arXiv subjects

Thierry Platini

Publications and source records attributed to Thierry Platini.

At least 19 recordsLinked to original sources

arXiv2025

Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems

Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit reset. The possibility of realizing discrete-time reset dynamics on quantum computers makes it important to investigate the steady-state properties of such dynamics. Here, we explore the behavior of generic discrete-time unitary dynamics interspersed by random reset events. For Poissonian resets, we compute the stationary state of the process and demonstrate, by taking a weak-reset limit, the existence of "resonances" in the quantum gates, allowing for the emergence of steady state density matrices which are not diagonal in the eigenbasis of the generator of the unitary gate. Such resonances are a genuine discrete-time feature and impact on quantum and classical correlations even beyond the weak-reset limit. Furthermore, we consider non-Poissonian reset processes and explore conditions for the existence of a steady state. We show that, when the reset probability vanishes sufficiently rapidly with time, the system does not approach a steady state. Our results highlight key differences between continuous-time and discrete-time stochastic resetting and may be useful to engineer states with controllable correlations on existing devices.

quant-ph↗

arXiv2024

Correlation distances in social networks

In this work we explore degree assortativity in complex networks, and extend its usual definition beyond that of nearest neighbours. We apply this definition to model networks, and describe a rewiring algorithm that induces assortativity. We compare these results to real networks. Social networks in particular tend to be assortatively mixed by degree in contrast to many other types of complex networks. However, we show here that these positive correlations diminish after one step and in most of the empirical networks analysed. Properties besides degree support this, such as the number of papers in scientific coauthorship networks, with no correlations beyond nearest neighbours. Beyond next-nearest neighbours we also observe a diasassortative tendency for nodes three steps away indicating that nodes at that distance are more likely different than similar.

physics.soc-ph↗

arXiv2023

The extraordinary story of Sinann -- the inspirational figure who gave her name to Ireland longest river -- and how she arose Ireland's resilient female icons

When local authorities recently selected a neoclassical male "river god head" of colonial origin to represent Ireland's longest river, it was welcomed as "harking back to Irish mythology". The council, local historians and townsfolk were unaware that in Irish mythology the figure associated with the river is a woman -- not a man. Her name is Sinann, and she had been written out of Ireland's national iconography after centuries of colonial destruction of Gaelic heritage. When mathematical investigation into Irish mythology brought Sinann's story to the people via local media, reaction was immediate. Street performances in support of Sinann were backed by letters in newspapers and a petition signed by hundreds of people demanding education about their heritage - and respect for women. How did this happen and what is the story behind Sinann, her diminution, and her rising? Here we recount how modern-day mathematics exposed the colonial imposter as stemming from the Ossianic controversy 250 years ago. We also discuss how a Victorian-era translation of her story from the original Irish turned what was an inspirational creation myth into a tale of a disobedient girl seeking knowledge to which she had no entitlement. This flawed narrative entered the public domain -- in encyclopaedias, on websites, and even in academic literature. Here we cast off colonial baggage to present a new, more accurate translation of Sinann's story alongside a new interpretation -- more amenable to a receptive public seeking enlightenment. Inspired by Sinann's rising, we also use artistic measures to invoke other Irish resilient female icons to rise up and take their rightful place in Irish iconography.

physics.soc-ph↗

arXiv2023

"The greatest Poet that has [n]ever existed" -- A Narrative Networks Analysis of the Poems of Ossian

Surprising as it may seem, applications of statistical methods to physics were inspired by the social sciences, which in turn are linked to the humanities. So perhaps it is not as unlikely as it might first appear for a group of statistical physicists and humanists to come together to investigate one of the subjects of Thomas Jefferson's poetic interests from a scientific point of view. And that is the nature of this article: a collaborative interdisciplinary analysis of the works of a figure Jefferson described as a ''rude bard of the North'' and ''the greatest Poet that has ever existed.'' In 2012, a subset of this team embraced an increase in interdisciplinary methods to apply the new science of complex networks to longstanding questions in comparative mythology. Investigations of network structures embedded in epic narratives allowed universal properties to be identified and ancient texts to be compared to each other. The approach inspired new challenges in mathematics, physics and even processes in industry, thereby illustrating how collaborations of this nature can be mutually beneficial and can capture the attention of a public, often ill-served by academic communication and dissemination. This article derives from these works, and from our consistent objective to help bridge the perceived gap between the natural sciences and the humanities. First we discuss the history of relationships between the two. Then we discuss the origins of the poems of Ossian and Jefferson's interests. We follow with our statistical approach in the next section. In the final section, we explore ideas for future research on these themes and discuss the potential of collaborative pursuits of human curiosity to overcome the two cultures dichotomy and embrace a scientific- and humanities-literate information age.

physics.soc-ph↗

arXiv2018

Steady-states of out-of-equlibrium inhomogeneous Richardson-Gaudin quantum integrable models in quantum optics

In this work we present numerical results for physical quantities in the steady-state obtained after a variety of product-states initial conditions are evolved unitarily, driven by the dynamics of quantum integrable models of the rational (XXX) Richardson-Gaudin family, which includes notably Tavis-Cummings models. The problem of interest here is one where a completely inhomogeneous ensemble of two-level systems (spins-1/2) are coupled to a single bosonic mode. The long-time averaged magnetisation along the z-axis as well as the bosonic occupation are evaluated in the diagonal ensemble by performing the complete sum over the full Hilbert space for small system sizes. These numerically exact results are independent of any particular choice of Hamiltonian and therefore describe general results valid for any member of this class of quantum integrable models built out of the same underlying conserved quantities. The collection of numerical results obtained can be qualitatively understood by a relaxation process for which, at infinitely strong coupling, every initial state will relax to a common state where each spin is in a maximally coherent superposition of its $\left|\uparrow\right>$ and $\left|\downarrow\right>$ states, i.e. they are in-plane polarised, and consequently the bosonic mode is also in a maximally coherent superposition of different occupation number states. This bosonic coherence being a feature of a superradiant state, we shall loosely use the term superradiant steady-state to describe it. A finite value of the coupling between the spins and the bosonic mode then leads to a long-time limit steady-state whose properties are qualitatively captured by a simple "dynamical" vision in which the coupling strength $V$ plays the role of a time $t_V$ at which this "relaxation process" towards the common strong coupling superradiant steady-state is interrupted.

cond-mat.mes-hall↗

arXiv2018

Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.

physics.bio-ph↗

arXiv2016

A Networks-Science Investigation into the Epic Poems of Ossian

In 1760 James Macpherson published the first volume of a series of epic poems which he claimed to have translated into English from ancient Scottish-Gaelic sources. The poems, which purported to have been composed by a third-century bard named Ossian, quickly achieved wide international acclaim. They invited comparisons with major works of the epic tradition, including Homer's Iliad and Odyssey, and effected a profound influence on the emergent Romantic period in literature and the arts. However, the work also provoked one of the most famous literary controversies of all time, colouring the reception of the poetry to this day. The authenticity of the poems was questioned by some scholars, while others protested that they misappropriated material from Irish mythological sources. Recent years have seen a growing critical interest in Ossian, initiated by revisionist and counter-revisionist scholarship and by the two-hundred-and-fiftieth anniversary of the first collected edition of the poems in 1765. Here we investigate Ossian from a networks-science point of view. We compare the connectivity structures underlying the societies described in the Ossianic narratives with those of ancient Greek and Irish sources. Despite attempts, from the outset, to position Ossian alongside the Homeric epics and to distance it from Irish sources, our results indicate significant network-structural differences between Macpherson's text and those of Homer. They also show a strong similarity between Ossianic networks and those of the narratives known as Acallam na Senórach (Colloquy of the Ancients) from the Fenian Cycle of Irish mythology.

physics.soc-ph↗

arXiv2015

Stochastic Analysis Of An Incoherent Feedforward Genetic Motif

Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory mechanisms to buffer noise. One such mechanism is the incoherent feedforward circuit. We analyze a simplistic version of this circuit, where an upstream regulator X affects both the production and degradation of a protein Y. Thus, any random increase in X's copy numbers would increase both production and degradation, keeping Y levels unchanged. To study its stochastic dynamics, we formulate this network into a mathematical model using the Chemical Master Equation formulation. We prove that if the functional dependence of Y's production and degradation on X is similar, then the steady-distribution of Y's copy numbers is independent of X. To investigate how fluctuations in Y propagate downstream, a protein Z whose production rate only depend on Y is introduced. Intriguingly, results show that the extent of noise in Z increases with noise in X, in spite of the fact that the magnitude of noise in Y is invariant of X. Such counter intuitive results arise because X enhances the time-scale of fluctuations in Y, which amplifies fluctuations in downstream processes. In summary, while feedforward systems can buffer a protein from noise in its upstream regulators, noise can propagate downstream due to changes in the time-scale of fluctuations.

q-bio.MN↗

arXiv2015

Entanglement replication via quantum repeated interactions

We study entanglement creation between two independent XX chains, which are repeatedly coupled locally to spin-1/2 Bell pairs. We show analytically that in the steady state the entanglement of the Bell pairs is perfectly transferred to the chains, generating large-scale interchain pair correlations. However, before the steady state is reached, within a growing causal region around the interacting locus the chains are found in a current driven nonquilibrium steady state (NESS). In the NESS, the chains cross entanglement decays exponentially with respect to the distance to the boundary sites with a typical length scale which is inversely proportional to the driving current.

quant-ph↗

arXiv2014

Exact distributions for stochastic gene expression models with bursting and feedback

Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play important roles in controlling noise in gene expression and phenotypic variation. A quantitative understanding of the impact of these factors requires analysis of the corresponding stochastic models. However, for stochastic models of gene expression with feedback and bursting, exact analytical results for protein distributions have not been obtained so far. Here, we analyze a model of gene expression with bursting and feedback regulation and obtain exact results for the corresponding protein steady-state distribution. The results obtained provide new insights into the role of bursting and feedback in noise regulation and optimization. Furthermore, for a specific choice of parameters, the system studied maps on to a two-state biochemical switch driven by a bursty input noise source. The analytical results derived thus provide quantitative insights into diverse cellular processes involving noise in gene expression and biochemical switching.

q-bio.MN↗

arXiv2013

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations, hence there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic 2-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of post-transcriptional and post-translational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

q-bio.MN↗

arXiv2011

Regulation by small RNAs via coupled degradation: mean-field and variational approaches

Regulatory genes called small RNAs (sRNAs) are known to play critical roles in cellular responses to changing environments. For several sRNAs, regulation is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs). The nonlinearity inherent in this regulatory scheme indicates that exact analytical solutions for the corresponding stochastic models are intractable. Here, we present a variational approach to analyze a well-studied stochastic model for regulation by sRNAs via coupled degradation. The proposed approach is efficient and provides accurate estimates of mean mRNA levels as well as higher order terms. Results from the variational ansatz are in excellent agreement with data from stochastic simulations for a wide range of parameters, including regions of parameter space where mean-field approaches break down. The proposed approach can be applied to quantitatively model stochastic gene expression in complex regulatory networks.

physics.bio-ph↗

arXiv2010

Dynamical phase transition of a 1D transport process including death

Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection $α$ and death of the last particle $δ$. The system presents a phase transition at $δ_c(α)$, where the average position of the last particle $ $ grows as $\sqrt{t}$. For $δ>δ_c$, a non equilibrium stationary state exists while for $δ<δ_c$ the asymptotic state presents a low density and max current phases. We discuss the scaling of the density and current profiles for parallel and sequential updates.

cond-mat.stat-mech↗

arXiv2009

Quantum Non-Equilibrium Steady States Induced by Repeated Interactions

We study the steady state of a finite XX chain coupled at its boundaries to quantum reservoirs made of free spins that interact one after the other with the chain. The two-point correlations are calculated exactly and it is shown that the steady state is completely characterized by the magnetization profile and the associated current. Except at the boundary sites, the magnetization is given by the average of the reservoirs' magnetizations. The steady state current, proportional to the difference in the reservoirs' magnetizations, shows a non-monotonous behavior with respect to the system-reservoir coupling strength, with an optimal current state for a finite value of the coupling. Moreover, we show that the steady state can be described by a generalized Gibbs state.

cond-mat.stat-mech↗

arXiv2008

Out-of-equilibrium bosons on a one-dimensional optical random lattice

We study the transport properties of a one-dimensional hard-core boson lattice gas coupled to two particle reservoirs at different chemical potentials generating a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-κ(τ)\nabla ρ$ where $τ$ is a typical timescale of the lattice fluctuations and $\nabla ρ$ the density gradient imposed %on the system by the reservoirs.

cond-mat.stat-mech↗

arXiv2008

Work fluctuations in quantum spin chains

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable XX quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.

cond-mat.stat-mech↗

arXiv2006

Relaxation in the XX quantum chain

We present the results obtained on the magnetisation relaxation properties of an XX quantum chain in a transverse magnetic field. We first consider an initial thermal kink-like state where half of the chain is initially thermalized at a very high temperature $T_b$ while the remaining half, called the system, is put at a lower temperature $T_s$. From this initial state, we derive analytically the Green function associated to the dynamical behaviour of the transverse magnetisation. Depending on the strength of the magnetic field and on the temperature of the system, different regimes are obtained for the magnetic relaxation. In particular, with an initial droplet-like state, that is a cold subsystem of finite size in contact at both ends with an infinite temperature environnement, we derive analytically the behaviour of the time-dependent system magnetisation.

cond-mat.stat-mech↗

arXiv2006

Gradient critical phenomena in the Ising quantum chain

We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling theory for the density profiles induced by the gradient perturbation which involves a characteristic length given by the width of the interface region. The scaling predictions are tested in the framework of the mean-field Ginzburg-Landau theory. Then we consider the Ising quantum chain in a linearly varying transverse field which corresponds to the extreme anisotropic limit of a classical two-dimensional Ising model. The quantum Hamiltonian can be diagonalized exactly in the scaling limit where the eigenvalue problem is the same as for the quantum harmonic oscillator. The energy density, the magnetization profile and the two-point correlation function are studied either analytically or by exact numerical calculations. Their scaling behaviour are in agreement with the predictions of the scaling theory.

cond-mat.other↗