Adaiabtic theorems and reversible isothermal processes

Isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for trajectories of states close to, but distinct from states of joint thermal equilibrium. A theorem characterizing reversible isothermal processes as quasi-static processes (''isothermal theorem'') is described. Corollaries concerning the changes of entropy and free energy in reversible isothermal processes and on the 0th law of thermodynamics are outlined

Endohedral terthiophene in zigzag carbon nanotubes: Density functional calculations

The inclusion and encapsulation of terthiophene (T3) molecules inside zigzag single-walled carbon nanotubes (CNTs) is addressed by density functional calculations. We consider the T3 molecule inside five semiconducting CNTs with diameters ranging from 9.6 to 12.7 Ang. Our results show that the T3 inclusion process is exothermic for CNTs with diameters larger than 9.5 Ang. The highest energy gain is found to be of 2 eV, decreasing as the CNT diameter increases. This notable effect of stabilization is attributed to the positively charged CNT inner space, as induced by its curvature, which is able to accommodate the neutral T3 molecule. The band structure of the T3@CNT system shows that T3 preserves its electronic identity inside the CNTs, superimposing their molecular orbitals onto the empty CNT band structure without hybridization. Our results predict that the electronic states added by the T3 molecules would give rise to optical effects and nonradiative relaxation from excited states.Comment: 5 pages, 5 figures, 1 table, accepted in PR

On the Atomic Photoeffect in Non-relativistic QED

In this paper we present a mathematical analysis of the photoelectric effect for one-electron atoms in the framework of non-relativistic QED. We treat photo-ionization as a scattering process where in the remote past an atom in its ground state is targeted by one or several photons, while in the distant future the atom is ionized and the electron escapes to spacial infinity. Our main result shows that the ionization probability, to leading order in the fine-structure constant, $\alpha$, is correctly given by formal time-dependent perturbation theory, and, moreover, that the dipole approximation produces an error of only sub-leading order in $\alpha$. In this sense, the dipole approximation is rigorously justified.Comment: 25 page

On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg-picture dynamics of "observables", thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato smoothing estimate (Lemma 6.1

A model with simultaneous first and second order phase transitions

We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two bond ordered phases, one with local ferromagnetic order and another with local antiferromagnetic order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and Swendsen. This last result generalizes the result of Shlosman and van Enter (cond-mat/0205455). We argue that these phenomena are quite general and should occur for a large class of potentials.Comment: 7 pages, 7 figures using pstricks and pst-coi

Discrete approximations to vector spin models

We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretising continuous-spin models, and show that, except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions.Comment: 12 page

An algal enzyme required for biosynthesis of the most abundant marine carotenoids.

Fucoxanthin and its derivatives are the main light-harvesting pigments in the photosynthetic apparatus of many chromalveolate algae and represent the most abundant carotenoids in the world's oceans, thus being major facilitators of marine primary production. A central step in fucoxanthin biosynthesis that has been elusive so far is the conversion of violaxanthin to neoxanthin. Here, we show that in chromalveolates, this reaction is catalyzed by violaxanthin de-epoxidase-like (VDL) proteins and that VDL is also involved in the formation of other light-harvesting carotenoids such as peridinin or vaucheriaxanthin. VDL is closely related to the photoprotective enzyme violaxanthin de-epoxidase that operates in plants and most algae, revealing that in major phyla of marine algae, an ancient gene duplication triggered the evolution of carotenoid functions beyond photoprotection toward light harvesting

Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. $\epsilon$-away below the two-boson threshold) spectrum of Fr\"ohlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension $d\geq 3$. It contains a single polaron branch defined for total momentum $p\in G^{(0)}$, where $G^{(0)}\subset {\mathbb R}^d$ is a bounded domain, and, for any $p\in {\mathbb R}^d$, a manifold of polaron + one-boson states with boson momentum $q$ in a bounded domain depending on $p$. The polaron becomes unstable and dissolves into the one boson manifold at the boundary of $G^{(0)}$. The dispersion laws and generalized eigenfunctions are calculated

Simulating the influence of primary biological aerosol particles on clouds by heterogeneous ice nucleation

Primary ice formation, which is an important process for mixed-phase clouds with an impact on their lifetime, radiative balance, and hence the climate, strongly depends on the availability of ice-nucleating particles (INPs). Supercooled droplets within these clouds remain liquid until an INP immersed in or colliding with the droplet reaches its activation temperature. Only a few aerosol particles are acting as INPs and the freezing efficiency varies among them. Thus, the fraction of supercooled water in the cloud depends on the specific properties and concentrations of the INPs. Primary biological aerosol particles (PBAPs) have been identified as very efficient INPs at high subzero temperatures, but their very low atmospheric concentrations make it difficult to quantify their impact on clouds. Here we use the regional atmospheric model COSMO–ART to simulate the heterogeneous ice nucleation by PBAPs during a 1-week case study on a domain covering Europe. We focus on three highly ice-nucleation-active PBAP species, Pseudomonas syringae bacteria cells and spores from the fungi Cladosporium sp. and Mortierella alpina. PBAP emissions are parameterized in order to represent the entirety of bacteria and fungal spores in the atmosphere. Thus, only parts of the simulated PBAPs are assumed to act as INPs. The ice nucleation parameterizations are specific for the three selected species and are based on a deterministic approach. The PBAP concentrations simulated in this study are within the range of previously reported results from other modeling studies and atmospheric measurements. Two regimes of PBAP INP concentrations are identified: a temperature-limited and a PBAP-limited regime, which occur at temperatures above and below a maximal concentration at around −10 ∘C, respectively. In an ensemble of control and disturbed simulations, the change in the average ice crystal concentration by biological INPs is not statistically significant, suggesting that PBAPs have no significant influence on the average state of the cloud ice phase. However, if the cloud top temperature is below −15 ∘C, PBAP can influence the cloud ice phase and produce ice crystals in the absence of other INPs. Nevertheless, the number of produced ice crystals is very low and it has no influence on the modeled number of cloud droplets and hence the cloud structure

Quantum spin systems at positive temperature

We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature $\beta$ and the magnitude of the quantum spins \CalS satisfy \beta\ll\sqrt\CalS. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with \CalS\gg1. The most notable examples are the quantum orbital-compass model on $\Z^2$ and the quantum 120-degree model on $\Z^3$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.Comment: 47 pages, version to appear in CMP (style files included