Exact dynamics and thermalization of an open bosonic quantum system in presence of a quantum phase transition induced by the environment

We derive the exact out-of-equilibrium Wigner function of a bosonic mode linearly coupled to a bosonic bath of arbitrary spectral density. Our solution does not rely on any master equation approach and it therefore also correctly describes a bosonic mode which is initially entangled with its environment. It has been recently suggested that non-Markovian quantum effects lead to dissi- pationless dynamics in the case of a strong coupling to a bath whose spectral density has a support bounded from below. We show in this work that such a system undergoes a quantum phase transi- tion at some critical bath coupling strength. The apparent dissipationless dynamics then correspond to the relaxation towards the new ground-state.Comment: 8 page

Controlling sliding droplets with optimal contact angle distributions and a phase field model

We consider the optimal control of a droplet on a solid by means of the static contact angle between the contact line and the solid. The droplet is described by a thermodynamically consistent phase field model from [Abels et al., Math. Mod. Meth. Appl. Sc., 22(3), 2012] together with boundary data for the moving contact line from [Qian et al., J. Fluid Mech., 564, 2006]. We state an energy stable time discrete scheme for the forward problem based on known results, and pose an optimal control problem with tracking type objective.TU Berlin, Open-Access-Mittel - 201

A Criterion for the Monoid Axiom in Enriched Bousfield Localizations

This paper proves a criterion for verifying the monoid axiom in enriched left Bousfield localizations

Rational enriched motivic spaces

Rational enriched motivic spaces are introduced and studied in this thesis to provide new models for connective and very effective motivic spectra with rational coefficients. We first study homological algebra for Grothendieck categories of functors enriched in Nisnevich sheaves with specific transfers A. Following constructions of Voevodsky for triangulated categories of motives and framed motivic-spaces, we introduce and study motivic structures on unbounded chain complexes of enriched functors yielding two new models of the triangulated category of big motives with A-tranfers DMA. We next dene enriched motivic spaces as certain enriched functors of simplicial A-sheaves. We then use the properties of enriched motivic spaces and the above reconstruction results to recover SH(k)>0,Q and SHveff(k)Q

Rational Enriched Motivic Spaces

Enriched motivic $\mathcal A$-spaces are introduced and studied in this paper, where $\mathcal A$ is an additive category of correspondences. They are linear counterparts of motivic $\Gamma$-spaces. It is shown that rational special enriched motivic $\widetilde{\mathrm{Cor}}$-spaces recover connective motivic bispectra with rational coefficients, where $\widetilde{\mathrm{Cor}}$ is the category of Milnor--Witt correspondences

Triangulated Categories of Big Motives via Enriched Functors

Based on homological algebra of Grothendieck categories of enriched functors, two models for Voevodsky's category of big motives with reasonable correspondences are given in this paper

Scaling behavior of the momentum distribution of a quantum Coulomb system in a confining potential

We calculate the single-particle momentum distribution of a quantum many-particle system in the presence of the Coulomb interaction and a confining potential. The region of intermediate momenta, where the confining potential dominates, marks a crossover from a Gaussian distribution valid at low momenta to a power-law behavior valid at high momenta. We show that for all momenta the momentum distribution can be parametrized by a $q$-Gaussian distribution whose parameters are specified by the confining potential. Furthermore, we find that the functional form of the probability of transitions between the confined ground state and the $n^{th}$ excited state is invariant under scaling of the ratio $Q^2/\nu_n$, where $Q$ is the transferred momentum and $\nu_n$ is the corresponding excitation energy. Using the scaling variable $Q^2/\nu_n$ the maxima of the transition probabilities can also be expressed in terms of a $q$-Gaussian.Comment: 6 pages, 5 figure