Quantum phases of atomic boson-fermion mixtures in optical lattices

The zero-temperature phase diagram of a binary mixture of bosonic and fermionic atoms in an one-dimensional optical lattice is studied in the framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the associated eigenvalue problems, ground state observables and the response to an external phase twist are evaluated. The stiffnesses under phase variations provide measures for the boson superfluid fraction and the fermionic Drude weight. Several distinct quantum phases are identified as function of the strength of the repulsive boson-boson and the boson-fermion interaction. Besides the bosonic Mott-insulator phase, two other insulating phases are found, where both the bosonic superfluid fraction and the fermionic Drude weight vanish simultaneously. One of these double-insulator phases exhibits a crystalline diagonal long-range order, while the other is characterized by spatial separation of the two species.Comment: 4 pages, 3 figures, using REVTEX

Social Welfare in One-sided Matching Markets without Money

We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent's utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first non-trivial performance guarantees for these natural mechanisms

Phase Diagram of Bosonic Atoms in Two-Color Superlattices

We investigate the zero temperature phase diagram of a gas of bosonic atoms in one- and two-color standing-wave lattices in the framework of the Bose-Hubbard model. We first introduce some relevant physical quantities; superfluid fraction, condensate fraction, quasimomentum distribution, and matter-wave interference pattern. We then discuss the relationships between them on the formal level and show that the superfluid fraction, which is the relevant order parameter for the superfluid to Mott-insulator transition, cannot be probed directly via the matter wave interference patterns. The formal considerations are supported by exact numerical solutions of the Bose-Hubbard model for uniform one-dimensional systems. We then map out the phase diagram of bosons in non-uniform lattices. The emphasis is on optical two-color superlattices which exhibit a sinusoidal modulation of the well depth and can be easily realized experimentally. From the study of the superfluid fraction, the energy gap, and other quantities we identify new zero-temperature phases, including a localized and a quasi Bose-glass phase, and discuss prospects for their experimental observation.Comment: 18 pages, 17 figures, using REVTEX

Exponential Time Complexity of Weighted Counting of Independent Sets

We consider weighted counting of independent sets using a rational weight x: Given a graph with n vertices, count its independent sets such that each set of size k contributes x^k. This is equivalent to computation of the partition function of the lattice gas with hard-core self-repulsion and hard-core pair interaction. We show the following conditional lower bounds: If counting the satisfying assignments of a 3-CNF formula in n variables (#3SAT) needs time 2^{\Omega(n)} (i.e. there is a c>0 such that no algorithm can solve #3SAT in time 2^{cn}), counting the independent sets of size n/3 of an n-vertex graph needs time 2^{\Omega(n)} and weighted counting of independent sets needs time 2^{\Omega(n/log^3 n)} for all rational weights x\neq 0. We have two technical ingredients: The first is a reduction from 3SAT to independent sets that preserves the number of solutions and increases the instance size only by a constant factor. Second, we devise a combination of vertex cloning and path addition. This graph transformation allows us to adapt a recent technique by Dell, Husfeldt, and Wahlen which enables interpolation by a family of reductions, each of which increases the instance size only polylogarithmically.Comment: Introduction revised, differences between versions of counting independent sets stated more precisely, minor improvements. 14 page

Popular matchings in the marriage and roommates problems

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases

Antibacterial activity of Mn(i) and Re(i) tricarbonyl complexes conjugated to a bile acid carrier molecule

A bifunctional cholic acid–bis(2-pyridylmethyl)amine (bpa) ligand featuring an amide linker was coordinated to a manganese(I) or rhenium(I) tricarbonyl moiety to give [M(bpa^cholamide)(CO)3] with M = Mn, Re in good yield and very high purity. Strong antibacterial activity was observed against four strains of methicillin-susceptible (MSSA) and methicillin-resistant (MRSA) Staphylococcus aureus, with minimum inhibitory concentrations (MICs) in the range of 2–3.5 μM. No difference in response was observed for the MSSA vs. MRSA strains. Activity was also independent of the nature of the metal center, as the Mn and Re complexes showed essentially identical MIC values. In contrast to some other metal carbonyl complexes, the activity seems to be unrelated to the release of carbon monoxide, as photoactivation of the Mn complex reduced the potency by a factor of 2–8. Both metal complexes were non-toxic in Galleria mellonella larvae at concentrations of up to 100× the MIC value. In vivo testing in Galleria larvae infected with MRSA/MSSA demonstrated a significant increase in overall survival rates from 46% in the control to 88% in the group treated with the metal complexes. ICP-MS analysis showed that the Mn and Re cholamide complexes are efficiently internalized by E. coli cells and do not interfere with membrane integrity, as evident from a lack of release of intracellular ATP. An increased sensitivity was observed in acrB, acrD, and mdt mutants that are defective in multidrug exporters, indicating that the compounds have an intracellular mechanism of action. Furthermore, E. coli mntP mutants defective in the gene encoding an Mn exporter were more sensitive than the wildtype, while inactivation of the regulator that controls expression of the Mn uptake proteins MntP and MntH slightly increased sensitivity to the compound. Single knockout mutants defective in genes linked to bile salt and oxidative stress response (dinF, yiaH, sodA, katE, and soxS) did not show increased sensitivity relative to the wild type. Overall, neither the cholic acid moiety nor the metal-carbonyl fragment alone appear to be responsible for the biological activity observed and thus the search for the primary intracellular target continues

Electronic dynamic Hubbard model: exact diagonalization study

A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wavefunction for two electrons occupying the same Wannier orbital is different from the product of single electron wavefunctions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transfered from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more 'dressed' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases, and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to 'undress', hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.Comment: Small changes following referee's comment

5-HT2C Agonists Modulate Schizophrenia-Like Behaviors in Mice

All FDA-approved antipsychotic drugs (APDs) target primarily dopamine D2 or serotonin (5-HT2A) receptors, or both; however, these medications are not universally effective, they may produce undesirable side effects, and provide only partial amelioration of negative and cognitive symptoms. The heterogeneity of pharmacological responses in schizophrenic patients suggests that additional drug targets may be effective in improving aspects of this syndrome. Recent evidence suggests that 5-HT2C receptors may be a promising target for schizophrenia since their activation reduces mesolimbic nigrostriatal dopamine release (which conveys antipsychotic action), they are expressed almost exclusively in CNS, and have weight-loss-promoting capabilities. A difficulty in developing 5-HT2C agonists is that most ligands also possess 5-HT2B and/or 5-HT2A activities. We have developed selective 5-HT2C ligands and herein describe their preclinical effectiveness for treating schizophrenia-like behaviors. JJ-3-45, JJ-3-42, and JJ-5-34 reduced amphetamine-stimulated hyperlocomotion, restored amphetamine-disrupted prepulse inhibition, improved social behavior, and novel object recognition memory in NMDA receptor hypofunctioning NR1-knockdown mice, and were essentially devoid of catalepsy. However, they decreased motivation in a breakpoint assay and did not promote reversal learning in MK-801-treated mice. Somewhat similar effects were observed with lorcaserin, a 5-HT2C agonist with potent 5-HT2B and 5-HT2A agonist activities, which is approved for treating obesity. Microdialysis studies revealed that both JJ-3-42 and lorcaserin reduced dopamine efflux in the infralimbic cortex, while only JJ-3-42 decreased it in striatum. Collectively, these results provide additional evidence that 5-HT2C receptors are suitable drug targets with fewer side effects, greater therapeutic selectivity, and enhanced efficacy for treating schizophrenia and related disorders than current APDs. Neuropsychopharmacology advance online publication, 12 April 2017; doi:10.1038/npp.2017.52