Thermodynamics of Adiabatically Loaded Cold Bosons in the Mott Insulating Phase of One-Dimensional Optical Lattices

In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.Comment: 10 pages, 6 figure

Bound hole states in a ferromagnetic (Ga,Mn)As environment

A numerical technique is developed to solve the Luttinger-Kohn equation for impurity states directly in k-space and is applied to calculate bound hole wave functions in a ferromagnetic (Ga,Mn)As host. The rich properties of the band structure of an arbitrarily strained, ferromagnetic zinc-blende semiconductor yields various features which have direct impact on the detailed shape of a valence band hole bound to an active impurity. The role of strain is discussed on the basis of explicit calculations of bound hole states.Comment: 9 pages, 10 figure

Ionic polaron in a Bose-Einstein condensate

The ground state properties of a degenerate bosonic gas doped with an ion are investigated by means of quantum Monte Carlo simulations in three dimensions. The system features competing length and energy scales, which result in vastly different polaronic properties compared to neutral quantum impurities. Depending on whether a two-body bound state is supported or not by the atom-ion potential, we identify a transition between a polaron regime amenable to a perturbative treatment in the limit of weak atom-ion interactions and a many-body bound state with vanishing quasi-particle residue composed of hundreds of atoms. In order to analyze the structure of the corresponding states we examine the atom-ion and atom-atom correlation functions. Our findings are directly relevant to experiments using hybrid atom-ion setups that have recently attained the ultracold regime.Comment: 11 pages, 6 figures, 1 tabl

A new duality transformation for fourth-order gravity

We prove that for non-linear L = L(R), the Lagrangians L and \hat L give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator is conformally invariant.Comment: 11 pages, LaTeX, no figures. Gen. Relat. Grav. in prin

Temperature in One-Dimensional Bosonic Mott insulators

The Mott insulating phase of a one-dimensional bosonic gas trapped in optical lattices is described by a Bose-Hubbard model. A continuous unitary transformation is used to map this model onto an effective model conserving the number of elementary excitations. We obtain quantitative results for the kinetics and for the spectral weights of the low-energy excitations for a broad range of parameters in the insulating phase. By these results, recent Bragg spectroscopy experiments are explained. Evidence for a significant temperature of the order of the microscopic energy scales is found.Comment: 8 pages, 7 figure

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface

Excess low energy photon pairs from pion annihilation at the chiral phase transition

The photon pair production by pion annihilation in a hot and dense medium at the chiral phase transition is investigated within a chiral quark model. As a direct consequence of this transition the $\sigma$ meson appears as a bound state in the domain of temperatures and chemical potentials where the condition $M_\sigma(T,\mu) \approx 2 M_\pi(T,\mu)$ is fulfilled. This effect results in a strong enhancement of the cross section for the pion annihilation process $2 \pi \to 2 \gamma$ compared with the vacuum case. The calculation of the photon pair production rate as function of the invariant mass shows a strong enhancement and narrowing of the $\sigma$ meson resonance at threshold due to chiral symmetry restoration.Comment: 15 pages, LaTeX, 6 figures, Phys. Lett.