We use the nonperturbative linear δ expansion method to evaluate analytically the coefficients c1 and c ′′ 2 which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by Tc = T0{1+c1an 1/3 +[c ′ 2 ln(an 1/3 )+c ′′ 2 ]a 2 n 2/3 +O(a 3 n)}, where T0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c1 to order-δ 2 with the result c1 = 3.06. Here, we push the calculation to the next two orders obtaining c1 = 2.45 at order-δ 3 and c1 = 1.48 at order-δ 4 . Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c ′′ 2 = 101.4, c ′′ 2 = 98.2 and c ′′ 2 = 82.9. Our analytical results seem to support the recent Monte Carlo estimates c1 = 1.32 ± 0.02 and c ′′ 2 = 75.7 ± 0.4.
We apply the nonperturbative optimized linear ␦ expansion method to the O(N) scalar field model in three dimensions to determine the transition temperature of a dilute homogeneous Bose gas. Our results show that the shift of the transition temperature ⌬T c /T c of the interacting model, compared with the ideal-gas transition temperature, really behaves as ␥an 1/3 where a is the s-wave scattering length and n is the number density. For Nϭ2 our calculations yield the value ␥ϭ3.059.
The irreversible transport of multi-component Bose-Einstein condensate (BEC) is investigated within the Stimulated Adiabatic Raman Passage (STIRAP) scheme. A general formalism for a single BEC in M-well trap is derived and analogy between multi-photon and tunneling processes is demonstrated. STIRAP transport of BEC in a cyclic triple-well trap is explored for various values of detuning and interaction between BEC atoms. It is shown that STIRAP provides a complete population transfer at zero detuning and interaction and persists at their modest values. The detuning is found not to be obligatory. The possibility of non-adiabatic transport with intuitive order of couplings is demonstrated. Evolution of the condensate phases and generation of dynamical and geometric phases are inspected. It is shown that STIRAP allows to generate the unconventional geometrical phase which is now of a keen interest in quantum computing.Comment: 9 pages, 6 figures. To be published in Laser Physics (v. 19, n.4, 2009
By using a close similarity between multi-photon and tunneling population transfer schemes, we propose robust adiabatic methods for the transport of Bose-Einstein condensate (BEC) in doubleand triple-well traps. The calculations within the mean-field approximation (Gross-Pitaevskii equation) show that irreversible and complete transport takes place even in the presence of the nonlinear effects caused by interaction between BEC atoms. The transfer is driven by adiabatic timedependent monitoring the barriers and well depths. The proposed methods are universal and can be applied to a variety of systems and scenarios.
The orbital M1 collective mode predicted for deformed clusters in a schematic model is studied in a self-consistent random-phase-approximation approach which fully exploits the shell structure of the clusters. The microscopic mechanism of the excitation is clarified and the close correlation with the E2 mode established. The study shows that the M1 strength of the mode is fragmented over a large energy interval. In spite of that, the fraction remaining at low energy, well below the overwhelming dipole plasmon resonance, is comparable to the strength predicted in the schematic model. The importance of this result in view of future experiments is stressed. PACS numbers: 36.40.Cg, 36.40.Gk, 36.40.Vz, 36.40.Wa Among the collective excitations which may occur in metal clusters, the magnetic dipole mode predicted for deformed clusters in a schematic model [1] has unique and appealing properties which deserve a deeper investigation. This excitation, which is the analog of the scissors mode predicted [2] and observed [3] in deformed nuclei, is promoted by rotational oscillations of the valence electrons against the jellium background. Indeed, in the semiclassical approach [1], the displacement field of the mode is composed of a rigid rotational velocity field plus a quadrupole term which comes from the boundary condition that the velocity flow vanishes on the deformed surface. The distortion of the momentum Fermi sphere generates a restoring force of the rotational oscillations. The mode is characterized by the magnetic quantum number K p 1 1 and falls at an excitation energywhereand v p are, respectively, the harmonic oscillator (HO) and the plasma frequencies; d is the deformation parameter, r s is the Wigner-Seitz radius, e F is the Fermi energy (r s 2.1 Å and e F 3.1 eV for Na clusters), and N e is the number of valence electrons in a cluster. The latter is related to the number N of atoms in a cluster by N N e or N N e 1 1 according to the fact that the cluster is neutral or has a positive charge Z 11. The mode gets a M1 strength given bywhere ᑣ 2͞3 N e m͗r 2 ͘ 2͞5r 2 s mN 5͞3 e is the collective mass parameter. As the formulas show, the M1 mode is peculiar of deformed clusters. Its occurrence would represent a unique and unambiguous fingerprint for the onset of quadrupole deformation. The main indicator of the deformation available so far is the splitting of the E1 resonance which, however, is often washed out or not properly resolved experimentally. The energy formula (1) reveals another appealing property. The M1 mode falls well below the energy of the overwhelming E1 resonance and, therefore, has good chances of being detected experimentally. In view of such a possibility, it is of the utmost importance to test the predictions of the schematic model by carrying out a microscopic calculation which fully exploits the shell structure of the clusters. Such a calculation should shed light on the microscopic mechanism which generates the mode and should reveal, eventually, new properties connected with the shell st...
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