arXiv subjects

Jean-Yves Fortin

Publications and source records attributed to Jean-Yves Fortin.

At least 19 recordsLinked to original sources

arXiv2022

Origin of the spontaneous oscillations in a simplified coagulation-fragmentation system driven by a source

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.

cond-mat.stat-mech↗

arXiv2021

Itinerant electrons on dilute frustrated Ising lattices

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.

cond-mat.stat-mech↗

arXiv2020

Charge oscillations in a simple model of interacting magnetic orbits

Exact eigenstates for a set of two or more interacting electronic orbits in a magnetic field are studied for a class of factorized Hamiltonians with coupled Fermi surfaces. We study the condition for the existence of annihilation-creation operators that allows for the construction of eigenstates. For the case of two interacting cyclotronic orbits, we consider the oscillations of the overlap function and the transfer of charge density between the orbits as function of the inverse field. The expressions of the Fourier frequencies are given in the semiclassical regime and they depend on the geometrical structure of the electronic bands. A generalization of this construction is provided for a chain of several interacting orbits with exact eigenfunctions.

quant-ph↗

arXiv2018

Do Fourier analysis yield reliable amplitude of quantum oscillations?

Quantum oscillations amplitude of multiband metals, such as high T c superconductors in the normal state, heavy fermions or organic conductors are generally determined through Fourier analysis of the data even though the oscillatory part of the signal is field-dependent. It is demonstrated that the amplitude of a given Fourier component can strongly depend on both the nature of the windowing (either flat, Hahn or Blackman window) and, since oscillations are obtained within finite field range, the window width. Consequences on the determination of the Fourier amplitude, hence on the effective mass are examined in order to determine the conditions for reliable data analysis.

cond-mat.str-el↗

arXiv2018

Modified stochastic fragmentation of an interval as an ageing process

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 $s\gg 1$ 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.

cond-mat.stat-mech↗

arXiv2017

de Haas-van Alphen oscillations with non-parabolic dispersions

de Haas-van Alphen oscillation spectrum of two-dimensional systems is studied for general power law energy dispersion, yielding a Fermi surface area of the form $S(E)\propto E^α$ for a given energy $E$. The case $α=1$ stands for the parabolic energy dispersion. It is demonstrated that the periodicity of the magnetic oscillations in inverse field can depend notably on the temperature. We evaluated analytically the Fourier spectrum of these oscillations to evidence the frequency shift and smearing of the main peak structure as the temperature increases.

cond-mat.str-el↗

arXiv2017

Quantum oscillations of a linear chain of coupled orbits with small effective masses: the organic metal $θ$-(BETS) 4 CoBr 4 (C 6 H 4 Cl 2 )

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)

cond-mat.str-el↗

arXiv2016

Transmission and tunneling probability in two-band metals: influence of magnetic breakdown on the Onsager phase of quantum oscillations

Tunneling amplitude through magnetic breakdown (MB) gap is considered for two bands Fermi surfaces illustrated in many organic metals. In particular, the S-matrix associated to the wave-function transmission through the MB gap for the relevant class of differential equations is the main object allowing the determination of tunneling probabilities and phases. The calculated transmission coefficients include a field-dependent Onsager phase. As a result, quantum oscillations are not periodic in 1/B for finite magnetic breakdown gap. Exact and approximate methods are proposed for computing ratio amplitudes of the wave-function in interacting two-band models.

cond-mat.str-el↗

arXiv2016

New insights on frequency combinations and 'forbidden frequencies' in de Haas-van Alphen spectrum of \k{appa}-(ET) 2 Cu(SCN) 2

De Haas-van Alphen oscillations of the organic metal \k{appa}-(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.

cond-mat.str-el↗

arXiv2015

Effect of electronic band dispersion curvature on de Haas-van Alphen oscillations

The effect of electronic band curvature, i.e. the deviation from parabolicity of electronic dispersion, on de Haas-van Alphen oscillations spectra is studied. Although the oscillations amplitude remain unaffected, it is demonstrated that non-quadratic terms of the Landau bands dispersion, which is particularly relevant in the case of Dirac fermions, induces a field- and temperature-dependent Onsager phase. As a result, a temperature-dependent shift of the de Haas-van Alphen oscillations frequency is predicted.

cond-mat.mes-hall↗

arXiv2015

Non-Lifshitz-Kosevich field-and temperature-dependent amplitude of quantum oscillations in the quasi-two dimensional metal $θ$-(ET) 4 ZnBr 4 (C 6 H 4 Cl 2 )

According to band structure calculations, the Fermi surface of the quasi-two dimensional metal $θ$-(ET) 4 ZnBr 4 (C 6 H 4 Cl 2) illustrates the linear chain of coupled orbits model. Accordingly, de Haas-van Alphen oscillations spectra recorded in pulsed magnetic field of up to 55 T evidence many Fourier components, the frequency of which are linear combinations of the frequencies relevant to the closed $α$ and the magnetic breakdown $β$ orbits. The field and temperature dependence of these component's amplitude are quantitatively accounted for by analytic calculations including, beyond the Lifshitz-Kosevich formula, second order terms in damping factors due to the oscillation of the chemical potential as the magnetic field varies. Whereas these second order terms are negligible for the orbits $α$, $β$ and 2$β$ -- $α$, they are solely responsible for the 'forbidden orbit' $β$ -- $α$ and its harmonic and have a significant influence on Fourier components such as 2$α$ and $β$ + $α$, yielding strongly non-Lifshitz-Kosevich behaviour in the latter case.

cond-mat.str-el↗

arXiv2014

Crossover properties of a one-dimensional reaction-diffusion process with a transport current

One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties in finite and semi-infinite one-dimensional chains. A set of particles freely hop between nearest-neighbor sites, with the additional condition that, when two particles meet, they merge instantaneously into one particle. A localized source of particle-current is imposed at the origin as well as a non-symmetric hopping rate between the left and right directions (particle drift). This model was previously studied with exact results for the particle density by Hinrichsen et al. [1] in the long-time limit. We are interested here in the crossover process between a scaling regime and long-time behavior, starting with a chain filled of particles. As in the previous reference [1], we employ the empty-interval-particle method, where the probability of finding an empty interval between two given sites is considered. However a different method is developed here to treat the boundary conditions by imposing the continuity and differentiability of the interval probability, which allows for a closed and unique solution, especially for any given initial particle configuration. In the finite size case, we find a crossover between the scaling regime and two different exponential decays for the particle density as function of the input current. Precise asymptotic expressions for the particle-density, and coagulation rate are given.

cond-mat.stat-mech↗

arXiv2014

De Haas-van Alphen oscillations in the compensated organic metal alpha-'pseudo-kappa'-(ET)4H3O[Fe(C2O4)3].(C6H4Br2)

Field-, temperature- and angle-dependent Fourier amplitude of de Haas-van Alphen (dHvA) oscillations are calculated for compensated two-dimensional (2D) metals with textbook Fermi surface (FS) composed of one hole and two electron orbits connected by magnetic breakdown. It is demonstrated that, taking into account the opposite sign of electron and hole orbits, a given Fourier component involves combination of several orbits, the contribution of which must be included in the calculations. Such FS is observed in the strongly 2D organic metal alpha-'pseudo-kappa'-(ET)4H3O[Fe(C2O4)3].(C6H4Br2), dHvA oscillations of which have been studied up to 55 T for various directions of the magnetic field with respect to the conducting plane. Calculations are in good quantitative agreement with the data.

cond-mat.str-el↗

arXiv2014

Grassmannian representation of the two-dimensional monomer-dimer model

We present an application of the Grassmann algebra to the problem of the monomer-dimer statistics on a two-dimensional square lattice. The exact partition function, or total number of possible configurations, of a system of dimers with a finite set of n monomers with fixed positions can be expressed via a quadratic fermionic theory. We give an answer in terms of a product of two pfaffians and the solution is closely related to the Kasteleyn result of the pure dimer problem. Correlation functions are in agreement with previous results, both for monomers on the boundary, where a simple exact expression is available in the discrete and continuous case, and in the bulk where the expression is evaluated numerically.

cond-mat.stat-mech↗

arXiv2014

Boundary crossover in non-equilibrium growth processes

The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near to the boundary than deep in the bulk. This is exemplified in the semi-infinite Edwards-Wilkinson model in one dimension, both from its exact solution and numerical simulations, as well as from simulations on the semi-infinite one-dimensional Kardar-Parisi-Zhang model. The non-stationary scaling of interface heights and widths is analyzed and a universal scaling form for the local height profile is proposed.

cond-mat.stat-mech↗

arXiv2013

Recent developments in the determination of the amplitude and phase of quantum oscillations for the linear chain of coupled orbits

De Haas-van Alphen oscillations are studied for Fermi surfaces (FS) illustrating the model proposed by Pippard in the early sixties, namely the linear chain of orbits coupled by magnetic breakdown. This FS topology is relevant for many multiband quasi-two dimensional (q-2D) organic metals such as $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$ and $θ$-(BEDT-TTF)$_4$CoBr$_4$(C$_6$H$_4$Cl$_2$) which are considered in detail. Whereas the Lifshits-Kosevich model only involves a first order development of field- and temperature-dependent damping factors, second order terms may have significant contribution on the Fourier components amplitude for such q-2D systems at high magnetic field and low temperature. The strength of these second order terms depends on the relative value of the involved damping factors, which are in turns strongly dependent on parameters such as the magnetic breakdown field, effective masses and, most of all, effective Landé factors. In addition, the influence of field-dependent Onsager phase factors on the oscillation spectra is considered.

cond-mat.str-el↗

arXiv2013

Dynamics of interval fragmentation and asymptotic distributions

We study the general fragmentation process starting from one element of size unity (E=1). At each elementary step, each existing element of size $E$ can be fragmented into $k\,(\ge 2)$ elements with probability $p_k$. From the continuous time evolution equation, the size distribution function $P(E;t)$ can be derived exactly in terms of the variable $z= -\log E$, with or without a source term that produces with rate $r$ additional elements of unit size. Different cases are probed, in particular when the probability of breaking an element into $k$ elements follows a power law: $p_k\propto k^{-1-η}$. The asymptotic behavior of $P(E;t)$ for small $E$ (or large $z$) is determined according to the value of $η$. When $η>1$, the distribution is asymptotically proportional to $t^{1/4}\exp[\sqrt{-αt\log E}][-\log E]^{-3/4}$ with $α$ being a positive constant, whereas for $η<1$ it is proportional to $E^{η-1}t^{1/4}\exp[\sqrt{-αt\log E}][-\log E]^{-3/4}$ with additional time-dependent corrections that are evaluated accurately with the saddle-point method.

cond-mat.stat-mech↗

arXiv2013

Random site dilution properties of frustrated magnets on a hierarchical lattice

We present a method to analyze magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal couplings of the original Hamiltonian. The two-dimensional model presented here possesses a macroscopic entropy at zero temperature in the large size limit, very close to the Pauling estimate for spin-ice on pyrochlore lattice, and a crossover towards a paramagnetic phase. The disorder due to dilution is taken into account by considering a replicated version of the recursion equations between partition functions at different lattice sizes. An analysis at first order in replica number allows for a systematic reorganization of the disorder configurations, leading to a recurrence scheme. This method is numerically implemented to evaluate the thermodynamical quantities such as specific heat and susceptibility in an external field.

cond-mat.dis-nn↗