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

Diffeomorphism Invariant Integrable Field Theories and Hypersurface Motions in Riemannian Manifolds

We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at which the hypersurface passes the point $x$. Equivalently, these motions may be described in a Hamiltonian formulation as the singlet sector of certain diffeomorphism invariant field theories. At least in some (infinite class of) cases, which could be viewed as a large-volume limit of Euclidean $M$-branesmoving in an arbitrary $M+1$-dimensional Riemannian manifold, the models are integrable: In the time-function formulation the equation becomes linear (with $\tau(x)$ a harmonic function on the embedding Riemannian manifold). We explicitly compute solutions to the large volume limit of Euclidean membrane dynamics in \Real^3 by methods used in electrostatics and point out an additional gradient flow structure in \Real^n. In the Hamiltonian formulation we discover infinitely many hierarchies of integrable, multidimensional, $N$-component theories possessing infinitely many diffeomorphism invariant, Poisson commuting, conserved charges.Comment: 15 pages, LATE

A no-ghost theorem for the bosonic Nappi-Witten string

We prove a no-ghost theorem for a bosonic string propagating in Nappi-Witten spacetime. This is achieved in two steps. We first demonstrate unitarity for a class of NW/U(1) modules: the norm of any state which is primary with respect to a chosen timelike U(1) is non-negative. We then show that physical states - states satisfying the Virasoro constraints - in a class of modules of an affinisation of the Nappi-Witten algebra are contained in the NW/U(1) modules. Similar to the case of strings on $AdS_3$, in order to saturate the spectrum obtained in light-cone quantization we are led to include modules with energy not bounded from below, which are related to modules with energy bounded from below by spectral flow automorphisms.Comment: 24 pages, 1 figur

Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.Comment: 5 pages, 2 figures; published versio

Directional emission from asymmetric resonant cavities

Asymmetric resonant cavities (ARCs) with highly non-circular but convex cross-sections are predicted theoretically to have high-Q whispering gallery modes with very anisotropic emission. We develop a ray dynamics model for the emission pattern and present numerical and experimental confirmation of the theory.Comment: 7 pages LaTeX, 3 postscript figure

Multiple high-pressure phase transitions in BiFeO3

We investigate the high-pressure phase transitions in BiFeO3 by single crystal and powder x-ray diffraction, as well as single crystal Raman spectroscopy. Six phase transitions are reported in the 0-60 GPa range. At low pressures, up to 15 GPa, 4 transitions are evidenced at 4, 5, 7 and 11 GPa. In this range, the crystals display large unit cells and complex domain structures, which suggests a competition between complex tilt systems and possibly off-center cation displacements. The non polar Pnma phase remains stable over a large pressure range between 11 and 38 GPa, where the distortion (tilt angles) changes only little with pressure. The two high-pressure phase transitions at 38 and 48 GPa are marked by the occurence of larger unit cells and an increase of the distorsion away from the cubic parent perovskite cell. We find no evidence for a cubic phase at high pressure, nor indications that the structure tends to become cubic. The previously reported insulator-to-metal transition at 50 GPa appears to be symmetry breaking.Comment: 11 pages, 8 figure

Mathematical modeling of proteome constraints within metabolism

Genome-scale metabolic models (GEMs) are widely used to predict phenotypes with the aid of constraint-based modeling. In order to improve the predictive power of these models, there have been many efforts on imposing biological constraints, among which proteome constraints are of particular interest. Here we describe the concept of proteome constraints and review proteome-constrained GEMs, as well as their advantages and applications. In addition, we discuss a key issue in the field, i.e., low coverage of enzyme-specific turnover rates, and subsequently provide a few solutions to solve it. We end with a discussion on the trade-off between model complexity and capability

In vitro turnover numbers do not reflect in vivo activities of yeast enzymes

Turnover numbers (kcat values) quantitatively represent the activity of enzymes, which are mostly measured in vitro. While a few studies have reported in vivo catalytic rates (kapp values) in bacteria, a large-scale estimation of kapp in eukaryotes is lacking. Here, we estimated kapp of the yeast Saccharomyces cerevisiae under diverse conditions. By comparing the maximum kapp across conditions with in vitro kcat we found a weak correlation in log scale of R2 = 0.28, which is lower than for Escherichia coli (R2 = 0.62). The weak correlation is caused by the fact that many in vitro kcat values were measured for enzymes obtained through heterologous expression. Removal of these enzymes improved the correlation to R2 = 0.41 but still not as good as for E. coli, suggesting considerable deviations between in vitro and in vivo enzyme activities in yeast. By parameterizing an enzyme-constrained metabolic model with our kapp dataset we observed better performance than the default model with in vitro kcat in predicting proteomics data, demonstrating the strength of using the dataset generated here

Topologic mixing on a microfluidic chip

Mixing two liquids on a microfluidic chip is notoriously hard because the small dimensions and velocities on the chip effectively prevent turbulence. We present a topological mixing scheme that exploits the laminarity of the flow to repeatedly fold the flow and exponentially increase the concentration gradients to obtain fast and efficient mixing by diffusion. It is based on helical flow channels with opposite chiralities that split, rotate, and recombine the fluid stream in a topology reminiscent of a series of Möbius bands. This geometry is realized in a simple six-stage, two-layer elastomer structure with a footprint of 400 μm×300 μm400μm×300μm per stage that mixes two solutions efficiently at Reynolds numbers between 0.1 and 2. This represents more than an order of magnitude reduction in the size of microfluidic mixers that can be manufactured in standard multilayer soft lithography techniques. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69745/2/APPLAB-84-12-2193-1.pd