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Présentation du LPT

Le LPT (UMR 5152, Laboratoire de Physique Théorique) est un laboratoire de recherche localisé sur le campus de l'Université Paul Sabatier de Toulouse. Il a été fondé en 1991 et a été créé administrativement en 2003. Les chercheurs du LPT étaient rattachés au Laboratoire de Physique Quantique au sein du Groupe de Physique Théorique. L'expertise du LPT couvre les domaines de la matière condensée et la matière molle ainsi que la physique statistique et la physique non-linéaire.

Le LPT est membre de la Fédération de recherche FeRMI (Fédération de recherche Matière et Interactions - FR2051), anciennement IRSAMC (Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes).

 

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We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the ADS/CFT context. One can think of random tensor networks are specific probabilistic models for tensors having some particular geometry dictated by a graph (or network) structure. We first introduce our model of RTN, obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). We study the entanglement spectrum of the resulting random spectrum along a given bipartition of the local Hilbert spaces. We provide the limiting eigenvalue distribution of the reduced density operator of the RTN state, in the limit of large local dimension. The limit value is described via a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, we provide an explicit formula for the limiting eigenvalue distribution using classical and free multiplicative convolutions. We discuss the physical implications of our results, allowing us to go beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN.

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In this work, we construct galactic halos in order to fit the rotation curves (RCs) of a sample of low surface brightness (LSB) galaxies. These halos are made of Fuzzy Dark Matter (FDM) with a multimode expansion of non-spherical modes that in average contribute to the appropriate density profile consisting of a core and an envelope needed to fit the rotation curves. These halos are constructed assuming a solitonic core at the center and two types of envelopes, Navarro-Frenk-White and Pseudo-Isothermal density profiles. The resulting FDM configurations are then evolved in order to show how the average density changes in time due to the secular dynamical evolution, along with a condensation process that lead to the growth of the solitonic core.

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Abstract During the April 2023 Brazil–China summit, the creation of a trade currency supported by the BRICS countries was proposed. Using the United Nations Comtrade database, providing the frame of the world trade network associated to 194 UN countries during the decade 2010–2020, we study a mathematical model of influence battle of three currencies, namely, the US dollar, the euro, and such a hypothetical BRICS currency. In this model, a country trade preference for one of the three currencies is determined by a multiplicative factor based on trade flows between countries and their relative weights in the global international trade. The three currency seed groups are formed by 9 eurozone countries for the euro, 5 Anglo-Saxon countries for the US dollar and the 5 BRICS countries for the new proposed currency. The countries belonging to these 3 currency seed groups trade only with their own associated currency whereas the other countries choose their preferred trade currency as a function of the trade relations with their commercial partners. The trade currency preferences of countries are determined on the basis of a Monte Carlo modeling of Ising type interactions in magnetic spin systems commonly used to model opinion formation in social networks. We adapt here these models to the world trade network analysis. The results obtained from our mathematical modeling of the structure of the global trade network show that as early as 2012 about 58% of countries would have preferred to trade with the BRICS currency, 23% with the euro and 19% with the US dollar. Our results announce favorable prospects for a dominance of the BRICS currency in international trade, if only trade relations are taken into account, whereas political and other aspects are neglected.

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We describe a complete methodology to bridge the scales between nanoscale molecular dynamics and (micrometer) mesoscale Monte Carlo simulations in lipid membranes and vesicles undergoing phase separation, in which curving molecular species are furthermore embedded. To go from the molecular to the mesoscale, we notably appeal to physical renormalization arguments enabling us to rigorously infer the mesoscale interaction parameters from its molecular counterpart. We also explain how to deal with the physical timescales at stake at the mesoscale. Simulating the as-obtained mesoscale system enables us to equilibrate the long wavelengths of the vesicles of interest, up to the vesicle size. Conversely, we then backmap from the meso- to the nano-scale, which enables us to equilibrate in turn the short wavelengths down to the molecular length-scales. By applying our approach to the specific situation of patterning a vesicle membrane, we show that macroscopic membranes can thus be equilibrated at all length-scales in achievable computational time offering an original strategy to address the fundamental challenge of timescale in simulations of large bio-membrane systems.

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In this work, building on state-of-the-art quantum Monte Carlo simulations, we perform systematic finite-size scaling of both entanglement and participation entropies for long-range Heisenberg chain with unfrustrated power-law decaying interactions. We find distinctive scaling behaviors for both quantum entropies in the various regimes explored by tuning the decay exponent $\alpha$, thus capturing non-trivial features through logarithmic terms, beyond the case of linear Nambu-Goldstone modes. Our systematic analysis reveals that the quantum entanglement information, hidden in the scaling of the two studied entropies, can be obtained to the same level of order parameters and other usual finite-size observables of quantum many-body lattice models. The analysis and results obtained here can readily apply to more quantum criticalities in 1D and 2D systems.

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