# José Luis LópezUniversity of Granada | UGR · Department of Applied Mathematics

José Luis López

Associate Professor

## About

52

Publications

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448

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Introduction

Additional affiliations

January 2003 - present

January 1998 - December 2006

**Universidad de Granada**

## Publications

Publications (52)

In this paper, we derive a variant of the classical Keller–Segel model of chemotaxis incorporating a growth term of logistic type for the cell population , say with , and a nonstandard chemical production–degradation mechanism involving first‐ and second‐order derivatives of the logarithm of the cell density, say with , via the ()‐hydrodynamical sy...

In this paper we investigate various forms of the chemical production-degradation mechanism in a chemotactic system of Keller–Segel type under which the existence of solitary wave solutions is guaranteed. Specifically, the existence of sech-type or compactly supported solitary wave solutions as well as exponential traveling wave profiles for the ce...

In this paper we derive a variant of the classical Keller-Segel model of chemotaxis incorporating a growth term of logistic type for the cell population n(t, x), say νn(1 − n) with ν > 0, and a nonstandard chemical production-degradation mechanism involving first and second order derivatives of the logarithm of the cell density, say f λab (n, nx, n...

In this paper we investigate various forms of the chemical production-degradation mechanism in a chemotactic system of Keller-Segel type under which the existence of solitary wave solutions is guaranteed. Specifically, the existence of sech-type or compactly supported soliton solutions as well as exponential traveling wave profiles for the cell con...

In this paper, global well-posedness of the non-Markovian Unruh–Zurek and Hu–Paz–Zhang master equations with nonlinear electrostatic coupling is demonstrated. They both consist of a Wigner–Poisson like equation subjected to a dissipative Fokker–Planck mechanism with time-dependent coefficients of integral type, which makes necessary to take into ac...

The purpose of this paper is to investigate the well-posedness in the (weighted) energy space of a Schrödinger-Poisson model with additional chiral nonlinearity proportional to the electric current j[ψ] = Im(ψψ x). More precisely, a unique mild solution of the nonlinear initial value problem iψ t + ψ xx = 1 2 |x| * |ψ| 2 ψ − λj[ψ]ψ , ψ(0, x) = ψ 0...

A derivation of the equation of motion satisfied by a prototype of the forward space–time Wigner distribution, that incorporates a Fourier transformation of truncated time shifts as compared with the standard Wigner distribution, is carried out in the case of a many-body system within the formalism of nonequilibrium Green's functions of quantum fie...

In this note, the Keller-Segel model of chemotaxis is shown to come up as the hydrodynamic system describing the evolution of the probability density n(t, x) and the argument S(t, x) of a wavefunction ψ = √ n e iS that solves a cubic Schrödinger equation with focusing interaction, frictional Kostin nonlinearity and Doebner-Goldin dissipation mechan...

In this paper, global well-posedness of the non-Markovian Unruh-Zurek and Hu-Paz-Zhang master equations with nonlinear electrostatic coupling is demonstrated. They both consist of a Wigner-Poisson like equation subjected to a dissipative Fokker-Planck mechanism with time-dependent coefficients of integral type, which makes necessary to take into ac...

In this paper, global well-posedness of the non-Markovian Unruh-Zurek and Hu-Paz-Zhang master equations with nonlinear electrostatic coupling is demonstrated. They both consist of a Wigner-Poisson like equation subjected to a dissipative Fokker-Planck mechanism with time-dependent coefficients of integral type, which makes necessary to take into ac...

In this paper, global well-posedness of the non-Markovian Unruh-Zurek and Hu-Paz-Zhang master equations with nonlinear electrostatic coupling is demonstrated. They both consist of a Wigner-Poisson like equation subjected to a dissipative Fokker-Planck mechanism with time-dependent coefficients of integral type, which makes necessary to take into ac...

El cine de Jean-Luc Godard apuesta desde el principio por la búsqueda de un lenguaje depurado y renovador, en el que el conocimiento científico ocupa un papel bastante destacado. En particular, el realizador ha asimilado e incorporado satisfactoriamente el pensamiento matemático a diferentes niveles de sus elementos discursivos, como pretendemos re...

A long time description of electrostatic Schrödinger-Poisson states, satisfying i∂tψ = − 1 2 ∆xψ + C |x| * x |ψ| 2 ψ , is provided in terms of a non-Markovian Wigner formalism through the choice of the simplest charge-preserving scale group, ψε(t, x) = ψ(ε −1 t, x), in which the position variable x ∈ R 3 remains unscaled while time t ∈ R + is sent...

A phase space description of Schrödinger dynamics is provided in terms of a quantum kinetic formalism relying on the introduction of an appropriate extension of the well–known Wigner transform, also accounting for time delocalizations. This ’space–time Wigner distribution’, built upon the framework of two–time correlation functions, is shown to be...

La ciencia ha estado presente en el hecho cinematográfico desde sus orígenes, ya como impulsora de la invención misma del cinematógrafo en el ocaso del siglo XIX, ya como promotora del continuo desarrollo técnico que los soportes audiovisuales han ido experimentando y garante de la calidad de la imagen y el sonido, a la vez que elemento propiciador...

This paper is intended to provide the reader with a review of
the authors’ latest results dealing with the modeling of quantum
dissipation/diffusion effects at the level of Schrödinger
systems, in connection with the corresponding phase space
and fluid formulations of such kind of phenomena, especially
in what concerns the role of the Fokker–Planck...

A nonlinear Schrödinger equation describing how a quantum particle interacts with its surrounding reservoir is derived from the Wigner–Fokker–Planck equation (WFPE) via stochastic (Nelsonian) mechanical techniques. This model can be reduced just to a logarithmic Schrödinger equation (LSE) through a suitable gauge transformation that allows to explo...

In this paper we investigate how a dissipative, nonlinear Schrödinger model (that might be called 'Full Logarithmic Schrödinger Equation' (FLSE) for future reference) stemming from a Nelsonian stochastic approach to quantum Fokker-Planck dynamics (represented by the quantum Fokker-Planck master equation in the Wigner picture) is reduced to the 'Pur...

The aim of this paper is to derive the quantum hydrodynamic system associated with the most general class of nonlinear Schrödinger equations accounting for Fokker-Planck type diffusion of the probability density, called of Doebner-Goldin. This 'Doebner-Goldin hydrodynamic system' is shown to be reduced in most cases to a simpler one of quantum Eule...

A quantum Navier-Stokes system for the particle, momentum, and energy densities
are formally derived from the Wigner-Fokker-Planck equation using a moment method.
The viscosity term depends on the particle density with a shear viscosity
coefficient which equals the quantum diffusion coefficient of the Fokker-Planck
collision operator. The main idea...

In this paper we make it mathematically rigorous the formulation of the following quantum Schrödinger–Langevin nonlinear operator for the wavefunctionAQSL=iℏ∂t+ℏ22mΔx−λ(Sψ−〈Sψ〉)−Θℏ[nψ,Jψ] in bounded domains via its mild interpretation. The a priori ambiguity caused by the presence of the multi-valued potential λSψ, proportional to the argument of t...

In this paper we make it mathematically rigorous the formulation of the following Quantum Schrödinger-Langevin nonlinear operator for the wavefunction
$$
{\cal{A}}_{QSL} = i \hbar \partial_t + \frac{\hbar^2}{2m} \Delta_x - \lambda \big( S_\psi - \langle S_\psi \rangle \big) - \Theta_\hbar[n_\psi, J_\psi]
$$
in bounded domains via its mild interpr...

In this paper we investigate the existence of a unique global mild solution in H1(R3) of the initial-boundary value problem associated with the logarithmic Schrödinger equation , with D>0 and σ∈R∖{0}.

In this paper we are concerned with the modeling of quantum dissipation and diffusion effects at the level of the multidimensional Schrödinger equation. Our starting point is the quantum Fokker–Planck master equation describing dissipative interactions (of mass and energy) of the particle ensemble with a thermal bath in thermodynamic equilibrium. W...

This paper1 is intended to constitute a review of some mathematical theories incorporating quantum corrections to the Schrödinger-Poisson
(SP) system. More precisely we shall focus our attention in the electrostatic Poisson potential with corrections of power
type.

In this paper, global well–posedness as well as regularity of very high temperature Caldeira–Leggett models with repulsive Poisson coupling are proved by using Green function techniques and Fokker–Planck smoothing arguments along with kinetic energy and elliptic estimates.

A global existence, uniqueness and regularity theorem is proved for the simplest Markovian Wigner–Poisson–Fokker–Planck model incorporating friction and dissipation mechanisms. The proof relies on Green function and energy estimates under mild formulation, making essential use of the Husimi function and the elliptic regularization of the Fokker–Pla...

We formally derive two nonlinear Ginzburg-Landau type models starting from the Wigner-Fokker-Planck system, which rules the evolution of a quantum electron gas interacting with a heat bath in thermodynamic equilibrium. These models mainly consist of a quantum, dissipative O(Planck 3) hydrodynamic/O(Planck 4) stochastic correction to the frictional...

This work is concerned with some extensions of the classical compressible Euler model of fluid dynamics in which the fluid internal energy is a measure-valued quantity. A first extension has been derived from the hydrodynamic limit of a kinetic model involving a specific class of collision operators [P. Degond and M. Lemou, Eur. J. Mech., B, Fluids...

The analysis of dissipative transport equations within the framework of open quantum systems with Fokker-Planck-type scattering is carried out from the perspective of a Wigner function approach. In particular, the well-posedness of the self-consistent whole-space problem in 3D is analyzed: existence of solutions, uniqueness and asymptotic behavior...

This work is concerned with some extensions of the classical compressible Euler model of fluid dynamics in which the fluid internal energy is a measure-valued quantity. A first extension was derived from the hydrodynamic limit of a kinetic model involving a specific class of collision operators typical from quasi-linear plasma theory (see Eur. J. M...

this paper is to prove some basic mathematical results concerned with a specific nonlinear 3D Schrodinger mixed--system including a correction to the Poisson term, the Slater approximation i# # x # j + C P # # j , # j = # j (x, t), j with t > 0, x and given initial data # j (x, 0) = # j (x), where n# is the charge density n# := . Here, (N) are the...

We introduce a family of nonlinear time-dependent scale transformations and use them to analyze the long-time behavior of the solutions to some kinetic models of Schrödinger, heat and Fokker-Planck type. Also, some
conservation laws and dispersion relations are derived at the rescaled level and at the long time. The wide generality of the rescaling...

This work is concerned with some extensions of the classical compressible Euler model of fluid dynamics in which the fluid internal energy is a measure-valued quantity. A first extension has been derived from the hydrodynamic limit of a kinetic model involving a specific class of collision operators \cite{deg.lem1}\cite{deg.lop.pey}. In these paper...

In this paper, we investigate the large-times behavior of weak solutions to the fourth-order degenerate parabolic equation u(t) = -(\u\(n)u(xxx))(x) modeling the evolution of thin films. In particular, for all n > 0, we prove exponential decay of u(x, t) towards its mean value (1/\Omega\) integral(Omega) u dx in L-1-norm for long times and we give...

This paper is devoted to describe the long-time asymptotics of electrons moving in a semiconductor crystal lattice. We consider a quantum model in the Schrödinger formalism for the semiconductor crystal with a
self-consistent Coulomb interaction and an external electric field, and use the semiclassical approach to obtain a kinetic transport equatio...

Using an appropriate scaling group for the 3-D Schrödinger-Poisson equation and the equivalence between the Schrödinger formalism and the Wigner representation of quantum mechanics it is proved that, when time goes to infinity, the limit of the rescaled self-consistent potential can be identified as the Coulomb potential. As consequence, Schrödinge...

A global existence theorem is presented for a kinetic problem of the form
t
f+v
x
f=Q(f), f(t=0)=f
0, where Q(f) is a simplified model wave–particle collision operator extracted from quasilinear plasma physics. Evaluation of Q(f) requires the computation of the mean velocity of the distribution f. Therefore, the assumptions on the data are such...

A global existence theorem is presented for a kinetic problem of the form $\partial_t f + v \cdot \nabla_x f = Q(f)$, $f(t=0) = f_0$, where $Q(f)$ is a simplified model wave-particle collision operator extracted from quasilinear plasma physics. Evaluation of $Q(f)$ requires the computation of the mean velocity of the distribution $f$. Therefore, th...

The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated.
The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model
still involves a kinetic variable, the particle energy in the rest frame of the fluid, but...

The equivalence between the Schrödinger formalism for pure quantum states and the Wigner representation of quantum mechanics, and the importance of the latter in semiconductor modelling motivates the analysis of the large-time behaviour for the Schrödinger-Poisson problem arising in this context. Using an appropriate rescaling group and some self-s...