We investigate the properties of strongly interacting bosons in two dimensions at zero temperature using mean-field theory, a variational Ansatz for the ground state wave function, and Monte Carlo methods. With on-site and short-range interactions a rich phase diagram is obtained. Apart from the homogeneous superfluid and Mott-insulating phases, inhomogeneous chargedensity wave phases appear, that are stabilized by the finite-range interaction.Furthermore, our analysis demonstrates the existence of a supersolid phase, in which both long-range order (related to the charge-density wave) and offdiagonal long-range order coexist. We also obtain the critical exponents for the various phase transitions.

We investigate the Coulomb blockade resonances and the phase of the transmission amplitude of a deformed ballistic quantum dot weakly coupled to leads. We show that preferred single-particle levels exist which stay close

We study the phase of the transmission amplitude through a disordered quantum dot in the Coulomb blockade regime. We calculate the phase dependence on gate voltage for a disorder configuration. We show that over a "period," consisting of a resonance and a transmission valley, the total phase change is 0 (mod2p). Deviations from this sum rule are small in the parameter (level spacing and /or charging energy). The disorder-averaged phase-phase correlation function is found showing interaction-induced correlations between phases at different gate voltages.

For a system of independent electrons moving in a common one-body potential V (r) an integral representation of Dirac's density matrix is evaluated in the approximation that V(r) at the point r is replaced by a linear potential with a gradient equal to the gradient of V at r. The particle density ᵨ, ∇ᵨ and the kinetic-energy density εk are derived from the density matrix. After eliminating the potential and its gradient a parametric representation for εk in terms of ᵨ and y = |∇ᵨ |½ ᵨ-⅔ is obtained. Explicit analytical expressions are given in the limits y → 0 and y → ∞ and compared with the inhomogeneity corrections of Kirzhnits and v. Weizsäcker.

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