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The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^dx=na0d, with nn the density, dd the dimensionality of the space (d=1,2,3d=1,2,3) and a_0a0 the ss-wave scattering length. The universal regime typically extends up to x\approx 0.001x≈0.001, while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes a_0a0 depend on the polarization angle \alphaα, so different combinations of n and \alphaα can lead to the same value of the gas parameter x. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large gas parameter values. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of xx that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.

Fusion energy stands out as a promising alternative for a future decarbonised energy system. In order to be sustainable, future fusion nuclear reactors will have to produce their own tritium. In the so-called breeding blanket of a reactor, the neutron bombardment of lithium will produce the desired tritium, but also helium, which can trigger nucleation mechanisms owing to the very low solubility of helium in liquid metals. An understanding of the underlying microscopic processes is important for improving the efficiency, sustainability and reliability of the fusion energy conversion process. The spontaneous creation of helium droplets or bubbles in the liquid metal used as breeding material in some designs may be a serious issue for the performance of the breeding blankets. This phenomenon has yet to be fully studied and understood. This work aims to provide some insight on the behaviour of lithium and helium mixtures at experimentally corresponding operating conditions (843 K and pressures between 108 and 1010 Pa). We report a microscopic study of the thermodynamic, structural and dynamical properties of lithium–helium mixtures, as a first step to the simulation of the environment in a nuclear fusion power plant. We introduce a new microscopic model devised to describe the formation of helium droplets in the thermodynamic range considered. Our model predicts the formation of helium droplets at pressures around 109 Pa, with radii between 1 and 2 Å. The diffusion coefficient of lithium (2 Å2/ps) is in excellent agreement with reference experimental data, whereas the diffusion coefficient of helium is in the range of 1 Å2/ps and tends to decrease as pressure increases.

This is a Reply to the Comment from F. Cinti and M. Boninsegni on our recent work on the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in a two-dimensional dipolar system [Bombín, Mazzanti, and Boronat, Phys. Rev. A 100, 063614 (2019)]. The main criticism about our work expressed in that Comment is that we did not explicitly report the two spatial contributions to the total superfluid fraction. Here we analyze our results for a point of the phase diagram corresponding to the stripe phase, close to the gas-to-stripe transition line, and for a temperature below the BKT critical temperature. The scaling with the system size of the contribution to the superfluid fraction, coming from the direction in which spatial order appears, shows that it remains finite in the thermodynamic limit, as we already stated in our original work. This allow us to state that the stripe phase is superfluid at low temperatures. Furthermore, we offer some comments that help to understand where the differences between the results of Cinti and Boninsegni and ours come from., This work has been supported by the Ministerio de Economia, Industria y Competitividad (MINECO, Spain), under Grant No. FIS2017-84114-C2-1-P.

A Bose gas under the effect of Raman Spin-Orbit Coupling (SOC) is analyzed using the Discrete Spin T-moves Diffusion Monte Carlo method. By computing the energy as well as the static structure factor and the superfluid fraction of the system, the emergence of an energetically favorable supersolid stripe state is observed, which is in agreement with recent observations. A significant enhancement of the stability of the stripe phase with respect to the mean-field prediction is observed when the strength of the inter-atomic correlations is increased. We also quantify and characterize the degree of superfluidity of the stripes and show that this quantity is mostly determined by the ratio between the Raman coupling and the square of the momentum difference between the pair of SOC inducing laser beams., Comment: 5 pages, 4 figures

We analyze the role played by quantum fluctuations on a Raman Spin-Orbit Coupled system in the stripe phase. We show that beyond mean-field effects stabilize the collapse predicted by mean-field theory and induce the emergence of two phases: a gas and a liquid, which also show spatial periodicity along a privileged direction. We show that the energetically favored phase is determined by the Raman coupling and the spin-dependent scattering lengths. We obtain the ground-state solution of the finite system by solving the extended Gross-Pitaevskii equation and find self-bound, droplet-like solutions that feature internal structure through a striped pattern. We estimate the critical number for binding associated to these droplets and show that their value is experimentally accessible. We report an approximate energy functional in order to ease the evaluation of the Lee-Huang-Yang correction in practical terms., Comment: 10 pages, 6 Figures

A two-dimensional quantum system of dipoles, with a polarization angle not perpendicular to the plane, shows a transition from a gas to a stripe phase. We have studied the thermal properties of these two phases using the path-integral Monte Carlo (PIMC) method. By simulating the thermal density matrix, PIMC provides exact results for magnitudes of interest such as the superfluid fraction and the one-body density matrix. As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. At fixed density and increasing the tilting angle, the transition temperature decreases in going from the gas to the stripe phase. Superfluidity in the perpendicular direction to the stripes is rather small close to the critical temperature but it becomes larger at lower temperatures, mainly close to the transition to the gas. Our results are in qualitative agreement with the supersolidity observed recently in a quasi-one-dimensional array of dipolar droplets.

Dipolar quantum droplets are exotic quantum objects that are self-bound due to the subtle balance of attraction, repulsion, and quantum correlations. Here we present a systematic study of the critical atom number of these self-bound droplets, comparing the experimental results with extended mean-field Gross-Pitaevskii equation and quantum Monte Carlo simulations of the dilute system. The respective theoretical predictions differ, questioning the validity of the current theoretical state-of-the-art description of quantum droplets within the extended Gross-Pitaevskii equation framework and indicating that correlations in the system are significant. Furthermore, we show that our system can serve as a sensitive testing ground for many-body theories in the near future.

We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive $1/r^3$ potential. This model can be realized with ultracold atoms or molecules, when their dipole moments are aligned in the confinement direction orthogonal to the plane. We characterize the unpolarized mixture by means of the Diffusion Monte Carlo technique. Computing the equation of state, we identify the regime of validity for a mean-field theory based on a low-density expansion and compare our results with the hard-disk model of repulsive fermions. At high density, we address the possibility of itinerant ferromagnetism, namely whether the ground state can be fully polarized in the fluid phase. Within the fixed-node approximation, we show that the accuracy of Jastrow-Slater trial wave functions, even with the typical two-body backflow correction, is not sufficient to resolve the relevant energy differences. By making use of the iterative-backflow improved trial wave functions, we observe no signature of a fully-polarized ground state up to the freezing density., Comment: 12 pages, 6 figures

Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultra-dilute binary Bose mixtures. We proceed beyond the beyond-mean-field approximation, and study liquid Bose mixtures using the variational hypernetted-chain Euler Lagrange method, which accounts for correlations non-perturbatively. Focusing on the case of a mixture of uniform density, as realized inside large saturated droplets, we study the conditions for stability against evaporation of one of the components (both chemical potentials need to be negative) and against liquid-gas phase separation (spinodal instability), the latter being accompanied by a vanishing speed of sound. Dilute Bose mixtures are stable only in a narrow range near an optimal ratio $\rho_1/\rho_2$ and near the total energy minimum. Deviations from a universal dependence on the s-wave scattering lengths are significant despite the low density., Comment: 5 pages, 5 figures

Learning algorithms for energy based Boltzmann architectures that rely on gradient descent are in general computationally prohibitive, typically due to the exponential number of terms involved in computing the partition function. In this way one has to resort to approximation schemes for the evaluation of the gradient. This is the case of Restricted Boltzmann Machines (RBM) and its learning algorithm Contrastive Divergence (CD). It is well-known that CD has a number of shortcomings, and its approximation to the gradient has several drawbacks. Overcoming these defects has been the basis of much research and new algorithms have been devised, such as persistent CD. In this manuscript we propose a new algorithm that we call Weighted CD (WCD), built from small modifications of the negative phase in standard CD. However small these modifications may be, experimental work reported in this paper suggests that WCD provides a significant improvement over standard CD and persistent CD at a small additional computational cost.

Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence (CD) learning algorithm, an approximation to the gradient of the data log-likelihood (logL). A simple reconstruction error is often used as a stopping criterion for CD, although several authors have raised doubts concerning the feasibility of this procedure. In many cases, the evolution curve of the reconstruction error is monotonic, while the logL is not, thus indicating that the former is not a good estimator of the optimal stopping point for learning. However, not many alternatives to the reconstruction error have been discussed in the literature. An estimation of the logL of the training data based on annealed importance sampling is feasible but computationally very expensive. In this manuscript, we present a simple and cheap alternative, based on the inclusion of information contained in neighboring states to the training set, as a stopping criterion for CD learning.

We study the superfluid properties of a system of fully polarized dipolar bosons moving in the $XY$ plane. We focus on the general case where the polarization field forms an arbitrary angle $\ensuremath{\alpha}$ with respect to the $Z$ axis, while the system is still stable. We use the diffusion Monte Carlo and the path integral ground state methods to evaluate the one-body density matrix and the superfluid fractions in the region of the phase diagram where the system forms stripes. Despite its oscillatory behavior, the presence of a finite large-distance asymptotic value in the $s$-wave component of the one-body density matrix indicates the existence of a Bose condensate. The superfluid fraction along the stripes direction is always close to 1, while in the $Y$ direction decreases to a small value that is nevertheless different from zero. These two facts confirm that the stripe phase of the dipolar Bose system is a clear candidate for an intrinsic supersolid without the presence of defects as described by the Andreev-Lifshitz mechanism.

We study the ground state of a bilayer system of dipolar bosons with dipoles oriented by an external field perpendicularly to the two parallel planes. By decreasing the interlayer distance, for a fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from an atomic to a pair superfluid. We investigate the excitation spectrum across this transition by using microscopic approaches. Quantum Monte Carlo methods are employed to obtain the static structure factors and intermediate scattering functions in imaginary time. The dynamic response is calculated using both the correlated basis functions (CBF) method and the approximate inversion of the Laplace transform of the quantum Monte Carlo imaginary time data. In the atomic phase, both density and spin excitations are gapless. However, in the pair-superfluid phase a gap opens in the excitation energy of the spin mode. For small separation between layers, the minimal spin excitation energy equals the binding energy of a dimer and is twice the gap value., Comment: 8 pages, 5 figures

We study the superfluid response, the energetic and structural properties of a one-dimensional ultracold Bose gas in an optical lattice of arbitrary strength. We use the Bose-Fermi mapping in the limit of infinitely large repulsive interaction and the diffusion Monte Carlo method in the case of finite interaction. For slightly incommensurate fillings we find a superfluid behavior which is discussed in terms of vacancies and interstitials. It is shown that both the excitation spectrum and static structure factor are different for the cases of microscopic and macroscopic fractions of defects. This system provides a extremely well-controlled model for studying defect-induced superfluidity., 14 pages, 13 figures, published version

Strongly interacting systems of dipolar bosons in three dimensions confined by harmonic traps are analyzed using the exact Path Integral Ground State Monte Carlo method. By adding a repulsive two-body potential, we find a narrow window of interaction parameters leading to stable ground- state configurations of droplets in a crystalline arrangement. We find that this effect is entirely due to the interaction present in the Hamiltonian without resorting to additional stabilizing mechanisms or specific three-body forces. We analyze the number of droplets formed in terms of the Hamiltonian parameters, relate them to the corresponding s-wave scattering length, and discuss a simple scaling model for the density profiles. Our results are in qualitative agreement with recent experiments showing a quantum Rosensweig instability in trapped Dy atoms., 5 pages, 4 figures

We study the dynamic structure function of ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We compare our result with the Bragg-scattering measurements in 85Rb by Papp et al. (Phys. Rev. Lett. 101:135301, 2008) and show that these experiments set very strict limits to the shape of the effective two-particle interaction ruling out the contact and hard spheres potentials. Using the Feshbach resonance approximation we derive the effective interaction, which turns out to be very similar to the soft spheres potential in momentum space. At large scattering lengths the interaction becomes universal and could be directly measured by Bragg scattering. We also discuss the experimental conditions needed for the appearance of the maxon-roton structure in the excitation spectrum and finally show that when the scattering length becomes larger than 2000 Bohr radii the uniform gas phase undergoes a phase transition into the density wave state.

We have studied the scaling of the interaction in Bose-Einstein condensates of ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We find that the effective interaction in the metastable, open channel, gaseous phase scales well with the scattering length in the range analyzed. Based on this we show that for increasing scattering lengths, or equivalently increasing densities, the system becomes less correlated, and that at large scattering lengths Bragg scattering experiments can directly measure the effective two-body potential in momentum space. This work is motivated by the recent Bragg-scattering measurements in 85Rb by Papp et al. [Phys. Rev. Lett. 101, 135301 (2008)], where the results in the line shifts show clear deviations from the simple contact interaction. We show that those results are well described by a soft spheres potential with parameters chosen to scale in scattering length units. So far the resolution in the experiments does not reveal details on the frequency dependence in the dynamic structure function S(k,ω) and we show that the Feynman spectrum determines the measured line shifts. We also construct the effective atom-atom interaction from two coupled channels, open and closed, assuming that the Feshbach resonance dominates the closed channel. The resonance energy and the scattering length a of the system are tunable by magnetic fields. We derive the T-matrix of such a system and use renormalization to calculate the bound state energy as a function of the magnetic field and make comparison with available experiments. The s-wave phase shifts determine the local, effective open-channel interaction, but if no scaling is used in the cut-off parameters of the renormalization the phase shift resembles more and more the ones obtained from the contact interaction with increasing scattering length. This leads to clear deviations from the measured line shift experiments.

We present results on the behavior of the dynamic structure function in the short wave length limit using the equation of motion method. The one-body continuity equation defines the self-energy, which becomes a functional of the fluctuating two-body correlation function. We evaluate the self-energy in this limit and show that sum rules up to the second moment, which requires the self-energy in the short wave length limit and zero frequency to be proportional to the kinetic energy per particle, are exactly satisfied. We compare our results with the impulse approximation and calculate the condensate fraction. An analytic expression for the momentum distribution is also derived.

One-dimensional Bose gas with contact interaction in optical lattices at zero temperature is investigated by means of the exact diffusion Monte Carlo algorithm. The results obtained from the fundamental continuous model are compared with those obtained from the lattice (discrete) Bose-Hubbard model, using exact diagonalization, and from the quantum sine-Gordon model. We map out the complete phase diagram of the continuous model and determine the regions of applicability of the Bose-Hubbard model. Various physical quantities characterizing the systems are calculated and it is demonstrated that the sine-Gordon model used for shallow lattices is inaccurate., 5 figures

A detailed discussion of the dynamic susceptibility of the two dimensional free Fermi gas at zero and finite temperature is presented. The behaviour and evolution of the coherent and incoherent components of the dynamic structure function with the temperature and momentum transfer are analyzed. Particular attention is paid to the way in which their relative contribution changes with respect to the ~T=0 case. The influence of thermal effects on the lowest order sum rules of the coherent and incoherent responses is also discussed. Finally, similar analysis are presented for the real part of the dynamic susceptibility.

We analyze the ground state of a system of dipolar bosons moving in the $XY$ plane and such that their dipolar moments are all aligned in a fixed direction in space. We focus on the general case where the polarization field forms a generic angle $\ensuremath{\alpha}$ with respect to the $Z$ axis. We use the path-integral ground-state method to analyze the static properties of the system as both $\ensuremath{\alpha}$ and the density $n$ vary over a wide range where the system is stable. We use the maximum of the static structure function as an order parameter to characterize the different phases and the transition lines among them. We find that, in addition to a superfluid gas and a solid phase, the system reaches a stripe phase at large tilting angles that is entirely induced by the anisotropic character of the interaction. We also show that the quantum phase transition from the gas to the stripe phase is of second order and report approximate values for the critical exponents.

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 figures

We report dynamical calculations for large-$q$ structure functions of liquid $^4$He at $T$=1.6 and 2.3 K and compare those with recent MARI data. We extend those calculations far beyond the experimental range $q\le 29\Ain$ in order to study the approach of the response to its asymptotic limit for a system with interactions having a strong short-range repulsion. We find only small deviations from theoretical $1/q$ behavior, valid for smooth $V$. We repeat an extraction by Glyde et al of cumulant coefficients from data. We argue that fits determine the single atom momentum distribution, but express doubt as to the extraction of meaningful Final State Interaction parameters.

Correlated-basis-function perturbation theory is used to evaluate the zero-temperature response S(q,\ensuremath{\omega}) of $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures for inelastic neutron scattering, at momentum transfers q ranging from 1.1 to 1.8 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$. We adopt a Jastrow correlated ground state and a basis of correlated particle-hole and phonon states. We insert correlated one-particle--one-hole and one- and two-phonon states to compute the second-order response. The decay of the one-phonon states into two-phonon states is accounted for in the boson-boson approximation. The full response is split into three partial components ${\mathit{S}}_{\mathrm{\ensuremath{\alpha}}\mathrm{\ensuremath{\beta}}}$(q,\ensuremath{\omega}), each of them showing a particle-hole bump and a one phonon, \ensuremath{\delta}-shaped peak, which stays separated from the multiphonon background. The cross term ${\mathit{S}}_{34}$(q,\ensuremath{\omega}) results to be of comparable importance to ${\mathit{S}}_{33}$(q,\ensuremath{\omega}) in the particle-hole sector and to ${\mathit{S}}_{44}$(q,\ensuremath{\omega}) in the phonon one. Once the response has been convoluted with the experimental broadening, the computed scattering function is in semiquantitative agreement with recent experimental measurements. \textcopyright{} 1996 The American Physical Society.

A study of final-state effects (FSE) on the dynamic structure function of superfluid {sup 4}He in the Gersch-Rodriguez formalism is presented. The main ingredients needed in the calculation are the momentum distribution and the semidiagonal two-body density matrix. The influence of these ground-state quantities on the FSE is analyzed. A variational form of {rho}{sub 2} is used, even though simpler forms turn out to give accurate results if properly chosen. Comparison to the experimental response at high momentum transfer is performed. The predicted response is quite sensitive to slight variations on the value of the condensate fraction, the best agreement with experiment being obtained with {ital n}{sub 0}=0.082. Sum rules of the FSE broadening function are also derived and commented. Finally, it is shown that Gersch-Rodriguez theory produces results as accurate as those coming from other more recent FSE theories. {copyright} {ital 1996 The American Physical Society.}

We present a quantum Monte Carlo study of two-dimensional dipolar Bose gases in the limit of zero temperature. The analysis is mainly focused on the anisotropy effects induced in the homogeneous gas when the polarization angle with respect to the plane is changed. We restrict our study to the regime where the dipolar interaction is strictly repulsive, although the strength of the pair repulsion depends on the vector interparticle distance. Our results show that the effect of the anisotropy in the energy per particle scales with the gas parameter at low densities as expected, and that this scaling is preserved for all polarization angles even at the largest densities considered here. We also evaluate the excitation spectrum of the dipolar Bose gas in the context of the Feynman approximation and compare the results obtained with the Bogoliubov ones. As expected, we find that these two approximations agree at very low densities, while they start to deviate from each other as the density increases. For the largest densities studied, we observe a significant influence of the anisotropy of the dipole-dipole interaction in the excitation spectrum., 6 pages, 6 figures

We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a nonperpendicular polarization with respect to the system plane. For sufficiently high density, an increase of the polarization angle leads to a density instability of the gas phase in the direction where the anisotropic interaction is strongest. Using a dynamic many-body theory, we calculate the dynamic structure function in the gas phase which shows the anisotropic dispersion of the excitations. We find that the energy of roton excitations in the strongly interacting direction decreases with increasing polarization angle and almost vanishes close to the instability. Exact path integral ground state Monte Carlo simulations show that this instability is indeed a quantum phase transition to a stripe phase, characterized by long-range order in the strongly interacting direction.

We use microscopic many-body theory to analyze the problem of itinerant ferromagnetism in a repulsive atomic Fermi gas of Hard Spheres. Using simple arguments, we show that the available theoretical predictions for the onset of the ferromagnetic transition predict a transition point at a density ($k_F a \sim 1$) that is too large to be compatible with the universal low-density expansion of the energy. We present new variational calculations for the hard-sphere Fermi gas, in the framework of Fermi hypperneted chain theory, that shift the transition to higher densities ($k_F a \sim 1.8$). Backflow correlations, which are mainly active in the unpolarized system, are essential for this shift.

We study the zero-temperature phase diagram of bosons interacting via screened Coulomb (Yukawa) potential by means of the diffusion Monte Carlo method. The Yukawa potential is used as a model interaction in the neutron matter, dusty plasmas and charged colloids. As shown by D. S. Petrov et al. [Phys. Rev. Lett. 99, 130407 (2007)], interactions between weakly bound molecules of heavy and light fermionic atoms are described by an effective Yukawa potential with a strength related to the heavy-light mass ratio M/m which might lead to crystallization in a two-dimensional geometry if the mass ratio of heavy-light fermions exceeds a certain critical value. In the present work we do a thorough study of the quantum three-dimensional Yukawa system. For strong interactions (equivalently, large mass ratios) the system experiences several phase transitions as the density is increased, passing from gas to solid and to gas phase again. Weakly interacting Yukawa particles do not crystallize at any density. We find the minimal interaction strength at which the crystallization happens. In terms of the two-component fermionic system, this strength corresponds to a heavy-light mass ratio of M/m ~ 180, so that it is impossible to realize the gas-crystal transition in a conventional bulk system. For the Yukawa model of fermionic mixtures we also analyze the possibility of building molecular systems with very large effective mass ratios by confining the heavy component to a sufficiently deep optical lattice. We show how the effective mass of the heavy component can be made arbitrarily large by increasing the lattice depth, thus leading to a tunable effective mass ratio that can be used to realize a molecular superlattice., Comment: added figure with finite-size dependence of the energy; comments and references added; title changed

The variational principle is used to show that the ground-state wave function of a one-body Schrodinger equation with a real potential is real, does not change sign, and is nondegenerate. As a consequence, if the Hamiltonian is invariant under rotations and parity transformations, the ground state must have positive parity and zero angular momentum.

We present a theoretical analysis of excitation modes in Bose-Einstein condensates of ultracold alkali-metal gases for large scattering lengths, showing clear deviations from the Bogoliubov prediction as seen by Papp et al.[Phys. Rev. Lett. 101, 135301 (2008)]. We construct the atom-atom interaction by deriving the T matrix of such systems from two coupled (open and closed) channels assuming that the Feshbach resonance dominates the latter. We calculate molecular bound-state energies as a function of the magnetic field and compare with available experiments. The s-wave phase shifts determine the local effective interaction with long-ranged repulsion and short-ranged attraction. We show that it becomes a universal function at large scattering lengths. Finally, we use this interaction to characterize the ground-state and elementary excitations of {sup 85}Rb, {sup 87}Rb, and {sup 23}Na gases. Good agreement with line shift experiments in {sup 85}Rb is achieved. We find that, at large scattering lengths, Bragg scattering experiments could directly measure the momentum dependence of the effective two-body potential.

A microscopic description of the zero energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole--dipole interaction, on the energy per particle, comparing the results with mean field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero energy two-body problem which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions., 9 figures, 1 table

Relevant features of the dynamic structure function S(q,\ensuremath{\omega}) in $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures at zero temperature are investigated starting from known properties of the ground state. Sum rules are used to fix rigorous constraints to the different contributions to S(q,\ensuremath{\omega}), coming from $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ elementary excitations, as well as to explore the role of the cross term ${\mathit{S}}^{(3,4)}$(q,\ensuremath{\omega}). Both the low-q (phonon-roton $^{4}\mathrm{He}$ excitations and 1p-1h $^{3}\mathrm{He}$ excitations) and high-q (deep-inelastic-scattering) ranges are discussed.

The feasibility of path integral Monte Carlo ground state calculations with very few beads using a high-order short-time Green's function expansion is discussed. An explicit expression of the evolution operator which provides dramatic enhancements in the quality of ground-state wave-functions is examined. The efficiency of the method makes possible to remove the trial wave function and thus obtain completely model-independent results still with a very small number of beads. If a single iteration of the method is used to improve a given model wave function, the result is invariably a shadow-type wave function, whose precise content is provided by the high-order algorithm employed., Comment: 4 pages