Local search for stable marriage problems with ties and incomplete lists

The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists. In this setting, we study the problem of finding a stable matching that marries as many people as possible. Stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. This problem is NP-hard. We tackle this problem using local search, exploiting properties of the problem to reduce the size of the neighborhood and to make local moves efficiently. Experimental results show that this approach is able to solve large problems, quickly returning stable matchings of large and often optimal size.Comment: 12 pages, Proc. PRICAI 2010 (11th Pacific Rim International Conference on Artificial Intelligence), Byoung-Tak Zhang and Mehmet A. Orgun eds., Springer LNA

Effective s- and p-Wave Contact Interactions in Trapped Degenerate Fermi Gases

The structure and stability of dilute degenerate Fermi gases trapped in an external potential is discussed with special emphasis on the influence of s- and p-wave interactions. In a first step an Effective Contact Interaction for all partial waves is derived, which reproduces the energy spectrum of the full potential within a mean-field model space. Using the s- and p-wave part the energy density of the multi-component Fermi gas is calculated in Thomas-Fermi approximation. On this basis the stability of the one- and two-component Fermi gas against mean-field induced collapse is investigated. Explicit stability conditions in terms of density and total particle number are given. For the single-component system attractive p-wave interactions limit the density of the gas. In the two-component case a subtle competition of s- and p-wave interactions occurs and gives rise to a rich variety of phenomena. A repulsive p-wave part, for example, can stabilize a two-component system that would otherwise collapse due to an attractive s-wave interaction. It is concluded that the p-wave interaction may have important influence on the structure of degenerate Fermi gases and should not be discarded from the outset.Comment: 18 pages, 11 figures (using RevTEX4

Phase transitions in spin-orbital coupled model for pyroxene titanium oxides

We study the competing phases and the phase transition phenomena in an effective spin-orbital coupled model derived for pyroxene titanium oxides ATiSi2O6 (A=Na, Li). Using the mean-field-type analysis and the numerical quantum transfer matrix method, we show that the model exhibits two different ordered states, the spin-dimer and orbital-ferro state and the spin-ferro and orbital-antiferro state. The transition between two phases is driven by the relative strength of the Hund's-rule coupling to the onsite Coulomb repulsion and/or by the external magnetic field. The ground-state phase diagram is determined. There is a keen competition between orbital and spin degrees of freedom in the multicritical regime, which causes large fluctuations and significantly affects finite-temperature properties in the paramagnetic phase.Comment: 4 pages, 6 figures, proceedings submitted to SPQS200

Efficient preparation and detection of microwave dressed-state qubits and qutrits with trapped ions

We demonstrate a method for preparing and detecting all eigenstates of a three-level microwave dressed system with a single trapped ion. The method significantly reduces the experimental complexity of gate operations with dressed-state qubits, as well as allowing all three of the dressed states to be prepared and detected, thereby providing access to a qutrit that is well protected from magnetic field noise. In addition, we demonstrate individual addressing of the clock transitions in two ions using a strong static magnetic field gradient, showing that our method can be used to prepare and detect microwave dressed states in a string of ions when performing multi-ion quantum operations with microwave and radio frequency fields. The individual addressability of clock transitions could also allow for the control of pairwise interaction strengths between arbitrary ions in a string using lasers

How chemistry controls electron localization in 3d1 perovskites: A Wannier-function study

In the series of 3d1 t2g perovskites, SrVO3--CaVO3--LaTiO3--YTiO3 the transition-metal d electron becomes increasingly localized and undergoes a Mott transition between CaVO3 and LaTiO3. By defining a low-energy Hubbard Hamiltonian in the basis of Wannier functions for the t2g LDA band and solving it in the single-site DMFT approximation, it was recently shown[1] that simultaneously with the Mott transition there occurs a strong suppression of orbital fluctuations due to splitting of the t2g levels. The present paper reviews and expands this work, in particular in the direction of exposing the underlying chemical mechanisms by means of ab initio LDA Wannier functions generated with the NMTO method. The Wannier functions for the t2g band exhibit covalency between the transition-metal t2g, the large cation-d, and the oxygen-p states; this covalency, which increases along the series, turns out to be responsible not only for the splittings of the t2g levels, but also for non-cubic perturbations of the hopping integrals, both of which are decisive for the Mott transition. We find good agreement with the optical and photoemission spectra, with the crystal-field splittings and orbital polarizations recently measured for the titanates, and with the metallization volume for LaTiO3. The metallization volume for YTiO3 is predicted. Using super-exchange theory, we reproduce the observed magnetic orders in LaTiO3 and YTiO3, but the results are sensitive to detail, in particular for YTiO3 which, without the Jahn-Teller distortion, would be AFM C- or A-type, rather than FM. Finally, we show that it possible to unfold the orthorhombic t2g LDA bandstructure to a pseudocubic zone. In this zone, the lowest band is separated from the two others by a direct gap and has a width, W_I, which is significantly smaller than that, W, of the entire t2g band. The progressive GdFeO3-type distortion favours electron localization by decreasing W, by increasing the splitting of the t2g levels and by decreasing W_I. Our conclusions concerning the roles of GdFeO3-type and JT distortions agree with those of Mochizuki and Imada [2].Comment: Published version, final. For high resolution figures see http://www.fkf.mpg.de/andersen/docs/pub/abstract2004+/pavarini_02.pd

Anisotropic Hubbard model on a triangular lattice -- spin dynamics in Ho Mn O_3

The recent neutron-scattering data for spin-wave dispersion in $\rm Ho Mn O_3$ are well described by an anisotropic Hubbard model on a triangular lattice with a planar (XY) spin anisotropy. Best fit indicates that magnetic excitations in $\rm Ho Mn O_3$ correspond to the strong-coupling limit $U/t > \sim 15$, with planar exchange energy $J=4t^2/U \simeq 2.5$meV and planar anisotropy $\Delta U \simeq 0.35$meV.Comment: 4 pages, 3 figure

A Quantum Monte Carlo Method and Its Applications to Multi-Orbital Hubbard Models

We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multi-orbital Hubbard models. Our formulation can be applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and inter-orbitals, intra-site exchange interaction and energy differences between orbitals. Based on our framework, we point out possible ways to investigate various phase transitions such as metal-insulator, magnetic and orbital order-disorder transitions without the minus sign problem. As an application, a two-band model is investigated by the projection QMC method and the ground state properties of this model are presented.Comment: 10 pages LaTeX including 2 PS figures, to appear in J.Phys.Soc.Jp

Low-energy neutron-deuteron reactions with N3LO chiral forces

We solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation we include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on Ay puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neutron quasi-free-scattering breakup configurations, for which large discrepancies between data and theory have been reported.Comment: 22 pages, 7 figure

Enhancement of the Deuteron-Fusion Reactions in Metals and its Experimental Implications

Recent measurements of the reaction d(d,p)t in metallic environments at very low energies performed by different experimental groups point to an enhanced electron screening effect. However, the resulting screening energies differ strongly for divers host metals and different experiments. Here, we present new experimental results and investigations of interfering processes in the irradiated targets. These measurements inside metals set special challenges and pitfalls which make them and the data analysis particularly error-prone. There are multi-parameter collateral effects which are crucial for the correct interpretation of the observed experimental yields. They mainly originate from target surface contaminations due to residual gases in the vacuum as well as from inhomogeneities and instabilities in the deuteron density distribution in the targets. In order to address these problems an improved differential analysis method beyond the standard procedures has been implemented. Profound scrutiny of the other experiments demonstrates that the observed unusual changes in the reaction yields are mainly due to deuteron density dynamics simulating the alleged screening energy values. The experimental results are compared with different theoretical models of the electron screening in metals. The Debye-H\"{u}ckel model that has been previously proposed to explain the influence of the electron screening on both nuclear reactions and radioactive decays could be clearly excluded.Comment: 22 pages, 12 figures, REVTeX4, 2-column format. Submitted to Phys. Rev. C; accepte