ABSTRACT
It is shown that the phenomenon of negative temperature essentially occurs in Bose-Einstein condensate due to the realization of the upper bound energy state utilizing a combination of expulsive harmonic oscillator and optical lattice potentials. We study the existence of quantum droplets at negative temperature and droplet-to-soliton crossover in the binary Bose-Einstein condensate mixture in the presence of bi-periodic optical lattices and expulsive-BOL confinements. Based on the beyond mean field approximation, we employ the extended Gross-Pitäevskii equation and calculate the exact analytical form of wavefunction solutions for BOL, expulsive-BOL confinements. An interesting transition of quantum droplets from positive to negative temperatures and the droplet-to-soliton crossover by modulating the disorder in BOL potential are illustrated. The affirmation of such crossover is performed by exploring the profile of atomic condensate density which smoothly transits from being a flat top density in optical lattice confinement to a bright soliton for BOL trap. Further, we confirm the crossover by exploring the energy per particle and the variation in the root mean square size of the condensate with respect to the potential depth of the BOL trap. Eventually, all of this aid us to construct a phase diagram in a space between the amplitude of BOL potential depth and particle number which reveals the formation of droplet and soliton phases. In expulsive-BOL confinement, it is seen that the impact of the expulsive trap is insignificant on atomic condensate density in the droplet phase and it becomes prominent in the soliton region. Further, the variation of total energy reveals that the amplitude of the expulsive oscillator strengthens the droplet phase and leads to an increase in the negative temperature of the considered system.
ABSTRACT
Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross-Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov-Kolokolov (VK) criterion and are found stable.
ABSTRACT
We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative temperature. This work is motivated by the first experimental discovery of negative temperature in Bose-Einstein condensate by Braun et al. We have considered an external confinement which is a combination of expulsive trap, bi-chromatic optical lattice trap, and linear trap. The present method is capable of providing the exact form of the condensate wavefunction, phase, nonlinearity and gain/loss. One of the consistency conditions is shown to map onto the Schrödinger equation, leading to a significant control over the dynamics of the system. We have modified the model by replacing the optical lattice trap by a bi-chromatic optical lattice trap, which imparts better localization at the central frustrated site, delineated through the variation of condensate fraction. Estimation of temperature and a numerical stability analysis are also carried out. Incorporation of an additional linear trap introduces asymmetry and the corresponding temporal dynamics reveal atom distillation at negative temperature.
ABSTRACT
UNLABELLED: We calculated the effects of the simulated Valsalva (V), liver (L) compression, and Trendelenburg (T) position on the cross-sectional area (CSA) of the right internal jugular vein by using planimetry (Aloka ultrasound machine) in 84 infants and young children. Eight combinations of positions and interventions were studied for each patient, with the patient supine, in the T position, during the simulated V maneuver, with L compression and a combination of maneuvers. Data were analyzed by using Friedman's chi(2) test and Wilcoxon's signed rank test. An increase of >25% in the CSA of the internal jugular vein was considered significant. In infants, the maximal mean increase achieved with the combination of all 3 maneuvers was only 17.4% +/- 16.1%. As a single maneuver, the simulated V was the most effective (11.6% +/- 11.5%). In children, the combination of all 3 maneuvers performed simultaneously produced a mean 65.9% (SD +/- 44.7%) increase in the CSA, which was larger than the increase by all other maneuvers alone or in a single combination (Friedman's test, P < 0.001 and Wilcoxon's test, P < 0.002). As a single maneuver, V produced the most increase (40.4% +/- 32.2%) compared with L compression (14.3% +/- 18.9%) or T position (24.3% +/- 27.1%). IMPLICATIONS: The combinations of simulated Valsalva, liver compression, and Trendelenburg maneuvers produce the maximal mean increase in the size of the internal jugular vein in infants and young children, with the Valsalva maneuver being the most effective single maneuver. This increase is significant in young children, but negligible in infants.
