171 citations · 786 across the 45 of their papers we have counts for
21 papers · 1 filter
Symmetric and antisymmetric cumulant hierarchies and Wick polynomials of operators
Jani Lukkarinen, Sakari Pirnes
There has been much progress in understanding mathematical foundations of kinetic theory in recent years, in particular, for the original model of a rarefied gas of classical parti…
Finite lattice kinetic equations for bosons, fermions, and discrete NLS
Jani Lukkarinen, Sakari Pirnes, Aleksis Vuoksenmaa
We introduce and study finite lattice kinetic equations for bosons, fermions, and discrete NLS. For each model this closed evolution equation provides an approximate description fo…
Generation of chaos in the cumulant hierarchy of the stochastic Kac model
Jani Lukkarinen, Aleksis Vuoksenmaa
We study the time-evolution of cumulants of velocities and kinetic energies in the stochastic Kac model for velocity exchange of particles, with the aim of quantifying how fast…
Coagulation equations with source leading to anomalous self-similarity
Marina A. Ferreira, Eugenia Franco, Jani Lukkarinen +2
We study the long-time behaviour of the solutions to Smoluchowski coagulation equations with a source term of small clusters. The source drives the system out-of-equilibrium, leadi…
Localization in stationary non-equilibrium solutions for multicomponent coagulation systems
Marina A. Ferreira, Jani Lukkarinen, Alessia Nota +1
We consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that t…
Estimation of local microcanonical averages in two lattice mean-field models using coupling techniques
Kalle Koskinen, Jani Lukkarinen
We consider an application of probabilistic coupling techniques which provides explicit estimates for comparison of local expectation values between label permutation invariant sta…
Stationary non-equilibrium solutions for coagulation systems
Marina A. Ferreira, Jani Lukkarinen, Alessia Nota +1
We study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous…
Multi-state condensation in Berlin-Kac spherical models
Jani Lukkarinen
We consider the Berlin-Kac spherical model for supercritical densities under a periodic lattice energy function which has finitely many non-degenerate global minima. Energy functio…
Kinetic theory and thermalization of weakly interacting fermions
Jani Lukkarinen
Weakly interacting quantum fluids allow for a natural kinetic theory description which takes into account the fermionic or bosonic nature of the interacting particles. In the simpl…
Harmonic chain with velocity flips: thermalization and kinetic theory
Jani Lukkarinen, Matteo Marcozzi, Alessia Nota
We consider the detailed structure of correlations in harmonic chains with pinning and a bulk velocity flip noise during the heat relaxation phase which occurs on diffusive time sc…
Kinetic theory of phonons in weakly anharmonic particle chains
Jani Lukkarinen
The aim of this review is to develop the kinetic theory of phonons in classical particle chains to a point which allows comparing the kinetic theory of normally conducting chains,…
Wick polynomials and time-evolution of cumulants
Jani Lukkarinen, Matteo Marcozzi
We show how Wick polynomials of random variables can be defined combinatorially as the unique choice which removes all "internal contractions" from the related cumulant expansions,…
Thermalization in harmonic particle chains with velocity flips
Jani Lukkarinen
We propose a new mathematical tool for the study of transport properties of models for lattice vibrations in crystalline solids. By replication of dynamical degrees of freedom, we…
Global well-posedness of the spatially homogeneous Hubbard-Boltzmann equation
Jani Lukkarinen, Peng Mei, Herbert Spohn
The Hubbard model is a simplified description for the evolution of interacting spin-1/2 fermions on a d-dimensional lattice. In a kinetic scaling limit, the Hubbard model can be as…
Energy fluctuations, hydrodynamics and local correlations in harmonic systems with bulk noises
Jani Lukkarinen
In this note, I summarise and comment on joint work with C. Bernardin, V. Kannan and J. L. Lebowitz concerning two harmonic systems with bulk noises whose nonequilibrium steady sta…
Weakly nonlinear Schrödinger equation with random initial data
Jani Lukkarinen, Herbert Spohn
It is common practice to approximate a weakly nonlinear wave equation through a kinetic transport equation, thus raising the issue of controlling the validity of the kinetic limit…
Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids
Jani Lukkarinen, Herbert Spohn
The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method develope…
Energy transport by acoustic modes of harmonic lattices
Lisa Harris, Jani Lukkarinen, Stefan Teufel +1
We study the large scale evolution of a scalar lattice excitation which satisfies a discrete wave-equation in three dimensions. We assume that the dispersion relation associated to…
Asymptotics of resolvent integrals: The suppression of crossings for analytic lattice dispersion relations
Jani Lukkarinen
We study the so called crossing estimate for analytic dispersion relations of periodic lattice systems in dimensions three and higher. Under a certain regularity assumption on the…
Kinetic Limit for Wave Propagation in a Random Medium
Jani Lukkarinen, Herbert Spohn
We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The d…
Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
Federico Bonetto, Joel L. Lebowitz, Jani Lukkarinen
We consider a d-dimensional harmonic crystal in contact with a stochastic Langevin type heat bath at each site. The temperatures of the "exterior" left and right heat baths are at…