We investigate the localization properties of single-particle eigenstates in bichromatic one-dimensional optical lattices. Whereas such a lattice with a sufficiently deep primary component and a suitably adjusted incommensurate secondary component provides an approximate realization of the Harper model, the system's self-duality is broken when the lattice is comparatively shallow. As a consequence, the sharp metal-insulator transition exhibited by Harper's model is replaced by a sequence of mobility edges in realistic bichromatic optical lattices that do not reach the tight-binding regime.

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We point out that the velocity of propagation of sound wavepackets in a Bose-Einstein condensate filling a three-dimensional cubic optical lattice undergoes a maximum with increasing lattice depth. For a realistic choice of parameters, the maximum sound velocity in a lattice condensate can exceed the sound velocity in a homogeneous condensate with the same average density by 30%. The maximum falls into the superfluid regime, and should be observable under currently achievable laboratory conditions. PACS numbers: 03.75.Lm 03.75.Kk 05.30.JpThere have been vigorous activities, and impressive achievements, concerning Bose-Einstein condensates in optical lattice potentials recently, both experimentally [1,2,3,4,5,6] and theoretically [7,8,9,10,11,12,13,14,15], culminating in the observation of the quantum phase transition from a superfluid to a Mott insulator with a condensate of 87 Rb atoms [5].On the theoretical side, substantial effort has been devoted to calculating the low-lying excitations of a condensate in an optical lattice, and thus the speed of sound, within the Bogoliubov theory [16,17,18]. In particular, it has been predicted that in a one-dimensional optical lattice the velocity of propagation of sound wavepackets decreases monotonically with increasing lattice depth [19,20]. In this letter, we argue that the situation is different for condensates in three-dimensional lattices: In this case the velocity of sound undergoes a pronounced maximum when the lattice is made successively deeper, which falls into the superfluid regime, and should be observable under currently achievable experimental conditions.We consider a 3d Bose-Einstein condensate subjected to a simple d-dimensional optical cosine latticewhere k L = 2π/λ denotes the wavenumber associated with the lattice-generating laser radiation of wavelength λ. For d = 1 we study the propagation of sound in the direction of the lattice, while assuming that the condensate remains homogeneous in the orthogonal plane. We also assume that the depth V 0 of the lattice be sufficiently deep so that only the lowest Bloch band needs to be taken into account. The velocity of sound propagation in a Bose-Einstein condensate filling the lattice then is given by the standard expression [19,20] where m * is the effective mass pertaining to the lowest band, and U is the inverse compressibility of the condensate in the lattice. In principle, also the effective mass m * appearing in eq. (2) does depend on the density of the condensate, and has to be determined by solving the Gross-Pitaevskii equation for the condensate in the lattice [7,11,13,18]. This is particularly pertinent if one considers a 1d lattice filled with an effectively 1d condensate, strongly confined by restoring potentials orthogonal to the lattice direction, so that the transversal degrees of freedom are frozen out entirely. If then each lattice site carries a comparatively large number of particles, nonlinear effects due to the meanfield interaction play a decisive role. In contrast, we focus here on trul...

The equation of state of solid caesium (body-centred cubic (bcc) and face-centred cubic (fcc) structures) is examined theoretically by means of ab initio calculations. The Helmholtz free energies are calculated for pressures (P ) up to 5 GPa and temperatures (T ) in the range 0 300 K. The electronic contributions are calculated within density-functional theory (local density approximation (LDA) and generalized gradient approximation (GGA)), whereas vibrational contributions to energy and entropy are calculated within the quasi-harmonic approximation. The thermal expansion coefficients ( ) of bcc as well as fcc Cs are calculated as functions of P and T . Both phases are predicted to have (P , T ) regimes where is negative. For the fcc phase, goes negative for P above 3.5 GPa (and up to the end of the stability range of the fcc phase) for all T . The value = 3.0 ×10-4 K-1 found for Cs at ambient conditions agrees with experiments, and so does the Debye temperature, 39.5 K. The calculation shows that the bcc fcc transition occurs at P 2.2 GPa and low T , and at a higher pressure, 3 GPa, at room temperature. The fcc phase becomes unstable around 4.3 GPa, where a transverse phonon mode with q along (110) becomes soft. The calculations do not indicate that this transition is isostructural (fcc fcc), a result which is at variance with earlier theoretical and experimental work.

The textbook calculation of the ground-state energy of a dilute gas of Bose particles is examined in detail, and certain mathematical inconsistencies are pointed out. On the basis of this analysis, a refined approach suitable for soft interaction potentials which lend themselves to a low-order Born approximation is developed. This procedure emphasizes the low-density character of the resulting formula for the ground-state energy, and avoids all divergent expressions at intermediate stages of the computation. It is stressed that the standard Bogoliubov approximation, if not augmented by some additional device, leads to an error which manifests itself already in the lowest order of the density. - PACS 03.75.Hh, 05.30.Jp, 03.65.Nk.