Laboratoire de Physique Théorique

de la Matière Condensée

 

Ces petites présentations sont données successivement par 2 ou 3 doctorant.e.s et post-doctorant.e.s du laboratoire.

Elles sont destinées à permettre aux doctorant.e.s et post-doctorant.e.s de présenter leur sujet dans une atmosphère bienveillante, constituée exclusivement de membres du LPTMC..
Chaque orateur a 30 ou 20 minutes (dont 5 de questions), selon son ancienneté.

Ces séminaires sont précédés d'une pause café/boissons/croissants/pains au chocolat à 10h25, et ont lieu à l'horaire du séminaire habituel, 10h45, dans la salle de cours du couloir 12-13 étage 5.

- Timothy FOLDES : Exploring the Coil-Globule Phase Transition: Spectral Analysis, Dynamical Characterization, and application to chromatin modelling.
Doctorant, sour la supervision de Maria Barbi

This presentation focuses on the fundamental phenomenon of the coil-globule phase transition in polymer physics and its role in understanding the structure an its role in understanding the structure and function of biological macromolecules. We first explore the application of spectral analysis to study the equilibrium polymer behavior across the coil-globule transition. We then investigate the dynamics of the polymer and aim to characterize the different phases involved. Finally, we delve into the applications to the modeling of chromatin, the complex of DNA and proteins that forms the chromosomes in eukaryotic cells.

 

 - David ALSPAUGH : Local density of state oscillations in laterally heterostructured topological insulator-semiconductor systems
Post-doctorant

We study local density of state (LDOS) oscillations arising from the scattering of electrons at atomic edge defects in topological insulator (TI) surfaces. To create edge scattering on the surface of a TI, we assume that half of its surface is covered with a semiconductor. In addition to modifying the TI states in the covered half, the presence of the semiconductor leads to a localized edge potential at the vacuum-semiconductor boundary. We study the induced LDOS by imposing time-reversal (TR) invariance and current conservation across the boundary. Additionally, we explore how the scattering of TI junctions with dissimilar spin textures and anisotropic Fermi velocities affect the modulations of the LDOS away from the junction edge. In all cases, for energies close to the Dirac point, we find that the decay envelope of the LDOS oscillations is insensitive to the scattering at the atomic edge defect, with a decay power given by \(x^{-3/2}\). Quantitative differences in the amplitude of these oscillations depend on the details of the interface and the spin textures, while the period of the oscillations is defined by the size of the Fermi surface.  

- Louise DELZESCAUX : Nonperturbative renormalization group approach to flat polymerized membrane bilayers
Doctorante en 2ème année, sous la supervision de Dominique Mouhanna

Phase transition is a key concept in physics. It is a physical process of transition between two states of a system, induced by a parameter which can be the temperature, a magnetic field, etc. This phenomenon is present in different areas of physics such as condensed matter or particle physics. The Mermin-Wagner Theorem states that there is no symmetry breaking in continuous system with short-range interactions of dimension equal or less than 2. However, polymerized membranes are 2d systems that display a crumpling transition between a high-temperature, crumpled, phase and a low temperature, flat, phase. In this seminar, I will talk about the flat phase of polymerized membranes - which, for instance, is relevant for graphene - and present briefly the renormalization group, the technique we use to study the fluctuations and the behavior of this phase. I will also introduce polymerized membrane bilayers, which is the system I am working on with Dominique Mouhanna for my Phd.

- Pierre RIZKALLAH : Microscopic models and hydrodynamic description for single-file diffusion

The situation where an active particle (called a tracer) diffuses in a complex environment arises in many biological systems (molecular motors, bacteria, micro-swimmers, algae...), but also in soft matter experiments with active colloids. When particles are confined in a one dimensional geometry like pores or narrow channels, the situation is called single-file diffusion because particles cannot bypass each other.
This strong geometrical constraint leads to an anomalous scaling ∼ √t for the mean and variance of the displacement of a driven tracer particle. Many microscopic models have been considered to describe this situation. We focus first on the paradigmatic simple exclusion process with a symmetric tracer and its description in terms of fluctuating hydrodynamics. We explain how we can obtain an exact expression for the tracer’s cumulant generating function and its correlations with its environment [1]. Then, we show how the hydrodynamic description can be adapted to describe single-file diffusion with a biased tracer. [2]

[1] Exact closure and solution for spatial correlations in single-file diffusion. A. Grabsch, A. Poncet, P. Rizkallah, P. Illien, O. Bénichou
Science Advances 8, eabm5043 (2022)
[2] Driven tracer in the Symmetric Exclusion Process: linear response and beyond. A. Grabsch, P. Rizkallah, P. Illien, O. Bénichou
arXiv:2207.13079. (accepted in Phys. Rev. Lett.)

- Léo REGNIER : Complete visitation statistics of one-dimensional random walks
Doctorant en 2ème année, sous la supervision d'Olivier Bénichou

Random walks are often used to describe exploration processes of a spatial domain, such as dynamics on the web or relaxation in disordered media. one of the most fundamental observable to describe this process is the number of distinct sites visited up to time t, N(t). This quantity has been extensively studied in the physical and mathematical litterature: its average, variance, single time distribution P(N(t)), or even its covariance Cov(N(t_1),N(t_2)) have been characterized. However, little was known about the multiple time distribution which is crucial to fully describe the exploration process.
In my talk, I will present the results given in [1], in which we determine the complete statistical statistical behavior of the stochastic process (N(t))_t>0, namely the probability that n_1, n_2, n_3... distinct sites are visited at times t_1, t_2, t_3... From this multiple-time distribution, we show that the visitation statistics of 1d random walks are temporally correlated and we quantify the non-Markovian nature of the process. We exploit these ideas to derive unexpected results for the two-time trapping problem and also to determine the visitation statistics of two important stochastic processes, the run-and-tumble particle and the biased random walk.

 

- Adriano ANGELONE : Disorder-free quantum glasses in quasicrystalline lattices
Post-doctorant

Quasicrystals, ordered but not periodic structures, have been originally discovered in the context of solid state physics, and have since inspired considerable research efforts thanks to their peculiar geometric properties. Their experimental realization in photonic systems and cold atom setups has generated further interest, resulting in many studies investigating the properties of interacting quantum particles moving in quasicrystalline lattice structures. One of the most interesting results of these works has been the discovery of Bose Glass (BG) states, globally localized but displaying local patches of delocalized particles. In all of these studies, however, the quasicrystalline substrates were accompanied by disorder, to closely model cold atom experimental platforms; this leaves open the question as to if and how the typical phase diagram of these systems changes in the disorder-free case.
In this talk, I will discuss recent results by my co-workers and I on a system of particles interacting via finite-range interactions on a disorder-free quasicrystalline lattice. Using numerically exact Path Integral Monte Carlo simulations, we obtain the first approximation-free phase diagram of a model in this setting, confirming the existence of a BG phase in the absence of disorder (at odds with previous mean-field predictions). Our results are of great interest given the perspective of laboratory engineering of disorder-free quasicrystalline systems via photonic experiments.

 

 

- Anna RITZ ZWILLING : Partition function for string-net models
Doctorante en 1ère année, sous la supervision de Jean-Noël Fuchs et Julien Vidal

The discovery of the fractional quantum Hall effect brought into light a new realm of phases of matter, called topologically-ordered phases. In two dimensions, these phases are characterized by exotic emergent excitations, known as anyons, with fractional quantum numbers and anyonic exchange statistics (i.e. neither bosonic nor fermionic). Another fundamental property of topologically-ordered phases is that the ground-state degeneracy depends on the surface topology (i.e. whether the system resides on a sphere, a torus, a pretzel...). The robustness of this degeneracy against local perturbations makes these systems promising candidates for topological quantum computation. Motivated by the latter, recent work has been dedicated to studying the fate of topological order at finite temperature.

In this talk, I will introduce a prominent exactly solvable toy-model for topologically-ordered phases, called string-net model, and present the calculation of its partition function.


- Jérémie KLINGER : Splitting Probabilities of Jump Processes
Doctorant en 3ème année, sous la supervision d'Olivier Bénichou

We derive a universal asymptotic form of the splitting probability of symmetric jump processes which quantifies the probability that the process crosses x before 0 starting from a given position 0 <= x0 <= x. Due to the discrete nature of the process, we show that this probability is non vanishing for the initial condition x0 = 0 and proves to be particularly relevant in applications to light scattering in heterogeneous media in realistic 3D slab geometries.


- Brieuc BENVEGNEN : Flocking in one dimension
Doctorant en 3ème année, sous la supervision d'Alexandre Solon

We study flocking in 1d using the active Ising model, a stochastic lattice gas in which particles self-propel in the direction controlled by the Ising spin they carry. Contrary to the passive Ising model, we observe an ordered phase where particles aggregate and move collectively. Symmetry is not broken though because the aggregate reverses stochastically its direction of motion due to the prominent effect of fluctuations. I will rationalize this behavior by explaining the dynamics of the aggregates and their reversals. At lower temperature, we observe static asters which are amenable to an analytic treatment.