Jean-Yves P Fortin | Université de Lorraine (original) (raw)

Papers by Jean-Yves P Fortin

Journal of Physics A: Mathematical and Theoretical

We consider a system of clusters of various sizes or masses, subject to aggregation and fragmenta... more We consider a system of clusters of various sizes or masses, subject to aggregation and fragmentation by collision with monomers or by self-disintegration. The aggregation rate for the cluster of size or mass k is given by a kernel proportional to k a , whereas the collision and disintegration kernels are given by λ k b and μ k a , respectively, with 0 ⩽ a , b ⩽ 1 and positive factors λ and µ. We study the emergence of oscillations in the phase diagram ( μ , λ ) for two models: ( a , b ) = ( 1 , 0 ) and ( 1 , 1 ) . It is shown that the monomer population satisfies a class of integral equations possessing oscillatory solutions in a finite domain in the plane ( μ , λ ) . We evaluate analytically this domain and give an estimate of the oscillation frequency. In particular, these oscillations are found to occur generally for small but nonzero values of the parameter µ, far smaller than λ.

Journal of Physics A: Mathematical and Theoretical

We consider a system of aggregated clusters of particles, subjected to coagulation and fragmentat... more We consider a system of aggregated clusters of particles, subjected to coagulation and fragmentation processes with mass dependent rates. Each monomer particle can aggregate with larger clusters, and each cluster can fragment into individual monomers with a rate directly proportional to the aggregation rate. The dynamics of the cluster densities is governed by a set of Smoluchowski equations, and we consider the addition of a source of monomers at constant rate. The whole dynamics can be reduced to solving a unique non-linear differential equation which displays self-oscillations in a specific range of parameters, and for a number of distinct clusters in the system large enough. This collective phenomenon is due to the presence of a fluctuating damping coefficient and is closely related to the Liénard self-oscillation mechanism observed in a more general class of physical systems such as the van der Pol oscillator.

Synthetic Metals, 2017

De Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations of the organic metal θ-(BETS) ... more De Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations of the organic metal θ-(BETS) 4 CoBr 4 (C 6 H 4 Cl 2) are studied in magnetic fields of up to 55 T at liquid helium temperatures. In line with Fermi surfaces (FS) illustrating the linear chain of coupled orbits, the observed Fourier components are linear combinations of the frequencies linked to the two basic orbits α and β, which have small effective masses compared to other organic metals with the same FS topology. Analytical formulas based on a second order development of the free energy within the canonical ensemble, not only account for the field and temperature dependence of the dHvA amplitudes but also for their relative values. In addition, strongly non-Lifshitz-Kosevich behaviours are quantitatively interpreted. In contrast, Shubnikov-de Haas oscillations are not accounted for by this model. short title: Quantum oscillations of θ-(BETS) 4 CoBr 4 (C 6 H 4 Cl 2

Abstract. We study the diffusion of a particle on a random lattice with fluctuating local connect... more Abstract. We study the diffusion of a particle on a random lattice with fluctuating local connectivity of average value q. This model is a basic description of relaxation processes in random media with geometrical defects. We analyze here the asymptotic behavior of the eigenvalue distribution for the Laplacian operator. We found that the localized states outside the mobility band and observed by Biroli and Monasson, in a previous numerical analysis [1], are described by saddle point solutions that breaks the rotational symmetry of the main action in the real space. The density of states is characterized asymptotically by a series of peaks with periodicity 1/q. PACS numbers: 75.10.Nr,12.40.Ee,67.80.MgAsymptotic behavior of the density of states on a random lattice 2 Diffusion on random graphs can be a useful problem for studying relaxation processes in glassy systems in general. Usually, the disorder arises from a random potential, impurities, but a random geometry can also play this...

Even though organic conductors have complicated crystalline structure with low symmetry and large... more Even though organic conductors have complicated crystalline structure with low symmetry and large unit cell, band structure calculations predict multiband quasi-two dimensional electronic structure yielding very simple Fermi surface in most cases. Although few puzzling experimental results are observed, data of numerous compounds are in agreement with calculations which make them suitable systems for studying magnetic quantum oscillations in networks of orbits connected by magnetic breakdown. The state of the art of this problematics is reviewed. To cite this article: A.

Abstract. We consider itinerant spinless fermions as moving defects in a dilute two-dimensional f... more Abstract. We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations and we analyze coupled selfconsistent mean-field equations of the Green functions after expressing the spin and fermion operators in terms of Grassmann variables. The specific heat and effective mass are analyzed with the solutions satisfying the symmetry imposed by the coupling layout. At low temperature, we find that these solutions induce stripes along the lines of couplings with the same sign, and that a low fermion density yields a small effective mass.

The European Physical Journal B, 2021

We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated ... more We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations, and we analyze coupled self-consistent mean-field equations of the Green functions after expressing the spin and fermion operators in terms of Grassmann variables. The specific heat and effective mass are analyzed with the solutions satisfying the symmetry imposed by the coupling layout. At low temperature, we find that these solutions induce stripes along the lines of couplings with the same sign, and that a low fermion density yields a small effective mass

Physica A: Statistical Mechanics and its Applications, 2020

Abstract We consider an open system in contact with a reservoir, where particles as well as energ... more Abstract We consider an open system in contact with a reservoir, where particles as well as energies can be exchanged between them, and present a description of the dynamics in terms of mixed (pseudo)spin and state variables. Specifically, a master equation is constructed out of the exchange rates for particles and for energies, which allows us to probe the system in the grand canonical description. In particular, employing the state resummation analysis, we obtain coupled time evolution equations for the probability distributions of the system as well as the environment. This is exemplified by a standard growth model, where the steady-state density function exhibits power-law behavior with the exponent depending on the microscopic parameters of the rate equations.

Journal of Statistical Mechanics: Theory and Experiment, 2018

We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism... more We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve the interval length. This leads to a set of segments of random sizes, with the accumulation of small fragments near the origin. This model is an example of record dynamics, with the presence of "quakes" and slow dynamics. The fragment size distribution is a universal inverse power law with logarithmic corrections. The exact distribution for the fragment number as function of time is simply related to the unsigned Stirling numbers of the first kind. Two-time correlation functions are defined and computed exactly. They satisfy scaling relations and exhibit aging phenomena. In particular the probability that the same number of fragments is found at two different times t > s is asymptotically equal to [4π log(s)] −1/2 when s ≫ 1 and the ratio t/s fixed, in agreement with the numerical simulations. The same process with a reset impedes the aging phenomena beyond a typical time scale defined by the reset parameter.

The European Physical Journal B, 2017

Journal of Physics A: Mathematical and Theoretical, 2020

We consider the stochastic dynamics of a system of diffusing clusters of particles on a finite pe... more We consider the stochastic dynamics of a system of diffusing clusters of particles on a finite periodic chain. A given cluster of particles can diffuse to the right or left as a whole and merge with other clusters; this process continues until all the clusters coalesce. We examine the distribution of the cluster numbers evolving in time, by means of a general time-dependent master equation based on a Smoluchowski equation for local coagulation and diffusion processes. Further, the limit distribution of the coalescence times is evaluated when only one cluster survives.

arXiv: Disordered Systems and Neural Networks, 2019

We study the variation of the mean cross section with the density of the samples in the quantum s... more We study the variation of the mean cross section with the density of the samples in the quantum scattering of a particle by a disordered target. The particular target we consider is modelled by a set of pointlike scatterers, each having an equal probability of being anywhere inside a sphere whose radius may be modified. We first prove that the scattering by a pointlike scatterer is characterized by a single phase shift δ which may take on any value in ]0 , π/2[ and that the scattering by N pointlike scatterers is described by a system of only N equations. We then show with the help of numerical calculations that there are two stages in the variation of the mean cross section when the density of the samples (the radius of the target) increases (decreases). The mean cross section first either increases or decreases, depending on whether the value of δ is less or greater than π/4 respectively, each one of the two behaviours being originated by double scattering; it always decreases as ...

In this article we present an alternative method to that developed by B. McCoy and T.T. Wu to obt... more In this article we present an alternative method to that developed by B. McCoy and T.T. Wu to obtain some exact results for the 2D Ising model with a general boundary magnetic field and for a finite size system. This method is a generalisation of ideas from V.N. Plechko presented for the 2D Ising model in zero field, based on the representation of the Ising model using a Grassmann algebra. A Gaussian 1D action is obtained for a general configuration of the boundary magnetic field. When the magnetic field is homogeneous, we check that our results are in agreement with McCoy and Wu’s previous work. This 1D action is used to compute in an efficient way the free energy in the special case of an inhomogeneous boundary magnetic field. This method is useful to obtain new exact results for interesting boundary problems, such as wetting transitions. PACS numbers: 02.30.Ik ; 05.50.+q ; 05.70.Fh Submitted to: J. Phys. A: Math. Gen.

A bstract. W e present in this article an exact study ofa rst order transition induced by an inho... more A bstract. W e present in this article an exact study ofa rst order transition induced by an inhom ogeneous boundary m agnetic eld in the 2D Ising m odel. From a previous analysis of the interfacial free energy in the discrete case (J. Phys. A :M ath. G en. 38,2849,2005)we identify,using an asym ptotic expansion in thetherm odynam ic lim it,thelineoftransition thatseparatestheregim ewhere the interface islocalised nearthe boundary from the one where itispropagating inside the bulk. In particular,the criticalline has a strong dependence on the aspect ratio ofthe lattice.

Journal of Physics: Condensed Matter, 2016

De Haas-van Alphen oscillations of the organic metal κ-(ET) 2 Cu(SCN) 2 have been measured up to ... more De Haas-van Alphen oscillations of the organic metal κ-(ET) 2 Cu(SCN) 2 have been measured up to 55 T at liquid helium temperatures. The Fermi surface of this charge transfer salt is a textbook example of linear chain of orbits coupled by magnetic breakdown. Accordingly, the oscillation spectrum is composed of linear combinations of the frequencies linked to the α and magnetic breakdown-induced β orbits. The field and temperature dependence of all the observed Fourier components, in particular the 'forbidden frequency' β − α which cannot correspond to a classical orbit, are quantitatively accounted for by analytical calculations based on a second order development of the free energy, i.e. beyond the first order Lifshitz-Kosevich formula.

Journal of Experimental and Theoretical Physics

The European Physical Journal B

Physical Review E

We consider a stochastic dynamics for a system of diffusing hard-core particles on a periodic cha... more We consider a stochastic dynamics for a system of diffusing hard-core particles on a periodic chain with asymmetric diffusion rules. A given cluster of particles can diffuse to the right as a whole but the particle located on the left boundary of the cluster is allowed to break-off from it and diffuse to the left. Clusters of particles can eventually merge with other clusters. These rules allow for the creation of clusters of different sizes. We discuss the size distribution of the clusters in the long time or steady state limit, as a function of the particle concentration c. We consider the general time dependent master equation based on Smoluchowski's theory for local cluster merging or fragmentation and diffusion processes, and study the solutions using the generating function in the large size limit. We found that there exists a critical density c * = √ 2 − 1 for which the cluster distribution decays like a power law with exponent 5/2.

Journal of Physics A: Mathematical and Theoretical

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk ... more Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.

Journal of Physics A: Mathematical and Theoretical

We consider a system of clusters of various sizes or masses, subject to aggregation and fragmenta... more We consider a system of clusters of various sizes or masses, subject to aggregation and fragmentation by collision with monomers or by self-disintegration. The aggregation rate for the cluster of size or mass k is given by a kernel proportional to k a , whereas the collision and disintegration kernels are given by λ k b and μ k a , respectively, with 0 ⩽ a , b ⩽ 1 and positive factors λ and µ. We study the emergence of oscillations in the phase diagram ( μ , λ ) for two models: ( a , b ) = ( 1 , 0 ) and ( 1 , 1 ) . It is shown that the monomer population satisfies a class of integral equations possessing oscillatory solutions in a finite domain in the plane ( μ , λ ) . We evaluate analytically this domain and give an estimate of the oscillation frequency. In particular, these oscillations are found to occur generally for small but nonzero values of the parameter µ, far smaller than λ.

Journal of Physics A: Mathematical and Theoretical

We consider a system of aggregated clusters of particles, subjected to coagulation and fragmentat... more We consider a system of aggregated clusters of particles, subjected to coagulation and fragmentation processes with mass dependent rates. Each monomer particle can aggregate with larger clusters, and each cluster can fragment into individual monomers with a rate directly proportional to the aggregation rate. The dynamics of the cluster densities is governed by a set of Smoluchowski equations, and we consider the addition of a source of monomers at constant rate. The whole dynamics can be reduced to solving a unique non-linear differential equation which displays self-oscillations in a specific range of parameters, and for a number of distinct clusters in the system large enough. This collective phenomenon is due to the presence of a fluctuating damping coefficient and is closely related to the Liénard self-oscillation mechanism observed in a more general class of physical systems such as the van der Pol oscillator.

Synthetic Metals, 2017

De Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations of the organic metal θ-(BETS) ... more De Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations of the organic metal θ-(BETS) 4 CoBr 4 (C 6 H 4 Cl 2) are studied in magnetic fields of up to 55 T at liquid helium temperatures. In line with Fermi surfaces (FS) illustrating the linear chain of coupled orbits, the observed Fourier components are linear combinations of the frequencies linked to the two basic orbits α and β, which have small effective masses compared to other organic metals with the same FS topology. Analytical formulas based on a second order development of the free energy within the canonical ensemble, not only account for the field and temperature dependence of the dHvA amplitudes but also for their relative values. In addition, strongly non-Lifshitz-Kosevich behaviours are quantitatively interpreted. In contrast, Shubnikov-de Haas oscillations are not accounted for by this model. short title: Quantum oscillations of θ-(BETS) 4 CoBr 4 (C 6 H 4 Cl 2

Abstract. We study the diffusion of a particle on a random lattice with fluctuating local connect... more Abstract. We study the diffusion of a particle on a random lattice with fluctuating local connectivity of average value q. This model is a basic description of relaxation processes in random media with geometrical defects. We analyze here the asymptotic behavior of the eigenvalue distribution for the Laplacian operator. We found that the localized states outside the mobility band and observed by Biroli and Monasson, in a previous numerical analysis [1], are described by saddle point solutions that breaks the rotational symmetry of the main action in the real space. The density of states is characterized asymptotically by a series of peaks with periodicity 1/q. PACS numbers: 75.10.Nr,12.40.Ee,67.80.MgAsymptotic behavior of the density of states on a random lattice 2 Diffusion on random graphs can be a useful problem for studying relaxation processes in glassy systems in general. Usually, the disorder arises from a random potential, impurities, but a random geometry can also play this...

Even though organic conductors have complicated crystalline structure with low symmetry and large... more Even though organic conductors have complicated crystalline structure with low symmetry and large unit cell, band structure calculations predict multiband quasi-two dimensional electronic structure yielding very simple Fermi surface in most cases. Although few puzzling experimental results are observed, data of numerous compounds are in agreement with calculations which make them suitable systems for studying magnetic quantum oscillations in networks of orbits connected by magnetic breakdown. The state of the art of this problematics is reviewed. To cite this article: A.

Abstract. We consider itinerant spinless fermions as moving defects in a dilute two-dimensional f... more Abstract. We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations and we analyze coupled selfconsistent mean-field equations of the Green functions after expressing the spin and fermion operators in terms of Grassmann variables. The specific heat and effective mass are analyzed with the solutions satisfying the symmetry imposed by the coupling layout. At low temperature, we find that these solutions induce stripes along the lines of couplings with the same sign, and that a low fermion density yields a small effective mass.

The European Physical Journal B, 2021

We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated ... more We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations, and we analyze coupled self-consistent mean-field equations of the Green functions after expressing the spin and fermion operators in terms of Grassmann variables. The specific heat and effective mass are analyzed with the solutions satisfying the symmetry imposed by the coupling layout. At low temperature, we find that these solutions induce stripes along the lines of couplings with the same sign, and that a low fermion density yields a small effective mass

Physica A: Statistical Mechanics and its Applications, 2020

Abstract We consider an open system in contact with a reservoir, where particles as well as energ... more Abstract We consider an open system in contact with a reservoir, where particles as well as energies can be exchanged between them, and present a description of the dynamics in terms of mixed (pseudo)spin and state variables. Specifically, a master equation is constructed out of the exchange rates for particles and for energies, which allows us to probe the system in the grand canonical description. In particular, employing the state resummation analysis, we obtain coupled time evolution equations for the probability distributions of the system as well as the environment. This is exemplified by a standard growth model, where the steady-state density function exhibits power-law behavior with the exponent depending on the microscopic parameters of the rate equations.

Journal of Statistical Mechanics: Theory and Experiment, 2018

We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism... more We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve the interval length. This leads to a set of segments of random sizes, with the accumulation of small fragments near the origin. This model is an example of record dynamics, with the presence of "quakes" and slow dynamics. The fragment size distribution is a universal inverse power law with logarithmic corrections. The exact distribution for the fragment number as function of time is simply related to the unsigned Stirling numbers of the first kind. Two-time correlation functions are defined and computed exactly. They satisfy scaling relations and exhibit aging phenomena. In particular the probability that the same number of fragments is found at two different times t > s is asymptotically equal to [4π log(s)] −1/2 when s ≫ 1 and the ratio t/s fixed, in agreement with the numerical simulations. The same process with a reset impedes the aging phenomena beyond a typical time scale defined by the reset parameter.

The European Physical Journal B, 2017

Journal of Physics A: Mathematical and Theoretical, 2020

We consider the stochastic dynamics of a system of diffusing clusters of particles on a finite pe... more We consider the stochastic dynamics of a system of diffusing clusters of particles on a finite periodic chain. A given cluster of particles can diffuse to the right or left as a whole and merge with other clusters; this process continues until all the clusters coalesce. We examine the distribution of the cluster numbers evolving in time, by means of a general time-dependent master equation based on a Smoluchowski equation for local coagulation and diffusion processes. Further, the limit distribution of the coalescence times is evaluated when only one cluster survives.

arXiv: Disordered Systems and Neural Networks, 2019

We study the variation of the mean cross section with the density of the samples in the quantum s... more We study the variation of the mean cross section with the density of the samples in the quantum scattering of a particle by a disordered target. The particular target we consider is modelled by a set of pointlike scatterers, each having an equal probability of being anywhere inside a sphere whose radius may be modified. We first prove that the scattering by a pointlike scatterer is characterized by a single phase shift δ which may take on any value in ]0 , π/2[ and that the scattering by N pointlike scatterers is described by a system of only N equations. We then show with the help of numerical calculations that there are two stages in the variation of the mean cross section when the density of the samples (the radius of the target) increases (decreases). The mean cross section first either increases or decreases, depending on whether the value of δ is less or greater than π/4 respectively, each one of the two behaviours being originated by double scattering; it always decreases as ...

In this article we present an alternative method to that developed by B. McCoy and T.T. Wu to obt... more In this article we present an alternative method to that developed by B. McCoy and T.T. Wu to obtain some exact results for the 2D Ising model with a general boundary magnetic field and for a finite size system. This method is a generalisation of ideas from V.N. Plechko presented for the 2D Ising model in zero field, based on the representation of the Ising model using a Grassmann algebra. A Gaussian 1D action is obtained for a general configuration of the boundary magnetic field. When the magnetic field is homogeneous, we check that our results are in agreement with McCoy and Wu’s previous work. This 1D action is used to compute in an efficient way the free energy in the special case of an inhomogeneous boundary magnetic field. This method is useful to obtain new exact results for interesting boundary problems, such as wetting transitions. PACS numbers: 02.30.Ik ; 05.50.+q ; 05.70.Fh Submitted to: J. Phys. A: Math. Gen.

A bstract. W e present in this article an exact study ofa rst order transition induced by an inho... more A bstract. W e present in this article an exact study ofa rst order transition induced by an inhom ogeneous boundary m agnetic eld in the 2D Ising m odel. From a previous analysis of the interfacial free energy in the discrete case (J. Phys. A :M ath. G en. 38,2849,2005)we identify,using an asym ptotic expansion in thetherm odynam ic lim it,thelineoftransition thatseparatestheregim ewhere the interface islocalised nearthe boundary from the one where itispropagating inside the bulk. In particular,the criticalline has a strong dependence on the aspect ratio ofthe lattice.

Journal of Physics: Condensed Matter, 2016

De Haas-van Alphen oscillations of the organic metal κ-(ET) 2 Cu(SCN) 2 have been measured up to ... more De Haas-van Alphen oscillations of the organic metal κ-(ET) 2 Cu(SCN) 2 have been measured up to 55 T at liquid helium temperatures. The Fermi surface of this charge transfer salt is a textbook example of linear chain of orbits coupled by magnetic breakdown. Accordingly, the oscillation spectrum is composed of linear combinations of the frequencies linked to the α and magnetic breakdown-induced β orbits. The field and temperature dependence of all the observed Fourier components, in particular the 'forbidden frequency' β − α which cannot correspond to a classical orbit, are quantitatively accounted for by analytical calculations based on a second order development of the free energy, i.e. beyond the first order Lifshitz-Kosevich formula.

Journal of Experimental and Theoretical Physics

The European Physical Journal B

Physical Review E

We consider a stochastic dynamics for a system of diffusing hard-core particles on a periodic cha... more We consider a stochastic dynamics for a system of diffusing hard-core particles on a periodic chain with asymmetric diffusion rules. A given cluster of particles can diffuse to the right as a whole but the particle located on the left boundary of the cluster is allowed to break-off from it and diffuse to the left. Clusters of particles can eventually merge with other clusters. These rules allow for the creation of clusters of different sizes. We discuss the size distribution of the clusters in the long time or steady state limit, as a function of the particle concentration c. We consider the general time dependent master equation based on Smoluchowski's theory for local cluster merging or fragmentation and diffusion processes, and study the solutions using the generating function in the large size limit. We found that there exists a critical density c * = √ 2 − 1 for which the cluster distribution decays like a power law with exponent 5/2.

Journal of Physics A: Mathematical and Theoretical

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk ... more Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.