Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types

The goal of this paper to determine the optimal horoball packing arrangements and their densities for all four fully asymptotic Coxeter tilings (Coxeter honeycombs) in hyperbolic 3-space $\mathbb{H}^3$. Centers of horoballs are required to lie at vertices of the regular polyhedral cells constituting the tiling. We allow horoballs of different types at the various vertices. Our results are derived through a generalization of the projective methodology for hyperbolic spaces. The main result states that the known B\"or\"oczky--Florian density upper bound for "congruent horoball" packings of $\mathbb{H}^3$ remains valid for the class of fully asymptotic Coxeter tilings, even if packing conditions are relaxed by allowing for horoballs of different types under prescribed symmetry groups. The consequences of this remarkable result are discussed for various Coxeter tilings.Comment: 26 pages, 10 figure

OPTIMALE KUGELPACKUNGEN FÜR DIE RAUMGRUPPEN F23, P432 UND F432

In this paper the optimal ball-packing is determined where the centres of balls form an orbit (with trivial stabilizer) of a particular crystallographic space group. The space groups are F23, P432, F432 which allow a unified method called the method of cones

Phase Separation of Superfluids in the Chain of Four-Component Ultracold Atoms

We investigate the competition of various exotic superfluid states in a chain of spin-polarized ultracold fermionic atoms with hyperfine spin $F = 3/2$ and s-wave contact interactions. We show that the ground state is an exotic inhomogeneous mixture in which two distinct superfluid phases --- spin-carrying pairs and singlet quartets --- form alternating domains in an extended region of the parameter space

SU(N) quantum spin models: A variational wavefunction study

The study of SU(N) quantum spin models is relevant to a variety of physical systems including ultracold atoms in optical lattices, and also leads to insights into novel quantum phases and phase transitions of SU(2) spin models. We use Gutzwiller projected fermionic variational wavefunctions to explore the phase diagram and correlation functions of SU(N) spin models in the self-conjugate representation, with Heisenberg bilinear and biquadratic interactions. In 1D, the variational phase diagram of the SU(4) spin chain is constructed by examining instabilities of the Gutzwiller projected free fermion ground state to various broken symmetries, and it agrees well with exact results.The spin and dimer correlations of the Gutzwiller projected free fermion state with N flavors of fermions are also in good agreement with exact and 1/N calculations for the critical points of SU(N) spin chains. In 2D, the variational phase diagram on the square lattice is obtained by studying instabilities of the Gutzwiller projected pi-flux state. The variational ground state of the pure Heisenberg model is found to exhibit long range Neel order for N=2,4 and spin Peierls order for N > 4. For N=4 and 6, biquadratic interactions lead to a complex phase diagram which includes an extended valence bond crystal in both cases, as well as a stable pi-flux phase for N=6. The spin correlations of the projected pi-flux state at N=4 are in good agreement with 1/N calculations. We find that this state also shows strongly enhanced dimer correlations, in qualitative accord with the large-N results. We compare our results with a recent QMC study of the SU(4) Heisenberg model.Comment: 22 pages, 7 figs, added references to arxiv versio

Possible phases of two coupled n-component fermionic chains

A two-leg ladder with $n$-component fermionic fields in the chains has been considered using an analytic renormalization group method. The fixed points and possible phases have been determined for generic filling as well as for a half-filled system and for the case when one of the subbands is half filled. A weak-coupling Luttinger-liquid phase and several strong-coupling gapped phases have been found. In the Luttinger liquid phase, for the most general spin dependence of the couplings, all $2n$ modes have different velocities if the interband scattering processes are scaled out, while $n$ doubly degenerate modes appear if the interband scattering processes remain finite. The role of backward-scattering, charge-transfer and umklapp processes has been analysed using their bosonic form and the possible phases are characterized by the number of gapless modes. As a special case the SU($n$) symmetric Hubbard ladder has been investigated numerically. It was found that this model does not scale to the Luttinger liquid fixed point. Even for generic filling gaps open up in the spectrum of the spin or charge modes, and the system is always insulator in the presence of umklapp processes

Spatially nonuniform phases in the one-dimensional SU(n) Hubbard model for commensurate fillings

The one-dimensional repulsive SU$(n)$ Hubbard model is investigated analytically by bosonization approach and numerically using the density-matrix renormalization-group (DMRG) method for $n=3,4$, and 5 for commensurate fillings $f=p/q$ where $p$ and $q$ are relatively prime. It is shown that the behavior of the system is drastically different depending on whether $q>n$, $q=n$, or $qn$, the umklapp processes are irrelevant, the model is equivalent to an $n$-component Luttinger liquid with central charge $c=n$. When $q=n$, the charge and spin modes are decoupled, the umklapp processes open a charge gap for finite $U>0$, whereas the spin modes remain gapless and the central charge $c=n-1$. The translational symmetry is not broken in the ground state for any $n$. On the other hand, when $q<n$, the charge and spin modes are coupled, the umklapp processes open gaps in all excitation branches, and a spatially nonuniform ground state develops. Bond-ordered dimerized, trimerized or tetramerized phases are found depending on the filling.Comment: 10 pages, 11 figure

Die wahl der richti-gen therapie bei verschidenen Krankheitbildern durch Registrierung mittels des Szirmaischen Myographen und durch die Berechnung des Reaktions-indexes (R. I.)

Die Autoren haben mit Hilfe des Szirmaischen Myographen auf Grund der Messung vor und nach der Behandlung den Reaktions-Index aus den Myogrammen erhalten. Mit dieser Methode la&#946;t sich in einer sehr kurzen Zeit bei verschiedenen Krankheiten die gunstigste Therapie auswahlen und deren Wirksamkeit in Prozenten auswerten.</p

Neues stomatologisches verfahren : Myologische bestimmung der funktion der kaumuskulatur bzw. des M. masseters mit dem Szirmaischen myotonometer

Die Autoren haben festgestellt, da&#946; man mit Hilfe des Myotonometers auf Grund von Kau- bzw. Masseterfunktionsmessung auf verschiedene stomatologische Krankheiten, bzw. auf verschiedene Veranderungen schliessen kann. Man kann feststellen, ob die Muskeln atrophisch sind oder nicht, was fur eine Prothese bei einzelnen Individuen der Funktion der Muskeln entspricht, ob eine Prothese schlecht ist, welche Verfahren fur die Orthodontie bzw. Prognathie notwendig sind und welche Medikamente eine gute stomatologische Wirkung haben. Auch die verschiedenen orthopadischen Fragen sind erleichtert.</p

Emergence of Quintet Superfluidity in the Chain of Partially Polarized Spin-3/2 Ultracold Atom

The system of ultracold atoms with hyperfine spin $F=3/2$ might be unstable against the formation of quintet pairs if the interaction is attractive in the quintet channel. We have investigated the behavior of correlation functions in a model including only s-wave interactions at quarter filling by large-scale density-matrix renormalization-group simulations. We show that the correlations of quintet pairs become quasi-long-ranged, when the system is partially polarized, leading to the emergence of various mixed superfluid phases in which BCS-like pairs carrying different magnetic moment coexist.Comment: 4 pages, 4 figures; significantly rewritten compared to the first versio