Oleg Lychkovskiy^{3, 4, 5}Evgeni Burovski^{6, 7}Matthew Malcomson^{8}Vadim V. Cheianov^{1}Mikhail B. Zvonarev^{9}*Physical Review Letters*, American Physical Society, 2018We examine stationary state properties of an impurity particle injected into a one-dimensional quantum gas. We show that the value of the impurity's end velocity lies between zero and the speed of sound in the gas, and is determined by the injection protocol. This way, the impurity's constant motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of Landau approach to superfluidity. We provide exact analytic results in the thermodynamic limit, and perform finite-size numerical simulations to demonstrate that the predicted phenomena are within the reach of the existing ultracold gases experiments.

- 1. Universiteit Leiden [Leiden]
- 2. Bogolyubov Institute for Theoretical Physics
- 3. Skoltech - Skolkovo Institute of Science and Technology [Moscow]
- 4. Steklov Mathematical Institute of Russian Academy of Sciences
- 5. Russian Quantum Center
- 6. National Research University Higher School of Economics [Moscow]
- 7. Science Center in Chernogolovka
- 8. Lancaster University
- 9. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Surface temperatures in New York City: Geospatial data enables the accurate prediction of radiative heat transfer

### Masoud Ghandehari

^{1}Thorsten Emig^{2, 3}Milad Aghamohamadnia^{1}*Scientific Reports*, Nature Publishing Group, 2018Three decades into the research seeking to derive the urban energy budget, the dynamics of the thermal exchange between the densely built infrastructure and the environment are still not well understood. We present a novel hybrid experimental-numerical approach for the analysis of the radiative heat transfer in New York City. The aim of this work is to contribute to the calculation of the urban energy budget, in particular the stored energy. Improved understanding of urban thermodynamics incorporating the interaction of the various bodies will have implications on energy conservation at the building scale, as well as human health and comfort at the urban scale. The platform presented is based on longwave hyperspectral imaging of nearly 100 blocks of Manhattan, and a geospatial radiosity model that describes the collective radiative heat exchange between multiple buildings. The close comparison of temperature values derived from measurements and the computed surface temperatures (including streets and roads) implies that this geospatial, thermodynamic numerical model applied to urban structures, is promising for accurate and high resolution analysis of urban surface temperatures.

- 1. NYU Tandon School of Engineering
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MSE2 - Multiscale Materials Science for Energy and Environment

## Superfluidity of identical fermions in an optical lattice: Atoms and polar molecules

### A. K. Fedorov

^{1}V. I. Yudson^{2}G. V. Shlyapnikov^{3, 4, 1}*AIP Conference Proceedings*, American Institute of Physics, 2018, 〈10.1063/1.5025460〉In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.

- 1. Russian Quantum Center
- 2. Institute of Spectroscopy
- 3. Wuhan Institute of Physics and Mathematics
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases

### L. Samaj

^{1}M. Trulsson^{2}E. Trizac^{3}*Soft Matter*, Royal Society of Chemistry, 2018We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner Strong-Coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of $d$ comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.

- 1. Institute of Physics
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

### Kanaya Malakar

^{1}V. Jemseena^{2}Anupam Kundu^{2}K. Vijay Kumar^{2}Sanjib Sabhapandit^{3}Satya N. Majumdar^{4}S. Redner^{5}Abhishek Dhar^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2018We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.

- 1. Presidency University
- 2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 3. Raman Research Institute
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Santa Fe Institute

## Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?

### Xiangyu Cao

^{1, 2}Alexandre Nicolas^{1}Denny Trimcev^{1, 3}Alberto Rosso^{1}*Soft Matter*, Royal Society of Chemistry, 2018, 14 (18), pp.3640 - 3651. 〈10.1039/C7SM02510F〉The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like `impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of California [Berkeley]
- 3. ENS Paris - École normale supérieure - Paris

## Singularities of Floquet scattering and tunneling

### H. Landa

^{1, 2}*Physical Review A*, American Physical Society, 2018, 97 (4), 〈10.1103/PhysRevA.97.042705〉We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive amplitude, making the S-matrix nonanalytic at a singular point. For the corresponding quasi-bound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low energy (s-wave) particles and their conversion to high energy outgoing (mostly p-) waves. We examine the relation of such Floquet singularities, lacking in an effective time independent approximation, with well known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power law forces and subject to periodic fields, e.g. co-trapped ions and atoms.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681