arXiv subjects

Sébastien Fumeron

Publications and source records attributed to Sébastien Fumeron.

At least 19 recordsLinked to original sources

arXiv2026

Fractal and Spectral Dimensions as Determinants of Thermal Ablation Outcomes in Cancer Tissues

Clinical thermal ablation outcomes display significant variability that classical bio-heat models cannot fully explain. One reason may lie in the fractal architecture of biological tissues, which has been identified as a robust biomarker directly correlated with cancer grades. This structural heterogeneity, together with memory effects (e.g., thermotolerance), causes heat transfer in living tissues to differ from Fourier diffusion, resulting in anomalous biological transport. In this work, we implemented a realistic fractal-fractional bio-heat model, with non-linear perfusion and PI-controlled power delivery, to quantify the role of tissue fractality in ablation outcomes. Our results reveal that the expansion of coagulation zones is jointly controlled by fractal geometry and its associated topological connectivity. These findings highlight spectral dimension as a key driver of clinical variability, successfully reproducing the reduced ablative efficacy in liver metastases compared to primary carcinomas, and provide evidence for topologically informed treatment strategies for the thermal ablation of malignant neoplasms.

cond-mat.stat-mech↗

arXiv2025

Generalised fractional Rabi problem

Fractional quantum dynamics provides a natural framework to capture nonlocal temporal behavior and memory effects in quantum systems. In this work, we analyze the physical consequences of fractional-order quantum evolution using a Green's function formulation based on the Caputo fractional derivative. Explicit iterative expressions for the evolved state are derived and applied to an extended two-level Rabi model, a paradigmatic setting for coherent quantum control. We find that even in the absence of external driving, the static Hamiltonian term induces non-trivial spin dynamics with damping features directly linked to the fractional temporal nonlocality. When a periodically varying driving field is introduced, the competition between energy injection and memory effects gives rise to a richer dynamical behavior, manifest in the evolution of spin polarization, autocorrelation function, and fidelity. Unlike the standard Rabi oscillations characterized by a fixed frequency, the fractional regime introduces controllable damping and dephasing governed by the degree of fractionality. These distinctive signatures could be observable through the Loschmidt echo and autocorrelation function, and would offer potential routes to probe fractional quantum dynamics experimentally. Our findings open pathways toward exploring memory-induced dynamical phenomena in other systems effectively described by a two-level approximation, such as graphene-like materials and topological SSH chains, where non-integer order evolution may reveal novel topological or relaxation effects.

quant-ph↗

arXiv2025

Bio-heat regimes in fractal-based models of tumors

Anomalous heat diffusion is investigated for biological tissues displaying a fractal structure and long-term thermal memory, which is modeled via a fractional derivative. For increasing values of the fractional derivation order, the tissue temperature displays three kinds of bio-heat regimes: damped (or sub-diffusive), critical damping and under-damped oscillations. The temperature profiles depend on the fractal dimension of the tissue but notably also on a parameter related to its topology: the spectral dimension. The parametric analysis reveals that these two parameters have antagonistic effects on the pseudo period of the temperature oscillations and their amplitudes. We discuss how our results might impact some treatment protocols.

physics.bio-ph↗

arXiv2024

Differential geometry, a possible avenue for thermal ablation in oncology?

We report a model for hyperthermia therapies based on heat diffusion in a biological tissue containing a topological defect. Biological tissues behave like active liquid crystals with the presence of topological defects which are likely to anchor tumors during the metastatic phase of cancer evolution and the therapy challenge is to destroy the cancer cells without damaging surrounding healthy tissues. The defect creates an effective non-Euclidean geometry for low-energy excitations, modifying the bio-heat equation. Applications to protocols of thermal ablation for various biological tissues (liver, prostate, and skin) is analyzed and discussed.

cond-mat.stat-mech↗

arXiv2024

Fractional diffusion equations interpolate between damping and waves

The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved and an application to Pennes bioheat model is presented. Generically, a wave-like transport at short times passes over to a diffusion-like behaviour at later times.

math-ph↗

arXiv2023

On the possibility of classical vacuum polarization and magnetization

It is common practice to take for granted the equality (up to the constant $\varepsilon_0$) of the electric displacement ($\bf{D}$) and electric ($\bf{E}$) field vectors in vacuum. The same happens with the magnetic field ($\bf{H}$) and the magnetic flux density ($\bf{B}$) vectors (up to the constant $μ_0^{-1}$). The fact that gravity may change this by effectively inducing dielectric or magnetic responses to the primary fields is commonly overlooked. It is the purpose of this communication to call attention to classical polarization or magnetization of the vacuum due to the concomitant presence of gravitational and electromagnetic sources. The formalism of differential forms (exterior calculus) is used since it provides a clear-cut way to achieve this. This work offers new routes for possible detection of various spacetime geometries via their electromagnetic manifestations and the way they influence light propagation.

gr-qc↗

arXiv2023

Geometric theory of topological defects: methodological developments and new trends

Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the art of the differential geometry of nematic liquid crystals, with a special emphasis on linear defects. We then discuss unexpected but deep connections with cosmology and high-energy-physics, and conclude with a review on defect engineering for transport phenomena.

cond-mat.soft↗

arXiv2022

Introduction to topological defects: from liquid crystals to particle physics

Liquid crystals are assemblies of rod-like molecules which self-organize to form mesophases, in-between ordinary liquids and anisotropic crystals. At each point, the molecules collectively orient themselves along a privileged direction, which locally defines an orientational order. Sometimes, this order is broken and singularities appear in the form of topological defects. This tutorial article is dedicated to the geometry, topology and physics of these defects. We introduce the main models used to describe the nematic phase and discuss the isotropic-nematic phase transition. Then, we present the different families of defects in nematics and examine some of their physical outcomes. Finally, we show that topological defects are universal patterns of nature, appearing not only in soft matter, but also in biology, cosmology, geology and even particle physics.

cond-mat.soft↗

arXiv2022

Diffusion in the presence of a chiral topological defect

We study the diffusion processes of a real scalar field in the presence of the distorsion field induced by a chiral topological defect. The defect modifies the usual Euclidean background geometry into a non-diagonal Riemann-Cartan geometry characterized by a singular torsion field. The new form of the diffusion equation is established and the scalar field distribution in the vicinity of the defect is investigated numerically. Results show a high sensitivity to the boundary conditions. In the transient regime, we find that the defect vorticity generates an angular momentum associated to the diffusion flow and we discuss its main properties.

hep-th↗

arXiv2022

Classical Kalb-Ramond field theory in curved spacetimes

We propose to develop the Kalb-Ramond theory in four-dimensional spacetime at the level of a classical field theory by following the same formal development steps as in Maxwell theory of standard electrodynamics. Solutions of Kalb-Ramond theory in the presence of static sources in various curved spacetimes are then analyzed. A question that we address here is that of a possible Kalb-Ramond polarization in curved spacetimes, like one can encounter a dielectric polarization in ordinary Maxwell electrodynamics in certain types of spacetimes.

gr-qc↗

arXiv2021

Magnetic and geometric effects on the electronic transport of metallic nanotubes

The investigation of curved low-dimensional systems is a topic of great research interest. Such investigations include two-dimensional systems with cylindrical symmetry. In this work, we present a numerical study of the electronic transport properties of metallic nanotubes deviating from the cylindrical form either by having a bump or a depression, and under the influence of a magnetic field. Under these circumstances, it is found that the nanotube may be used as an energy high-pass filter for electrons. It is also shown that the device can be used to tune the angular momentum of transmitted electrons.

cond-mat.mes-hall↗

arXiv2020

Improving student understanding of electrodynamics: the case for differential forms

The illuminating role of differential forms in electromagnetism is seldom discussed in the classroom. It is the aim of this article to bring forth some of the relevant insights that can be learnt from a differential forms approach to E\&M. The article is self-contained in that no previous knowledge of forms is needed to follow it through. The effective polarization of the classical vacuum due to a uniform gravitational field and of the quantum vacuum in the Casimir effect are used to illustrate the power and easiness of interpretation of differential forms in dealing with electromagnetism in nontrivial situations. We hope that this article motivates the physics teacher to bring the subject of differential forms to the classroom.

gr-qc↗

arXiv2020

Spin current generation and control in carbon nanotubes by combining rotation and magnetic field

We study the quantum dynamics of ballistic electrons in rotating carbon nanotubes in the presence of a uniform magnetic field. When the field is parallel to the nanotube axis, the rotation-induced electric field brings about the spin-orbit interaction which, together with the kinetic, inertial, and Zeeman terms, compose the Schrödinger-Pauli Hamiltonian of the system. Full diagonalization of this Hamiltonian yields the eigenstates and eigenenergies leading to the calculation of the charge and spin currents. Our main result is the demonstration that, by suitably combining the applied magnetic field intensity and rotation speed, one can tune one of the currents to zero while keeping the other one finite, giving rise to a spin current generator.

cond-mat.mes-hall↗

arXiv2018

Optical concentrator from a hyperbolic liquid crystal metamaterial

We examine the optical properties of two different configurations of a cylindrical device made from a hyperbolic metamaterial with optical axis defined by circular and radial director fields. The hyperbolic metamaterial is an uniaxial anisotropic medium for which the ratio between ordinary and extraordinary permittivities is negative, leading to a particular effective geometry with two timelike coordinates in the metric (Kleinian signature). By using differential geometry tools we are able to perform a comparison between a simple geometrical optics treatment and the wave formalism that shows the concentration of light along the cylinder axis for the case of the circular field configuration, whatever the injection conditions are.

physics.optics↗

arXiv2017

Cosmology in the laboratory: an analogy between hyperbolic metamaterials and the Milne universe

This article shows that the compactified Milne universe geometry, a toy model for the big crunch/big bang transition, can be realized in hyperbolic metamaterials, a new class of nanoengineered systems which have recently found its way as an experimental playground for cosmological ideas. On one side, Klein-Gordon particles, as well as tachyons, are used as probes of the Milne geometry. On the other side, the propagation of light in two versions of a liquid crystal-based metamaterial provides the analogy. It is shown that ray and wave optics in the metamaterial mimic, respectively, the classical trajectories and wave function propagation, of the Milne probes, leading to the exciting perspective of realizing experimental tests of particle tunneling through the cosmic singularity, for instance.

gr-qc↗

arXiv2017

The wiggly cosmic string as a waveguide for massless and massive fields

We examine the effect of a wiggly cosmic string for both massless and massive particle propagation along the string axis. We show that the wave equation that governs the propagation of a scalar field in the neighborhood of a wiggly string is formally equivalent to the quantum wave equation describing the hydrogen atom in two dimensions. We further show that the wiggly string spacetime behaves as a gravitational waveguide in which the quantized wave modes propagate with frequencies that depend on the mass, string energy density, and string tension. We propose an analogy with an optical fiber, defining an effective refractive index likely to mimic the cosmic string effect in the laboratory.

gr-qc↗

arXiv2017

Using torsion to manipulate spin currents

We address the problem of quantum particles moving on a manifold characterised by the presence of torsion along a preferential axis. In fact, such a torsion may be taylored by the presence of a single screw dislocation, whose Burgers vector measures the torsion amplitude. The problem, first treated in the relativistic limit describing fermions that couple minimally to torsion, is then analysed in the Pauli limit We show that torsion induces a geometric potential and also that it couples generically to the phase of the wave function, giving rise to the possibility of using torsion to manipulate spin currents in the case of spinor wave functions. These results emerge as an alternative strategy for using screw dislocations in the design of spintronic-based devices.

cond-mat.mes-hall↗

arXiv2016

Retrieving the saddle-splay elastic constant $K_{24}$ of nematic liquid crystals from an algebraic approach

The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant $K_{24}$. However, the usual methods to retrieve the latter involves an adjusting of computational parameters through the visual comparisons between the experimental light interference pattern or a $^{2}H-NMR$ spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparisons, we develop an algebraic method for obtaining of saddle-splay elastic constant $K_{24}$. Considering an escaped-radial disclination inside a capillary tube with radius $R_{0}$ of tens of micrometers, we use a metric approach to study the propagation of the light (in the scalar wave approximation), near to the surface of the tube and to determine the light interference pattern due to the defect. The latter is responsible for the existence of a well-defined interference peak associated to a unique angle $ϕ_{0}$. Since this angle depends on factors such as refractive indexes, curvature elastic constants, anchoring regime, surface anchoring strength and radius $R_{0}$, the measurement of $ϕ_{0}$ from the interference experiments involving two different radii allows us to algebraically retrieve $K_{24}$. Our method allowed us to give the first reported estimation of $K_{24}$ for the lyotropic chromonic liquid crystal Sunset Yellow FCF: $K_{24}=2.1\ pN$.

cond-mat.soft↗