We revisit statistical wavefunction properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength λ, the strength functions F k (E) are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio ξ 2 and the information entropy S info during this crossover, thereby extending the known behavior valid in the Gaussian domain into much of the Breit-Wigner domain. Our method also allows us to derive the scaling law for the duality point λ = λ d , where F k (E), ξ 2 and S info in both the weak (λ = 0) and strong mixing (λ = ∞) basis coincide aswhere m is the number of fermions. As an application, the ansatz function for strength functions is used in describing the Breit-Wigner to Gaussian transition seen in neutral atoms CeI to SmI with valence electrons changing from 4 to 8.

We demonstrate the possibility of realizing sub-Planck scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecule, produces cat-like states, responsible for the above phenomenon. We investigate the phase space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck scale structures. The optimal parameter ranges are specified for observing these features. [4] demonstrated that appropriate superposition of some of these states with a classical action A can lead to sub-Planck scale structures in phase space. These sub-Planck scale structures in the phase space are characterized by an area 2 /A. Apart from their counter intuitive nature and theoretical significance, the above scale has been shown to control the effectiveness of decoherence, a subject of tremendous current interest in the area of quantum computation and information. Zurek's realization made use of dynamical systems which exhibit chaotic behavior in the classical domain. Recently a cavity QED realization involving the mesoscopic superposition of the compass states have been given [5]. In principle, one could also use superpositions of cat-like states arising in quantum optical systems with large Kerr non-linearity [2].In this paper, we demonstrate the possibility of realizing sub-Planck scale structures in the mesoscopic superposition of molecular wave packets, which involves vibrational levels. The time evolution of an initial wave packet, taken here as the SU(2) coherent state (CS) of the Morse potential produces cat-like states. These arise due to the quadratic dependence of the energy on the vibrational quantum number. The superposition of these states is responsible for the above phenomena. We study the spatio-temporal structure of these states, paying special attention to the fractional revival, which gives rise to four coherent states required for the observation of the sub-Planck structure. This structure can be clearly explained through the interference phenomena in phase space. For this, we investigate the phase space dynamics of the coherent state through the Wigner function ap- * e-mail: sanjana@prl.ernet.in † e-mail: Aravind.Chiruvell001@students.umb.edu ‡ e-mail: jay@prl.ernet.in § e-mail: prasanta@prl.ernet.in proach and identify the optimal parameter ranges for a clear observation of these features. Morse potential is well-known to capture the vibrational dynamics of a number of diatomic molecules [6,7,8,9,10]. It is worth mentioning that the phenomena of revival and fractional revival [11,12,13] have been experimentally observed in wave packets involving vibrational levels [14]. Creation of the wave packets and observation of their dynamics are carried out through pump-probe method [15]. The control and analysis of molecular dynamics is achieved through ultrashort femtosecond laser...

We find the existence of sub-Planck scale structures in the Pöschl-Teller potential, which is an exactly solvable potential with both symmetric and asymmetric features. We analyze these structures in both cases by looking at the Wigner distribution of the state evolved from an initial coherent state up to various fractional revival times. We also investigate the sensitivity to perturbations of the Pöschl-Teller potential and we verify that, similar to the harmonic oscillator, the presence of sub-Planck structure in phase space is responsible for a high sensitivity to phase-space displacements.

We study the effect of decoherence on the sub-Planck scale structures of the vibrational wave packet of a molecule. The time evolution of these wave packets is investigated under the influence of a photonic or phononic environment. We determine the master equation describing the reduced dynamics of the wave-packet and analyze the sensitivity of the sub-Planck structures against decoherence in the case of a hydrogen iodide (HI) molecule.

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.