Quantum Monte Carlo simulation of a two-dimensional Bose gas

The equation of state of a homogeneous two-dimensional Bose gas is calculated using quantum Monte Carlo methods. The low-density universal behavior is investigated using different interatomic model potentials, both finite-ranged and strictly repulsive and zero-ranged supporting a bound state. The condensate fraction and the pair distribution function are calculated as a function of the gas parameter, ranging from the dilute to the strongly correlated regime. In the case of the zero-range pseudopotential we discuss the stability of the gas-like state for large values of the two-dimensional scattering length, and we calculate the critical density where the system becomes unstable against cluster formation.Comment: 6 pages, 5 figures, 1 tabl

Single-particle vs. pair superfluidity in a bilayer system of dipolar bosons

We consider the ground state of a bilayer system of dipolar bosons, where dipoles are oriented by an external field in the direction perpendicular to the parallel planes. Quantum Monte Carlo methods are used to calculate the ground-state energy, the one-body and two-body density matrix, and the superfluid response as a function of the separation between layers. We find that by decreasing the interlayer distance for fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from a single-particle to a pair superfluid. The single-particle superfluid is characterized by a finite value of both the atomic condensate and the super-counterfluid density. The pair superfluid phase is found to be stable against formation of many-body cluster states and features a gap in the spectrum of elementary excitations.Comment: 4 figure

Beyond Tonks-Girardeau: strongly correlated regime in quasi-one-dimensional Bose gases

We consider a homogeneous 1D Bose gas with contact interactions and large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using a variational {\it ansatz} for the many-body wavefunction, we show that for small densities the gas-like state is stable and the corresponding equation of state is well described by a gas of hard rods. By calculating the compressibility of the system, we provide an estimate of the critical density at which the gas-like state becomes unstable against cluster formation. Within the hard-rod model we calculate the one-body density matrix and the static structure factor of the gas. The results show that in this regime the system is more strongly correlated than a Tonks-Girardeau gas. The frequency of the lowest breathing mode for harmonically trapped systems is also discussed as a function of the interaction strength.Comment: 4 pages, 4 figure

High-momentum dynamic structure function of liquid 3He-4He mixtures: a microscopic approach

The high-momentum dynamic structure function of liquid 3He-4He mixtures has been studied introducing final state effects. Corrections to the impulse approximation have been included using a generalized Gersch-Rodriguez theory that properly takes into account the Fermi statistics of 3He atoms. The microscopic inputs, as the momentum distributions and the two-body density matrices, correspond to a variational (fermi)-hypernetted chain calculation. The agreement with experimental data obtained at $q=23.1$ \AA$^{-1}$ is not completely satisfactory, the comparison being difficult due to inconsistencies present in the scattering measurements. The significant differences between the experimental determinations of the 4He condensate fraction and the 3He kinetic energy, and the theoretical results, still remain unsolved.Comment: 18 pages, 11 figures, to appear in Phys. Rev.

Formal Model Engineering for Embedded Systems Using Real-Time Maude

This paper motivates why Real-Time Maude should be well suited to provide a formal semantics and formal analysis capabilities to modeling languages for embedded systems. One can then use the code generation facilities of the tools for the modeling languages to automatically synthesize Real-Time Maude verification models from design models, enabling a formal model engineering process that combines the convenience of modeling using an informal but intuitive modeling language with formal verification. We give a brief overview six fairly different modeling formalisms for which Real-Time Maude has provided the formal semantics and (possibly) formal analysis. These models include behavioral subsets of the avionics modeling standard AADL, Ptolemy II discrete-event models, two EMF-based timed model transformation systems, and a modeling language for handset software.Comment: In Proceedings AMMSE 2011, arXiv:1106.596

Momentum distributions in ^3He-^4He liquid mixtures

We present variational calculations of the one-body density matrices and momentum distributions for ^3He-^4He mixtures in the zero temperature limit, in the framework of the correlated basis functions theory. The ground-state wave function contains two- and three-body correlations and the matrix elements are computed by (Fermi)Hypernetted Chain techniques. The dependence on the ^3He concentration (x_3) of the ^4He condensate fraction $(n_0^{(4)})$ and of the ^3He pole strength (Z_F) is studied along the P=0 isobar. At low ^3He concentration, the computed ^4He condensate fraction is not significantly affected by the ^3He statistics. Despite of the low x_3 values, Z_F is found to be quite smaller than that of the corresponding pure ^3He because of the strong ^3He-^4He correlations and of the overall, large total density \rho. A small increase of $n_0^{(4)}$ along x_3 is found, which is mainly due to the decrease of \rho respect to the pure ^4He phase.Comment: 23 pages, 7 postscript figures, Revte

Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study

We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value $a$ of the s-wave scattering length of the two-body potential. For $a>0$ and $a$ smaller than the inverse Fermi wavevector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length $a_m=0.6 a$. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.Comment: 4 pages, 3 figures. Version accepted for publication in Phys. Rev. Lett.. Figure 3 removed. Expanded discussion of correlation functions. New figure 4. Calculation of pair correlation functions improved: more statistics and extrapolation technique to remove residual dependences on the trial wave function. Added comparison with Bogoliubov theory. References adde

Progress in Monte Carlo calculations of Fermi systems: normal liquid 3He

The application of the diffusion Monte Carlo method to a strongly interacting Fermi system as normal liquid $^3$He is explored. We show that the fixed-node method together with the released-node technique and a systematic method to analytically improve the nodal surface constitute an efficient strategy to improve the calculation up to a desired accuracy. This methodology shows unambiguously that backflow correlations, when properly optimized, are enough to generate an equation of state of liquid $^3$He in excellent agreement with experimental data from equilibrium up to freezing.Comment: 14 pages, 3 eps figure