arXiv subjects

François Leyvraz

Publications and source records attributed to François Leyvraz.

5 recordsLinked to original sources

arXiv2026

Beyond Whittle: exact finite-time multispectral statistics from a single Brownian trajectory in a harmonic trap

Power spectral densities are often interpreted through ensemble averages and long-time asymptotics. In many experiments, however, only a single finite record is available, so spectral estimators remain broadly distributed and the usual independence assumptions across frequencies need not hold. Here we develop an exact finite-$T$ multispectral theory for an overdamped Brownian particle in a harmonic trap. For a collection of frequencies $\{ω_i\}$, we obtain an exact characterization of the joint law of the finite-time estimators $\{S(ω_i,T)\}$, together with a covariance-explicit Gaussian representation for the associated Fourier projections. This representation makes the observation-window-induced inter-frequency correlations explicit and shows how they vanish as $T\to\infty$, thereby recovering the asymptotic Whittle picture. We then use this structure to formulate a hierarchy of spectral likelihoods for inference from a single trajectory, ranging from the factorized Whittle approximation to blockwise covariance-aware approximations in frequency space. Monte Carlo simulations validate the finite-time theory and quantify the effect of neglected cross-frequency correlations on single-trajectory estimates of the trap parameters. Our results provide a controlled finite-time benchmark for spectral inference beyond the asymptotic regime.

cond-mat.stat-mech↗

arXiv2019

Electron optics in phosphorene pn junctions: Negative reflection and anti super-Klein tunneling

Ballistic electrons in phosphorene $pn$ junctions show optical-like phenomena. Phosphorene is modeled by a tight-binding Hamiltonian that describes its electronic structure at low energies, where the electrons behave in the zigzag direction as massive Dirac fermions and in the orthogonal armchair direction as Schrödinger electrons. Applying the continuum approximation, we derive the electron optics laws in phosphorene $pn$ junctions, which show very particular and unusual properties. Due to the anisotropy of the electronic structure, these laws depend strongly on the orientation of the junction with respect to the sublattice. Negative and anomalous reflection are observed for tilted junctions, while the typical specular reflection is found only, if the junction is parallel to the zigzag or armchair edges. Moreover, omni-directional total reflection, called anti-super Klein tunneling, is observed if the junction is parallel to the armchair edge. Applying the nonequilibrium Green's function method on the tight-binding model, we calculate numerically the current flow. The good agreement of both approaches confirms the atypical transport properties, which can be used in nano-devices to collimate and filter the electron flow, or to switch its direction.

cond-mat.mes-hall↗

arXiv2017

Quantum estimation of unknown parameters

We discuss the problem of finding the best measurement strategy for estimating the value of a quantum system parameter. In general the optimum quantum measurement, in the sense that it maximizes the quantum Fisher information and hence allows one to minimize the estimation error, can only be determined if the value of the parameter is already known. A modification of the quantum Van Trees inequality, which gives a lower bound on the error in the estimation of a random parameter, is proposed. The suggested inequality allows us to assert if a particular quantum measurement, together with an appropriate estimator, is optimal. An adaptive strategy to estimate the value of a parameter, based on our modified inequality, is proposed.

quant-ph↗

arXiv2015

Three dimensional diffusion with helical persistence

We formulate the the problem of persistent diffusion in three dimensions from the perspective of the Frenet--Serret equations. In contrast to one and two dimensional systems, in three dimensions persistent diffusion is, in general, a third order process. In this paper we derive a Fokker--Planck equation for the process and we calculate its effective diffusion constant. We also provide expressions for the asymptotic average displacement of the walk, as well as explicit expressions for the Fourier--Laplace transform of the correlations between the tangent, normal and binormal vectors of the motion.

cond-mat.soft↗

arXiv2007

Competitive nucleation and the Ostwald rule in a generalized Potts model with multiple metastable phases

We introduce a simple nearest-neighbor spin model with multiple metastable phases, the number and decay pathways of which are explicitly controlled by the parameters of the system. With this model we can construct, for example, a system which evolves through an arbitrarily long succession of metastable phases. We also construct systems in which different phases may nucleate competitively from a single initial phase. For such a system, we present a general method to extract from numerical simulations the individual nucleation rates of the nucleating phases. The results show that the Ostwald rule, which predicts which phase will nucleate, must be modified probabilistically when the new phases are almost equally stable. Finally, we show that the nucleation rate of a phase depends, among other things, on the number of other phases accessible from it.

cond-mat.stat-mech↗