# Stam NicolisUniversity of Tours | UFR · Département de Physique

Stam Nicolis

PhD, HDR

## About

88

Publications

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Introduction

Stam Nicolis currently works at the Département de Physique, University of Tours. Stam does research in Mathematical Physics, Elementary Particle Physics and Computational Physics. One current project is 'models for discrete and random near horizon black hole geometries.'
Another is understanding how supersymmetry describes the consistent description of thermal, disorder, or quantum fluctuations; this is related, also, to work on the description of fluctuations in magnetic systems using Nambu mechanics, a generalization of Hamiltonian mechanics.

Additional affiliations

September 1995 - present

## Publications

Publications (88)

We construct Arnol'd cat map lattice field theories (ACML) with linear symplectic interactions, of tuneable locality in one or higher dimensions. The construction is based on the determination of special couplings for a system of $n$ maps, the dynamics of each of which is described by a $k-$Fibonacci sequence. They provide examples of lattice field...

Simplified models are a necessary steppingstone for understanding collective neural network dynamics, in particular the transitions between different kinds of behavior, whose universality can be captured by such models, without prejudice. One such model, the cortical branching model (CBM), has previously been used to characterize part of the univer...

According to the holographic picture of 't Hooft and Susskind, the black hole entropy, $S_{\rm BH}$, is carried by the chaotic microscopic degrees of freedom, that live in the near horizon geometry and have a Hilbert space of states of finite dimension, $d=\exp(S_{\rm BH})$. In previous work we have proposed that the near horizon geometry, when the...

The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the functional integral for the noise, with which the physical degrees of freedom are in equilibrium. The absolut...

Nutation has been recognized as of great significance for spintronics; but justifying its presence has proven to be a hard problem. In this paper, we show that nutation can be understood as emerging from a systematic expansion of a kernel that describes the history of the interaction of a magnetic moment with a bath of colored noise. The parameter...

The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the functional integral for the noise, with which the physical degrees of freedom are in equilibrium. The absolut...

The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the functional integral for the noise, with which the physical degrees of freedom are in equilibrium. The absolut...

Topological insulators are materials where current does not flow through the bulk, but along the boundaries, only. They are of particular practical importance, since it is considerably more difficult, by “conventional” means, to affect their transport properties, than for the case of conventional materials. They are, thus, particularly robust to pe...

Nutation has been recognized as of great significance for spintronics; but justifying its presence has proven to be a hard problem, since overdamping has long been assumed to wash out its effects. In this paper we show that nutation can be understood as emerging from a systematic expansion of a kernel that describes the history of the interaction o...

At short time scales, the inertia term becomes relevant for the magnetization dynamics of ferromagnets and leads to nutation for the magnetization vector. For the case of spatially extended magnetic systems, for instance, Heisenberg spin chains with the isotropic spin-exchange interaction, this leads to the appearance of a collective excitation, th...

We show that the fluctuations of the periodic orbits of deterministically chaotic systems can be captured by supersymmetry, in the sense that they are repackaged in the contribution of the absolute value of the determinant of the noise fields, defined by the equations of motion.

We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as in terms of a stochastic formulation. At the level of the deterministic equations, we deduce relations between...

Topological insulators are materials where current does not flow through the bulk, but along the boundaries, only. They are of particular practical importance, since it is considerably more difficult, by "conventional" means, to affect their transport properties, than for the case of conventional materials. They are, thus, particularly robust to pe...

We show that the fluctuations of the periodic orbits of deterministically chaotic systems can be captured by supersymmetry, in the sense that they are repackaged in the contribution of the absolute value of the determinant of the noise fields, defined by the equations of motion.

In this paper, we study the switching properties of the dynamics of magnetic moments that interact with an elastic medium. To do so, we construct a Hamiltonian framework that can take into account the dynamics in phase space of the variables that describe the magnetic moments in a consistent way. It is convenient to describe the magnetic moments as...

The inertia term becomes relevant for the magnetization dynamics of ferromagnets at short time scales and leads to nutation motion of the magnetization vector. In the simplest model, of a Heisenberg spin chain with isotropic spin-exchange interaction, the occurrence of a "nutation wave" is analytically demonstrated and numerically confirmed. The co...

This is the fulltext of the updated version of http://arxiv.org/abs/1405.0820

Update, available at http://arxiv.org/abs/1405.0820. The consistent closure of any quantum mechanical model of single particle dynamics, in the path integral formalism, is described by the absolute value of a certain determinant. The properties of this new term can be deduced by measuring the correlation functions of composite functions of the posi...

We present and study in detail the construction of a discrete and finite arithmetic geometry AdS$_2[N]$ and show that an appropriate scaling limit exists, as $N\to\infty,$ that can be identified with the universal AdS$_2$ radial and time near horizon geometry of extremal black holes. The AdS$_2[N]$ geometry has been proposed as a toy model for desc...

In this paper we propose a Hamiltonian framework for the dynamics of magnetic moments, in interaction with an elastic medium, that can take into account the dynamics in phase space of the variables that describe the magnetic moments in a consistent way. While such a description involves describing the magnetic moments as bilinears of anticommuting...

In this paper we propose a Hamiltonian framework for the dynamics of magnetic moments, in interaction with an elastic medium, that can take into account the dynamics in phase space of the variables that describe the magnetic moments in a consistent way. While such a description involves describing the magnetic moments as bilinears of anticommuting...

A phenomenological model is constructed, that captures the effects of coupling magnetic and elastic degrees of freedom, in the presence of external, stochastic perturbations, in terms of the interaction of magnetic moments with a bath, whose individual degrees of freedom cannot be resolved and only their mesoscopic properties are relevant. In the p...

We propose a functional integral framework for the derivation of hierarchies of Landau-Lifshitz-Bloch (LLB) equations that describe the flow toward equilibrium of the first and second moments of the magnetization. The short-scale description is defined by the stochastic Landau-Lifshitz-Gilbert equation, under both Markovian or non-Markovian noise,...

In this supplemental material, the functional calculation associated to the derivation of hierarchies of Landau-Lifshitz-Bloch (LLB) equations, as presented in the main body of the article, is reviewed in details. A very general step-by-step derivation is presented, from simple definitions (such as the correlation function of the noise, or the Lang...

A phenomenological model is constructed, that captures the effects of coupling magnetic and elastic degrees of freedom, in the presence of external, stochastic perturbations, in terms of the interaction of magnetic moments with a bath, whose individual degrees of freedom cannot be resolved and only their mesoscopic properties are relevant. In the p...

We show that it is possible to consistently describe dynamical systems, whose equations of motion are of degree higher than two, in the microcanonical ensemble, even if the higher derivatives aren't coordinate artifacts. Higher time derivatives imply that there are more than one Hamiltonians, conserved quantities due to time translation invariance,...

Based on our recent work on the discretization of the radial \(\hbox {AdS}_2\) geometry of extremal BH horizons, we present a toy model for the chaotic unitary evolution of infalling single-particle wave packets. We construct explicitly the eigenstates and eigenvalues for the single-particle dynamics for an observer falling into the BH horizon, wit...

We describe a formulation of the group action principle, for linear Nambu flows, that explicitly takes into account all the defining properties of Nambu mechanics and illustrate its relevance by showing how it can be used to describe the off-shell states and superpositions thereof that define the transition amplitudes for the quantization of Larmor...

We study a generalization of the Langevin equation, that describes fluctuations, of commuting degrees of freedom, for scalar field theories with worldvolumes of arbitrary dimension, following Parisi and Sourlas and correspondingly generalizes the Nicolai map. Supersymmetry appears inevitably, as defining the consistent closure of system+fluctuation...

The consequences of coupling magnetic and elastic degrees of freedom, where spins and deformations are carried by point-like objects subject to local interactions, are studied, theoretically and by detailed numerical simulations. From the constrained Lagrangians we derive consistent equations of motion for the coupled dynamical variables. In order...

The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of a damped magnetization vector that can be understood as a generalization of Larmor spin precession. The LLG equation cannot be deduced from the Hamiltonian framework, by introducing a coupling to a usual bath, but requires the introduction of additional constraints. It is shown th...

When nano-magnets are coupled to random external sources, their magnetization becomes a random variable, whose properties are defined by an induced probability density, that can be reconstructed from its moments, using the Langevin equation, for mapping the noise to the dynamical degrees of freedom. When the spin dynamics is discretized in time, a...

We present a toy model for the chaotic unitary scattering of single particle wave packets on the radial AdS$_2$ geometry of extremal BH horizons. Based on our recent work for the discretization of the AdS$_2$ space-time, which describes a finite and random geometry, by modular arithmetic, we investigate the validity of the eigenstate thermalization...

The Fokker--Planck equation describes the evolution of a probability distribution towards equilibrium--the flow parameter is the equilibration time. Assuming the distribution remains normalizable for all times, it is equivalent to an open hierarchy of equations for the moments. Ways of closing this hierarchy have been proposed; ways of explicitly s...

We study the relation between the partition function of a non--relativistic particle, that describes the equilibrium fluctuations implicitly, and the partition function of the same system, deduced from the Langevin equation, that describes the fluctuations explicitly, of a bath with additive white--noise properties. We show that both can be related...

A functional calculus approach is applied to the derivation of evolution equations for the moments of the magnetization dynamics of systems subject to stochastic fields. It allows us to derive a general framework for obtaining the master equation for the stochastic magnetization dynamics, that is applied to both, Markovian and non-Markovian dynamic...

A stochastic approach for the description of the time evolution of the magnetization of nanomagnets is proposed , that interpolates between the Landau-Lifshitz-Gilbert and the Landau-Lifshitz-Bloch approximations, by varying the strength of the noise. Its finite autocorrelation time, i.e. when it may be described as colored, rather than white, is,...

Statistical averaging theorems allow us to derive a set of equations for the averaged magnetization dynamics in the presence of colored (non-Markovian) noise. The non-Markovian character of the noise is described by a finite auto-correlation time, τ , that can be identified with the finite response time of the thermal bath to the system of interest...

We propose a stochastic approach for the description of the time evolution of the magnetization of nano-magnets, that interpolates between the Landau–Lifshitz–Gilbert and the Landau–Lifshitz–Bloch approximations , by varying the strength of the noise. In addition, we take into account the autocorrelation time of the noise and explore the consequenc...

We review an explicit regularization of the AdS$_2$/CFT$_1$ correspondence,
that preserves all isometries of bulk and boundary degrees of freedom. This
scheme is useful to characterize the space of the unitary evolution operators
that describe the dynamics of the microstates of extremal black holes in four
spacetime dimensions. Using techniques fro...

In order to perceive that a physical system evolves in time, two requirements
must be met: (a) it must be possible to define a "clock" and (b) it must be
possible to make a copy of the state of the system, that can be reliably
retrieved to make a comparison. We investigate what constraints quantum
mechanics poses on these issues, in light of recent...

The Landau-Lifshitz-Gilbert equations for the evolution of the magnetization, in presence of an external torque, can be cast in the form of the Lorenz equations and, thus, can describe chaotic fluctuations. To study quantum effects, we describe the magnetization by matrices, that take values in a Lie algebra. The finite dimensionality of the repres...

We study quantum mechanics in one space dimension in the stochastic
formalism. We show that the partition function of the theory is, in fact,
equivalent to that of a model, whose action is explicitly invariant (up to
surface terms) under supersymmetry transformations--but whose invariance under
the stochastic identities is not obvious, due to an ap...

A generalization of the Lorenz equations is proposed where the variables take
values in a Lie algebra. The finite dimensionality of the representation
encodes the quantum fluctuations, while the non-linear nature of the equations
can describe chaotic fluctuations. We identify a criterion, for the appearance
of such non-linear terms. This depends on...

The conformational complexity of chain-like macromolecules such as proteins and other linear polymers is much larger than that of point-like atoms and molecules. Unlike particles, chains can bend, twist, and even become knotted. Thus chains might also display a much richer phase structure. Unfortunately, it is not very easy to characterize the phas...

We propose a finite discretization for the black hole, near horizon, geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS$_2 =SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$. We implement its discretization by replacing the set of real numbers $\mathbb{R...

We study quantum mechanics in the stochastic formulation, using the
functional integral approach. The noise term enters the classical action as a
local contribution of anticommuting fields. The partition function is not
invariant under ${\mathcal N}=1$ SUSY, but can be obtained from a, manifestly,
supersymmetric expression, upon fixing a local ferm...

We use anticommuting variables to study probability distributions of random
variables, that are solutions of Langevin's equation. We show that the
probability density always enjoys "worldpoint supersymmetry". The partition
function, however, may not. We find that the domain of integration can acquire
a boundary, that implies that the auxiliary fiel...

We write the partition function for a lattice gauge theory, with compact
gauge group, exactly in terms of unconstrained variables and show that, in the
mean field approximation, the dynamics of pure gauge theories, invariant under
compact, continuous,groups of rank 1 is the same for all. We explicitly obtain
the equivalence for the case of SU(2) an...

Field theories with extra dimensions live in a limbo. While their classical
solutions have been the subject of considerable study, their quantum aspects
are difficult to control. A special class of such theories are anisotropic
gauge theories. The anisotropy was originally introduced to localize chiral
fermions. Their continuum limit is of practica...

The current flow from the bulk is due to the anomaly on the brane-but the absence of current flow is not, necessarily, due to anomaly cancellation, but to the absence of the chiral zero modes themselves, due to the existence of the layered phase. This can be understood in terms of the difference between the Chern-Simons terms in three and five dime...

We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus T_N^3 represented by elements of the group SL(3,Z_N). These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three dimensional toroidal phase space and are characterized by invariant vectors, a, of T_N^3. We qu...

The extra dimensional defects that are introduced to generate the lattice chiral zero modes are not simply a computational trick, but have interesting physical consequences. After reviewing what is known about the layered phase they can generate, I argue how it is possible to simulate Yang-Mills theories with reduced systematic errors and speculate...

We study an extension of the Hopfield model, where a certain number of "privileged" (or "marked") patterns enters the Hebb rule with weight 1, while the remaining enter with weight γ < 1. Both sets are infinite. Assuming replica symmetry, the zero-temperature capacity vs. γ and overlap vs. γ diagrams are calculated and compared with numerical simul...

An extension of the Hopfield model is studied, whereby a certain number of privileged patterns are marked, during the learning process. The replica trick is used in studying the retrieval properties of such networks. The relevance of the extension to other biological processes is also discussed.

We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the non-commutative 2-torus, T_{2^n}^2$ and thus is relevant for non-commutative field theories as well as theories of q...

We construct quantum evolution operators on the space of states, that realize the metaplectic representation of the modular group SL(2,Z_2^n). This representation acts in a natural way on the coordinates of the non-commutative 2-torus and thus is relevant for noncommutative field theories as well as theories of quantum space-time. The larger class...

An algorithm is proposed for calculating the energy of ion-dipole interactions in concentrated organic electrolytes. The ion-dipole interactions increase with increasing salt concentration and must be taken into account when the activation energy for the conductivity is calculated. In this case, the contribution of ion-dipole interactions to the ac...

We construct the unitary evolution operators that realize the quantization of linear maps of SL(2,R) over phase spaces of arbitrary integer discretization N and show the non-trivial dependence on the arithmetic nature of N. We discuss the corresponding uncertainty principle and construct the corresponding coherent states, that may be interpreted as...

We explore the phase diagram of the 5-D anisotropic Abelian Higgs model by Monte Carlo simulations. In particular, we study the transition between the confining phase and the four dimensional layered Higgs phase. We find that, in a certain region of the lattice parameter space, this transition can be first order and that each layer moves into the H...

We find 3-brane Higgs and Coulomb phases in the 5D Abelian Higgs Model and
determine the transition surfaces that separate them from the usual bulk
phases.

We explore the phase diagram of the five-dimensional anisotropic Abelian
Higgs model by Monte Carlo simulations. In particular, we study the transition
between the confining phase and the four dimensional layered Higgs phase. We
find that, in a certain region of the lattice parameter space, this transition
can be first order and that each layer mov...

We establish the phase diagram of the five-dimensional
anisotropic abelian Higgs model by mean field techniques and Monte
Carlo simulations. The anisotropy is encoded in the gauge couplings as
well as in the Higgs couplings. In addition to the usual bulk phases
(confining, Coulomb and Higgs) we find four-dimensional ``layered''
phases (3-branes) at...

We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this representation acts in a natural way on the coordinates of the non-commutative 2-torus,T^2, and thus is relevant...

Motivated by the recent findings of Wiegmann-Zabrodin and Faddeev-Kashaev, concerning the appearance of the quantum symmetry in the problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce a modification of the tight binding Azbel-Hofstadter Hamiltonian, that is a specific spin-S Euler top that can be considered as its `class...

The fluctuations of the maximum Lyapunov exponent of a product of random matrices are studied analytically and numerically. It is shown that they may be expressed as a sum of two terms, one related to the order of matrices within the product, the other to fluctuations of the number of matrices of a given type. This result is then applied to the one...

We develop number theoretic tools that allow us to perform computations
relevant for the quantum mechanics over finite fields of arbitrary, odd
size, with the same speed-up that is enjoyed by the fast Fourier
transform.

We explicitly construct the quantization of classical linear maps of SL(2, ℝ) on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that finite quantum mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of...

The mean field theory of gauge theories with anisotropic couplings shows that they possess a layered phase, in addition to the usual confining and Coulomb phases. We find that the layered to Coulomb phase transition is second order in the absence, as well as in the presence of fermions. This is supported by Monte Carlo simulations and leads to the...

We study the effect of mixing two rules on the dynamics of one-dimensional cellular automata by large scale numerical simulations. We calculate the decay of the magnetization for the Domany-Kinzel automaton (XOR/AND mixing) to its equilibrium value in the three phases. This requires system sizes in excess of 1 million sites. We also find severe fin...

We study Abelian gauge theories with anisotropic couplings in 4 + D dimensions. A layered phase is present, in the absence as well as in the presence of fermions. A line of second order transitions separates the layered from the Coulomb phase, if D ⩽ 3.

Chiral defect fermions on the lattice in 4 + 1 dimensions are analyzed using mean field theory. The fermion propagator has a localized chiral model in weak coupling but loses it when the coupling in the unphysical fifth direction becomes too large. A layered phase à la Fu-Nielsen appears where the theory is vector-like in every layer.

We present a numerical method for the study of the stability-capacity diagram of the Ising perceptron that is readily scalable, thus providing the opportunity to resolve some open issues on this problem. We also discuss the possibility of studying multi-layer systems.

The authors study the fluctuations of the two-point correlation function in one-dimensional disordered spin models. These survive even in the thermodynamic limit and, in order to reconstruct their probability distribution from the moments, they study a set of generalised correlation lengths zeta q. These moments may also be calculated within the tr...

The retrieval properties of attractor neural networks are studied, subject to a modification of the representation of the stimulus input. In the present study the stimulus imposes an initial state on the network and then remains as a persistent potential input (local field) of weakened amplitude, but containing the same number of errors as the init...

The stability-capacity diagram of a fully connected neural network, whose bonds take the values 1 and -1 with equal probability, is determined numerically. Two different optimization methods (simulated annealing and tabu search) are used and their relevant features are discussed. The results indicate the existence of a region, in the stability-capa...

Discrete curved-space models are a useful paradigm for complex dense-packed structures such as metallic glasses. The idea is to define an ideal structure in a curved space where a given local packing arrangement may propagate and then introduce decurving defects to map it onto a realistic flat-space structure. In the following we study the effect o...

Les verres métalliques peuvent être considérés, dans une bonne approximation, comme des empilements aléatoires de sphères interagissant avec de simples potentiels de paires. C'est raisonnable, d'un point de vue géométrique, puisque l'unité de l'empilement compact à trois dimensions, le tétraèdre, ne remplit pas l'espace euclidien. Il pave un espace...

Erratum for Europhys. Lett.1 (11) 571-578 (1986)

Polytopes have proved to be interesting ideal models for the description of many disordered systems. We present here a new method for introducing disciplination lines in a polytope. These lines are members of a fibration of S3 by great circles. In the compact structure case, the disclinated polytopes are in one-to-one correspondance with triangulat...

We construct quantum evolution operators on the space of states, that realize the metaplectic representation of the modular group SL(2, Z2n). This representation acts in a natural way on the coordinates of the non-commutative 2-torus, T22n and thus is relevant for noncommutative field theories as well as theories of quantum space-time. The larger c...