Using diffusion Monte Carlo simulations we have investigated the ground state of a symmetric electron-hole bilayer and determined its phase diagram at T = 0. We find clear evidence of an excitonic condensate, whose stability however is affected by an in-layer electronic correlation. This stabilizes the electron-hole plasma at large values of the density or interlayer distance, and the Wigner crystal at low density and large distance. We have also estimated pair correlation functions and low-order density matrices to give a microscopic characterization of correlations as well as to try and estimate the condensate fraction.

The ground state and structure of a one-dimensional Bose gas with dipolar repulsions is investigated at zero temperature by a combined Reptation Quantum Monte Carlo (RQMC) and bosonization approach. A non trivial Luttinger-liquid behavior emerges in a wide range of intermediate densities, evolving into a Tonks-Girardeau gas at low density and into a classical quasi-ordered state at high density. The density dependence of the Luttinger exponent is extracted from the numerical data, providing analytical predictions for observable quantities, such as the structure factor and the momentum distribution. We discuss the accessibility of such predictions in current experiments with ultracold atomic and molecular gases. More recent experiments have demonstrated that the range of the interactions can also be manipulated. Dipole interactions with long-range anisotropic character have been observed in 52 Cr atoms [7] after exploiting the large magnetic moments of this atomic species, that is µ d ≈ 6µ B with µ B being the Bohr magneton. A BEC containing up to 50000 52 Cr atoms has then been obtained below a transition temperature T c ≃ 700nK [8] and its dynamical behavior is being investigated [9]. Promising proposals to tune and shape the dipolar interaction strength in quantum gasees of heteronuclear polar molecules have more recently been suggested [10]. Significant theoretical predictions have accompanied such realizations [11]. The stability diagram of anisotropic confined dipolar gases has been predicted to be governed by the trapping geometry [12,13], as corroborated by Path-Integral QMC studies [14]. Different conclusions are reached by more recent Diffusion QMC simulations including the dependence of a on the dipole interaction [15]. PACSTuning of the interactions can be combined with the enhancement of quantum fluctuations after reducing their dimensionality by e.g. storing them in elongated traps [16,17], which could be relevant to applications such as precision measurements [18], quantum computing [19], atomtronic quantum devices, and theoretical investigations of novel quantum phase transitions [20].In the case of quasi one-dimensional (1D) condensates with short-range interactions, a rich phenomenology is known to emerge from the collective character of the single-particle degrees of freedom, despite the absence of broken symmetries [21]. Bosons are known to arrange in a Luttingerliquid state, with single particles being replaced by collective density excitations [22,23]. Strong repulsion may also lead to the fermionization of interacting bosons in the so-called Tonks-Girardeau (TG) regime [24,25,26]. Experiments in elongated traps have provided evidence for such 1D fluctuations [16].In the case of quasi-1D condensates with dipolar interactions, an interesting question arises whether the quantum fluctuations are sufficiently enhanced to drive the BEC in a strong-coupling regime. More recent Diffusion QMC simulations [27] for a homogeneous 1D dipolar Bose gas have revealed a crossover behavior with increasing li...

A standard perturbative expansion around the mean-field solution is used to derive the low-energy effective action for superconductors at T = 0. Taking into account the density fluctuations at the outset we get the effective action where the density ρ is the conjugated momentum to the phase θ of the order parameter. In the hydrodynamic regime, the dynamics of the superconductor is described by a time dependent non-linear Schrödinger equation (TDNLS) for the field Ψ(x) = ρ 2 e iθ . The evolution of the density fluctuations in the crossover from weak-coupling (BCS) to strong-coupling (Bose condensation of localized pairs) superconductivity is discussed for the attractive Hubbard model. In the bosonic limit, the TDNLS equation reduces to the the Gross-Pitaevskii equation for the order parameter, as in the standard description of superfluidity. The conditions under which a phase-only action can be derived in the presence of a long-range interaction to describe the physics of the superconductivity of "bad metals" are discussed.

Using available quantum Monte Carlo predictions for a strictly 2D electron gas, we estimate the spin susceptibility of electrons in actual devices taking into account the effect of the finite transverse thickness and finding very good agreement with experiments. A weak disorder, as found in very clean devices and/or at densities not too low, just brings about a minor enhancement of the susceptibility.

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