Spectral analysis of a model for quantum friction

Abstract

An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity with a magnitude which is typically proportional to a power of its speed. We study here the quantum equivalent of a classical Hamiltonian model for this friction phenomenon that was proposed in [11]. More precisely, we study the spectral properties of the quantum Hamiltonian and compare the quantum and classical situations. Under suitable conditions on the infrared behaviour of the model, we prove that the Hamiltonian at fixed total momentum has no ground state except when the total momentum vanishes, and that its spectrum is otherwise absolutely continuous. 1 arXiv:1512.05704v1 [math-ph]

Cherenkov radiation with massive bosons and quantum friction

“…This model happens to be substantially simpler to study than the Nelson model, precisely due to the fact that vibration fields are uncoupled in space, and we shall thus be able to further treat the case of massless bosons for this model. In the sequel, we aim at a detailed understanding of friction effects in the weak coupling regime, improving on previous results in [9]. 1.3.1.…”

“…The same analysis can be repeated for instance for Fröhlich's polaron model [33]. -For the quantum friction model with massless bosons introduced in [5,9], previous results were also limited by the lack of regularity [9]. Appealing to our modification procedure, we cure again all regularity issues and reduce to the application of regular Mourre theory.…”

“…We naturally expect to further complement this with a scattering resonance description. As this problem basically concerns the perturbation of an embedded eigenvalue in continuous spectrum and as the relevant interaction Hamiltonian in QFT models is not relatively compact, even this perturbative analysis at weak coupling is a nontrivial problem for which still only partial results are available [3,10,34,15,9]. Note that a different line of research concerns the reduced dynamics of the non-relativistic particle in the kinetic limit: in [46,16,11], it is shown to take form of a Boltzmann equation describing the slowdown of the particle.…”

“…Quantum friction model. We turn to the quantum version [5,9] of a translationinvariant Hamiltonian model for friction introduced by Bruneau and De Bièvre [6]. It describes a non-relativistic quantum particle moving through a translation-invariant medium consisting of uncoupled quantized vibration fields at each point in space.…”

Numerical investigation of Landau damping in dynamical Lorentz gases

“…Complementary studies of the model (1a)-(1b) can be found in [1,11,12,13,27,32], with connections to stochastic homogenization and to the classical Lorentz problems. We also refer to [8] for a quantum version of the model, and further connection to the Cherenkov radiation.…”