A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates

We assume the macroscopic wave function of a Bose-Einstein condensate as a superposition of Gaussian wave packets, with time-dependent complex width parameters, insert it into the mean-field energy functional corresponding to the Gross-Pitaevskii equation (GPE) and apply the time-dependent variational principle. In this way the GPE is mapped onto a system of coupled equations of motion for the complex width parameters, which can be analyzed using the methods of nonlinear dynamics. We perform a stability analysis of the fixed points of the nonlinear system, and demonstrate that the eigenvalues of the Jacobian reproduce the low-lying quantum mechanical Bogoliubov excitation spectrum of a condensate in an axisymmetric trap.Comment: 7 pages, 3 figures, Proceedings of the "8th International Summer School/Conference Let's Face Chaos Through Nonlinear Dynamics", CAMTP, University of Maribor, Slovenia, 26 June - 10 July 201

Relation between the eigenfrequencies of Bogoliubov excitations of Bose-Einstein condensates and the eigenvalues of the Jacobian in a time-dependent variational approach

We study the relation between the eigenfrequencies of the Bogoliubov excitations of Bose-Einstein condensates, and the eigenvalues of the Jacobian stability matrix in a variational approach which maps the Gross-Pitaevskii equation to a system of equations of motion for the variational parameters. We do this for Bose-Einstein condensates with attractive contact interaction in an external trap, and for a simple model of a self-trapped Bose-Einstein condensate with attractive 1/r interaction. The stationary solutions of the Gross-Pitaevskii equation and Bogoliubov excitations are calculated using a finite-difference scheme. The Bogoliubov spectra of the ground and excited state of the self-trapped monopolar condensate exhibits a Rydberg-like structure, which can be explained by means of a quantum defect theory. On the variational side, we treat the problem using an ansatz of time-dependent coupled Gaussians combined with spherical harmonics. We first apply this ansatz to a condensate in an external trap without long-range interaction, and calculate the excitation spectrum with the help of the time-dependent variational principle. Comparing with the full-numerical results, we find a good agreement for the eigenfrequencies of the lowest excitation modes with arbitrary angular momenta. The variational method is then applied to calculate the excitations of the self-trapped monopolar condensates, and the eigenfrequencies of the excitation modes are compared.Comment: 15 pages, 12 figure

Novel properties of the Kohn-Sham exchange potential for open systems: application to the two-dimensional electron gas

The properties of the Kohn-Sham (KS) exchange potential for open systems in thermodynamical equilibrium, where the number of particles is non-conserved, are analyzed with the Optimized Effective Potential (OEP) method of Density Functional Theory (DFT) at zero temperature. The quasi two-dimensional electron gas (2DEG) is used as an illustrative example. The main findings are that the KS exchange potential builds a significant barrier-like structure under slight population of the second subband, and that both the asymptotic value of the KS exchange potential and the inter-subband energy jump discontinuously at the one-subband (1S) -> two-subband (2S) transition. The results obtained in this system offer new insights on open problems of semiconductors, such as the band-gap underestimation and the band-gap renormalization by photo-excited carriers.Comment: 7 pages, 3 figures, uses epl.cls(included), accepted for publication in Europhysics Letter

Interpolated wave functions for nonadiabatic simulations with the fixed-node quantum Monte Carlo method

Simulating nonadiabatic effects with many-body wave function approaches is an open field with many challenges. Recent interest has been driven by new algorithmic developments and improved theoretical understanding of properties unique to electron-ion wave functions. Fixed-node diffusion Monte Caro is one technique that has shown promising results for simulating electron-ion systems. In particular, we focus on the CH molecule for which previous results suggested a relatively significant contribution to the energy from nonadiabatic effects. We propose a new wave function ansatz for diatomic systems which involves interpolating the determinant coefficients calculated from configuration interaction methods. We find this to be an improvement beyond previous wave function forms that have been considered. The calculated nonadiabatic contribution to the energy in the CH molecule is reduced compared to our previous results, but still remains the largest among the molecules under consideration.Comment: 7 pages, 3 figure

Non-adiabatic and time-resolved photoelectron spectroscopy for molecular systems

We quantify the non-adiabatic contributions to the vibronic sidebands of equilibrium and explicitly time-resolved non-equilibrium photoelectron spectra for a vibronic model system of Trans-Polyacetylene. Using exact diagonalization, we directly evaluate the sum-over-states expressions for the linear-response photocurrent. We show that spurious peaks appear in the Born-Oppenheimer approximation for the vibronic spectral function, which are not present in the exact spectral function of the system. The effect can be traced back to the factorized nature of the Born-Oppenheimer initial and final photoemission states and also persists when either only initial, or final states are replaced by correlated vibronic states. Only when correlated initial and final vibronic states are taken into account, the spurious spectral weights of the Born-Oppenheimer approximation are suppressed. In the non-equilibrium case, we illustrate for an initial Franck-Condon excitation and an explicit pump-pulse excitation how the vibronic wavepacket motion of the system can be traced in the time-resolved photoelectron spectra as function of the pump-probe delay

Involvement of Noradrenergic Neurotransmission in the Stress- but not Cocaine-Induced Reinstatement of Extinguished Cocaine-Induced Conditioned Place Preference in Mice: Role for β-2 Adrenergic Receptors

The responsiveness of central noradrenergic systems to stressors and cocaine poses norepinephrine as a potential common mechanism through which drug re-exposure and stressful stimuli promote relapse. This study investigated the role of noradrenergic systems in the reinstatement of extinguished cocaine-induced conditioned place preference by cocaine and stress in male C57BL/6 mice. Cocaine- (15 mg/kg, i.p.) induced conditioned place preference was extinguished by repeated exposure to the apparatus in the absence of drug and reestablished by a cocaine challenge (15 mg/kg), exposure to a stressor (6-min forced swim (FS); 20–25°C water), or administration of the α-2 adrenergic receptor (AR) antagonists yohimbine (2 mg/kg, i.p.) or BRL44408 (5, 10 mg/kg, i.p.). To investigate the role of ARs, mice were administered the nonselective β-AR antagonist, propranolol (5, 10 mg/kg, i.p.), the α-1 AR antagonist, prazosin (1, 2 mg/kg, i.p.), or the α-2 AR agonist, clonidine (0.03, 0.3 mg/kg, i.p.) before reinstatement testing. Clonidine, prazosin, and propranolol failed to block cocaine-induced reinstatement. The low (0.03 mg/kg) but not high (0.3 mg/kg) clonidine dose fully blocked FS-induced reinstatement but not reinstatement by yohimbine. Propranolol, but not prazosin, blocked reinstatement by both yohimbine and FS, suggesting the involvement of β-ARs. The β-2 AR antagonist ICI-118551 (1 mg/kg, i.p.), but not the β-1 AR antagonist betaxolol (10 mg/kg, i.p.), also blocked FS-induced reinstatement. These findings suggest that stress-induced reinstatement requires noradrenergic signaling through β-2 ARs and that cocaine-induced reinstatement does not require AR activation, even though stimulation of central noradrenergic neurotransmission is sufficient to reinstate

Sequential and compartmentalized action of Rabs, SNAREs, and MAL in the apical delivery of fusiform vesicles in urothelial umbrella cells

Uroplakins (UPs) are major differentiation products of urothelial umbrella cells and play important roles in forming the permeability barrier and in the expansion/stabilization of the apical membrane. Further, UPIa serves as a uropathogenic Escherichia coli receptor. Although it is understood that UPs are delivered to the apical membrane via fusiform vesicles (FVs), the mechanisms that regulate this exocytic pathway remain poorly understood. Immunomicroscopy of normal and mutant mouse urothelia show that the UP-delivering FVs contained Rab8/11 and Rab27b/Slac2-a, which mediate apical transport along actin filaments. Subsequently a Rab27b/Slp2-a complex mediated FV–membrane anchorage before SNARE-mediated and MAL-facilitated apical fusion. We also show that keratin 20 (K20), which forms a chicken-wire network ∼200 nm below the apical membrane and has hole sizes allowing FV passage, defines a subapical compartment containing FVs primed and strategically located for fusion. Finally, we show that Rab8/11 and Rab27b function in the same pathway, Rab27b knockout leads to uroplakin and Slp2-a destabilization, and Rab27b works upstream from MAL. These data support a unifying model in which UP cargoes are targeted for apical insertion via sequential interactions with Rabs and their effectors, SNAREs and MAL, and in which K20 plays a key role in regulating vesicular trafficking