arXiv subjects

Luigi Barletti

Publications and source records attributed to Luigi Barletti.

At least 19 recordsLinked to original sources

arXiv2026

A mathematical model for the Einstein-Podolsky-Rosen argument

We study a nonrelativistic system made of two quantum particles constrained to move on a line and a spin located at a fixed point of the line. Initially the two particles are in a maximally entangled state and the spin is down. The first particle interacts with the spin while the second particle is free, i.e., it does not interact neither with the first particle nor with the spin. We rigorously prove that there is a correlation between the state of the spin and the state of the second particle. More precisely, we show that, in a suitable scaling limit, if the first particle flips the spin, then the second particle possesses a definite momentum in the direction opposite to the spin.

math-ph↗

arXiv2022

Quantum Navier-Stokes equations for electrons in graphene

The Chapman-Enskog method, in combination with the quantum maximum entropy principle, is applied to the Wigner equation in order to obtain quantum Navier-Stokes equations for electrons in graphene in the isothermal case. The derivation is based on the quantum version of the maximum entropy principle and follows the lines of Ringhofer-Degond-Méhats' theory (J. Stat. Phys. 112, 2003 and Z. Angew. Math. Mech. 90, 2010). The model obtained in this way is then semiclassically expanded up to $\mathcal{O}(\hbar^2)$.

cond-mat.mes-hall↗

arXiv2021

Formal derivation of quantum drift-diffusion equations with spin-orbit interaction

Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interactions of Rashba type are formally derived from a collisional Wigner equation. The collisions are modeled by a Bhatnagar-Gross-Krook-type operator describing the relaxation of the electron gas to a local equilibrium that is given by the quantum maximum entropy principle. Because of non-commutativity properties of the operators, the standard diffusion scaling cannot be used in this context, and a hydrodynamic time scaling is required. A Chapman-Enskog procedure leads, up to first order in the relaxation time, to a system of nonlocal quantum drift-diffusion equations for the charge density and spin vector densities. Local equations including the Bohm potential are obtained in the semiclassical expansion up to second order in the scaled Planck constant. The main novelty of this work is that all spin components are considered, while previous models only consider special spin directions.

math.AP↗

arXiv2020

Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interaction

Quantum drift-diffusion equations are derived for a two-dimensional electron gas with spin-orbit interaction of Rashba type. The (formal) derivation turns out to be a non-standard application of the usual mathematical tools, such as Wigner transform, Moyal product expansion and Chapman-Enskog expansion. The main peculiarity consists in the fact that a non-vanishing current is already carried by the leading-order term in the Chapman-Enskog expansion. To our knowledge, this is the first example of quantum drift-diffusion equations involving the full spin vector. Indeed, previous models were either quantum bipolar (involving only the spin projection on a given axis) or full spin but semiclassical.

math-ph↗

arXiv2020

Mathematical modelling of charge transport in graphene heterojunctions

A typical graphene heterojunction device can be divided into two classical zones, where the transport is basically diffusive, separated by a "quantum active region" (e.g., a locally gated region), where the charge carriers are scattered according to the laws of quantum mechanics.In this paper we derive a mathematical model of such a device, where the classical regions are described by drift-diffusion equations and the quantum zone is seen as an interface where suitable transmission conditions are imposed that take into account the quantum scattering process. Numerical simulations show good agreement with experimental data.

cond-mat.mes-hall↗

arXiv2020

A mathematical walk into the paradox of Bloch oscillations

We describe mathematically the apparently paradoxical phenomenon that an electronic current in a semiconductor can flow because of collisions, and not despite them. A transport model of charge transport in a one-dimensional semiconductor crystal is considered, where each electron follows the periodic hamiltonian trajectories, determined by the semiconductor band structure, and undergoes non-elastic collisions with a phonon bath. Starting from the detailed phase-space model, a closed system of ODEs is obtained for averaged quantities. Such a simplified model is nevertheless capable of describing transient Bloch oscillations, their damping and the consequent onset of a steady current flow, which is in good agreement with the available experimental data.

cond-mat.stat-mech↗

arXiv2020

On a nonlinear parabolic problem arising in the quantum diffusive description of a degenerate fermion gas

This article studies, both theoretically and numerically, a nonlinear drift-diffusion equation describing a gas of fermions in the zero-temperature limit. The equation is considered on a bounded domain whose boundary is divided into an "insulating" part, where homogeneous Neumann conditions are imposed, and a "contact" part, where nonhomogeneous Dirichlet data are assigned. The existence of stationary solutions for a suitable class of Dirichlet data is proven by assuming a simple domain configuration. The long-time behavior of the time-dependent solution, for more complex domain configurations, is investigated by means of numerical experiments.

math.AP↗

arXiv2020

Some results on discrete eigenvalues for the Stochastic Nonlinear Schroedinger Equation in fiber optics

We study a stochastic Nonlinear Schroedinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In particular, we focus on the propagation of discrete eigenvalues along a focusing fiber. Since the stochastic NLSE is not exactly integrable by means of the NFT, then we use a perturbation approach, where we assume that the signal-to-noise ratio is high. The zeroth-order perturbation leads to the deterministic NLSE while the first-order perturbation allows to describe the statistics of the discrete eigenvalues. This is important to understand the properties of the channel for recently devised optical transmission techniques, where the information is encoded in the nonlinear Fourier spectrum.

nlin.PS↗

arXiv2020

Quantum transmission conditions for diffusive transport in graphene with steep potentials

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

math-ph↗

arXiv2020

Adding decoherence to the Wigner equation

Starting from the detailed description of the single-collision decoherence mechanism proposed by Adami, Hauray and Negulescu, we derive a Wigner equation endowed with a decoherence term of a fairly general form. This equation is shown to contain well known decoherence models, such as the Wigner-Fokker-Planck equation, as particular cases. The effect of the decoherence mechanism on the dynamics of the macroscopic moments (density, current, energy) is illustrated by deriving the corresponding set of balance laws. The issue of large-time asymptotics of our model is addressed in the particular, although physically relevant, case of gaussian solutions. It is shown that the addition of a Caldeira-Legget friction term provides the asymptotic behaviour that one expects on the basis of physical considerations.

quant-ph↗

arXiv2020

Spectrally accurate space-time solution of Manakov systems

In this paper, we study the numerical solution of Manakov systems by using a spectrally accurate Fourier decomposition in space, coupled with a spectrally accurate time integration. This latter relies on the use of spectral Hamiltonian boundary Value Methods. The used approach allows to conserve all the physical invariants of the systems. Some numerical tests are reported.

math.NA↗

arXiv2019

Quantum electronic trasport in graphene: a kinetic and fluid-dynamic approach

We derive a fluid-dynamic model for electron transport near a Dirac point in graphene. The derivation is based on the minimum entropy principle, which is exploited in order to close fluid-dynamic equations for quantum mixed states. To this aim we make two main approximations: the usual semiclassical approximation ($\hbar \ll 1$) and a new one, namely the `strongly-mixed state' approximation. Particular solutions of the fluid-dynamic equations are discussed which are of physical interest.

math-ph↗

arXiv2017

Hybrid classical-quantum models for charge transport in graphene with sharp potentials

We give a concise account on the derivation of hybrid quantum-classical models for stationary electron transport in graphene, in presence of sharp potential steps of barriers. A quantum region (an asymptotically thin strip around the potential step or barrier) is coupled through the quantum scattering data to a classical region, where electron transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of the Chapman-Enskog method, which requires the introduction of a boundary layer corrector and the discussion of a system of coupled Milne problems.

math-ph↗

arXiv2016

Hamiltonian control of Kuramoto oscillators

Many coordination phenomena are based on a synchronisation process, whose global behaviour emerges from the interactions among the individual parts. Often in Nature, such self-organising mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are however cases where synchronisation acts against the stability of the system; for instance in the case of engineered structures, resonances among sub parts can destabilise the whole system. In this Letter we propose an innovative control method to tackle the synchronisation process based on the use of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronisation. We present our results on the paradigmatic Kuramoto model but the applicability domain is far more large.

nlin.AO↗

arXiv2016

Hydrodynamic equations for an electron gas in graphene

In this paper we review, and extend to the non-isothermal case, some results concerning the application of the maximum entropy closure technique to the derivation of hydrodynamic equations for particles with spin-orbit interaction and Fermi-Dirac statistics. In the second part of the paper we treat in more details the case of electrons on a graphene sheet and investigate various asymptotic regimes.

math-ph↗

arXiv2015

Signal-noise interaction in nonlinear optical fibers: a hydrodynamic approach

We present a new perturbative approach to the study of signal-noise interactions in nonlinear optical fibers. The approach is based on the hydrodynamic formulation of the nonlinear Schrödinger equation that governs the propagation of light in the fiber. Our method is discussed in general and is developed in more details for some special cases, namely the small-dispersion regime, the continuous-wave (CW) signal and the solitonic pulse. The accuracy of the approach is numerically tested in the CW case.

physics.optics↗

arXiv2015

Numerical Methods for the Inverse Nonlinear Fourier Transform

We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the proposed method requires the lowest number of operations

math.NA↗

arXiv2014

Quantum transport in crystals: effective-mass theorem and k.p Hamiltonians

In this paper the effective mass approximation and k.p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k.p and effective mass models, well known in solid-state physics, are proved to be close (in strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.

math-ph↗