Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases

We compute the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions where spatially varying superfluid phases are favored over homogeneous phases. We obtain estimates for critical values of the temperature, mass and spin imbalance, above which these phases disappear. Finally, we show that an intriguing relation exists between the general structure of the phase diagram and the binding energies of the underlying two-body bound-state problem.Comment: 5 pages, 3 figure

Phase structure of mass- and spin-imbalanced unitary Fermi gases

We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass ratios of the spin-down and spin-up fermions greater than three. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.Comment: 17 pages, 7 figure

Zero-temperature equation of state of mass-imbalanced resonant Fermi gases

We calculate the zero-temperature equation of state of mass-imbalanced resonant Fermi gases in an ab initio fashion, by implementing the recent proposal of imaginary-valued mass difference to bypass the sign problem in lattice Monte Carlo calculations. The fully non-perturbative results thus obtained are analytically continued to real mass imbalance to yield the physical equation of state, providing predictions for upcoming experiments with mass-imbalanced atomic Fermi gases. In addition, we present an exact relation for the rate of change of the equation of state at small mass imbalances, showing that it is fully determined by the energy of the mass-balanced system.Comment: 5 pages, 2 figures, 2 table

Fermi gases with imaginary mass imbalance and the sign problem in Monte Carlo calculations

Fermi gases in strongly coupled regimes, such as the unitary limit, are inherently challenging for many-body methods. Although much progress has been made with purely analytic methods, quantitative results require ab initio numerical approaches, such as Monte Carlo (MC) calculations. However, mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations due to the infamous sign problem. It was recently pointed out that the sign problem, for finite spin imbalance, can be circumvented by resorting to imaginary polarizations and analytic continuation. Large parts of the phase diagram spanned by temperature and polarization then become accessible to MC calculations. We propose to apply a similar strategy to the mass-imbalanced case, which opens up the possibility to study the associated phase diagram with MC calculations. In particular, our analysis suggests that a detection of a (tri-)critical point in this phase diagram is possible. We also discuss calculations in the zero-temperature limit with our approach.Comment: 5 pages, 3 figure

Thermal equation of state of polarized fermions in one dimension via complex chemical potentials

We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate- to strong-coupling regime, and cover a wide range of temperatures and spin imbalances.Comment: 14 pages, 19 figures; published versio

Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps

We analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ Density Functional Theory in the local density approximation. Depending on the values of the control parameters measuring mass and spin imbalance, we observe that three regions exist in the trap, namely: a superfluid region at the center, surrounded by a mixed region of resonantly interacting spin-up and spin-down fermions, and finally a fully polarized phase surrounding the previous two regions. We also find regimes in the phase diagram where the existence of a superfluid region at the center of the trap is not energetically favored. We point out the limitations of our approach at the present stage, and call for more detailed (ab initio) studies of the equation of state of uniform, mass-imbalanced unitary Fermi gases.Comment: 10 pages, 7 figure

High-momentum tails from low-momentum effective theories

In a recent work \cite{Anderson:2010aq}, Anderson \emph{et al.} used the renormalization group (RG) evolution of the momentum distribution to show that, under appropriate conditions, operator expectation values exhibit factorization in the two-nucleon system. Factorization is useful because it provides a clean separation of long- and short-distance physics, and suggests a possible interpretation of the universal high-momentum dependence and scaling behavior found in nuclear momentum distributions. In the present work, we use simple decoupling and scale-separation arguments to extend the results of Ref. \cite{Anderson:2010aq} to arbitrary low-energy $A$-body states. Using methods that are reminiscent of the operator product expansion (OPE) in quantum field theory, we find that the high-momentum tails of momentum distributions and static structure factors factorize into the product of a universal function of momentum that is fixed by two-body physics, and a state-dependent matrix element that is the same for both and is sensitive only to low-momentum structure of the many-body state. As a check, we apply our factorization relations to two well-studied systems, the unitary Fermi gas and the electron gas, and reproduce known expressions for the high-momentum tails of each.Comment: 22 pages, 0 figure

Simultaneous quantitative and allele-specific expression analysis with real competitive PCR

Background: For a diploid organism such as human, the two alleles of a particular gene can be expressed at different levels due to X chromosome inactivation, gene imprinting, different local promoter activity, or mRNA stability. Recently, imbalanced allelic expression was found to be common in human and can follow Mendelian inheritance. Here we present a method that employs real competitive PCR for allele-specific expression analysis. Results: A transcribed mutation such as a single nucleotide polymorphism ( SNP) is used as the marker for allele-specific expression analysis. A synthetic mutation created in the competitor is close to a natural mutation site in the cDNA sequence. PCR is used to amplify the two cDNA sequences from the two alleles and the competitor. A base extension reaction with a mixture of ddNTPs/ dNTP is used to generate three oligonucleotides for the two cDNAs and the competitor. The three products are identified and their ratios are calculated based on their peak areas in the MALDI-TOF mass spectrum. Several examples are given to illustrate how allele-specific gene expression can be applied in different biological studies. Conclusions: This technique can quantify the absolute expression level of each individual allele of a gene with high precision and throughput

Opioid receptor activation triggering downregulation of cAMP improves effectiveness of anti-cancer drugs in treatment of glioblastoma

Glioblastoma are the most frequent and malignant human brain tumors, having a very poor prognosis. The enhanced radio- and chemoresistance of glioblastoma and the glioblastoma stem cells might be the main reason why conventional therapies fail. The second messenger cyclic AMP (cAMP) controls cell proliferation, differentiation, and apoptosis. Downregulation of cAMP sensitizes tumor cells for anti-cancer treatment. Opioid receptor agonists triggering opioid receptors can activate inhibitory Gi proteins, which, in turn, block adenylyl cyclase activity reducing cAMP. In this study, we show that downregulation of cAMP by opioid receptor activation improves the effectiveness of anti-cancer drugs in treatment of glioblastoma. The µ-opioid receptor agonist D,L-methadone sensitizes glioblastoma as well as the untreatable glioblastoma stem cells for doxorubicin-induced apoptosis and activation of apoptosis pathways by reversing deficient caspase activation and deficient downregulation of XIAP and Bcl-xL, playing critical roles in glioblastomas' resistance. Blocking opioid receptors using the opioid receptor antagonist naloxone or increasing intracellular cAMP by 3-isobutyl-1-methylxanthine (IBMX) strongly reduced opioid receptor agonist-induced sensitization for doxorubicin. In addition, the opioid receptor agonist D,L-methadone increased doxorubicin uptake and decreased doxorubicin efflux, whereas doxorubicin increased opioid receptor expression in glioblastomas. Furthermore, opioid receptor activation using D,L-methadone inhibited tumor growth significantly in vivo. Our findings suggest that opioid receptor activation triggering downregulation of cAMP is a promising strategy to inhibit tumor growth and to improve the effectiveness of anti-cancer drugs in treatment of glioblastoma and in killing glioblastoma stem cells