Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wavepacket

The dynamics of the momentum distribution and the reduced single-particle density matrix (RSPDM) of a Tonks-Girardeau (TG) gas is studied in the context of Bragg-reflections of a many-body wavepacket. We find strong suppression of a Bragg-reflection peak for a dense TG wavepacket; our observation illustrates dependence of the momentum distribution on the interactions/wavefunction symmetry. The momentum distribution is calculated with a fast algorithm based on a formula expressing the RSPDM via a dynamically evolving single-particle basis

Lieb-Liniger gas in a constant force potential

We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for the Lieb-Liniger model in a linear (constant force) potential (the constructed exact stationary solutions are referred to as the Lieb-Liniger-Airy wave functions). The ground state properties of the gas in the wedge-like trapping potential are calculated in the strongly interacting regime by using Girardeau's Fermi-Bose mapping and the pseudopotential approach in the $1/c$-approximation ($c$ denotes the strength of the interaction). We point out that quantum dynamics of Lieb-Liniger wave packets in the linear potential can be calculated by employing an $N$-dimensional Fourier transform as in the case of free expansion

Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions

The asymptotic form of the wave functions describing a freely expanding Lieb-Liniger gas is derived by using a Fermi-Bose transformation for time-dependent states, and the stationary phase approximation. We find that asymptotically the wave functions approach the Tonks-Girardeau (TG) structure as they vanish when any two of the particle coordinates coincide. We point out that the properties of these asymptotic states can significantly differ from the properties of a TG gas in a ground state of an external potential. The dependence of the asymptotic wave function on the initial state is discussed. The analysis encompasses a large class of initial conditions, including the ground states of a Lieb-Liniger gas in physically realistic external potentials. It is also demonstrated that the interaction energy asymptotically decays as a universal power law with time, $E_\mathrm{int}\propto t^{-3}$.Comment: Section VI added to v2; published versio

Laser assisted tunneling in a Tonks-Girardeau gas

We investigate the applicability of laser assisted tunneling in a strongly interacting one-dimensional Bose gas (the Tonks-Girardeau gas) in optical lattices. We find that the stroboscopic dynamics of the Tonks-Girardeau gas in a continuous Wannier-Stark-ladder potential, supplemented with laser assisted tunneling, effectively realizes the ground state of one-dimensional hard-core bosons in a discrete lattice with nontrivial hopping phases. We compare observables that are affected by the interactions, such as the momentum distribution, natural orbitals and their occupancies, in the time-dependent continuous system, to those of the ground state of the discrete system. Stroboscopically, we find an excellent agreement, indicating that laser assisted tunneling is a viable technique for realizing novel ground states and phases with hard-core one-dimensional Bose gases.Comment: 17 pages, 5 figure

Fermi-Bose transformation for the time-dependent Lieb-Liniger gas

Exact solutions of the Schrodinger equation describing a freely expanding Lieb-Liniger (LL) gas of delta-interacting bosons in one spatial dimension are constructed. The many-body wave function is obtained by transforming a fully antisymmetric (fermionic) time-dependent wave function which obeys the Schrodinger equation for a free gas. This transformation employs a differential Fermi-Bose mapping operator which depends on the strength of the interaction and the number of particles.Comment: 4+ pages, 1 figure; added reference

The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas

We study the reduced single-particle density matrix (RSPDM), the momentum distribution, natural orbitals and their occupancies, of dark "soliton" (DS) states in a Tonks-Girardeau gas. DS states are specially tailored excited many-body eigenstates, which have a dark solitonic notch in their single-particle density. The momentum distribution of DS states has a characteristic shape with two sharp spikes. We find that the two spikes arise due to the high degree of correlation observed within the RSPDM between the mirror points ($x$ and $-x$) with respect to the dark notch at $x=0$; the correlations oscillate rather than decay as the points $x$ and $-x$ are being separated.Comment: 9 pages, 8 figure

Recent Tectonic Activity in the Imotsko Polje Area

Displacements of the Adriatic microplate, particularly of its southern part, are of crucial importance for the understanding of recent tectonic movements. Deformations of the structural fabric and the resulting tectonic activity also encompass the studied area. There are four most active fault zones - Mosor-Biokovo, Zagvozd-Vrgorac-Metkovic, Trilj-Tihaljina-Capljina and Imotski-Medjugorje-Popovo polje. In the explored area, these zones delimit the Imotsko polje. The calculated regional stress is oriented in the range between 10-190° and 350-170°. The relationship between the orientation of structural units and stress enables reverse displacements, most frequently in the direction of the south and south-east. The change in stress orientation in the Mt. Biokovo hinterland makes the aforementioned fault zones surrounding the Imotsko polje favourably oriented in respect to the stress, thus enabling dextral horizontal tectonic transport of the structures in different fault blocks. In the two fault zones - Trilj-Tihaljina-Capljina and Imotski-Medjugorje-Popovo polje, there are 98 outcrops suitable for the structural geology measurements. The obtained data on the local stress orientation and spatial displacement of structures are the most important. The character of faults and the most active fault sections are marked, as well as the local structures that are formed due to strong horizontal component of structural displacement in the studied fault zones. Recent tectonic activity is confirmed by the occurrence of earthquakes. Spatial distribution of the earthquake epicentres depicts zones of seismotectonic activity that are related to the aforementioned most important fault zones. Two of the fault zones - Trilj-Tihaljina-Capljina and Imotski-Medjugorje-Popovo polje are especially well marked by earthquakes occurring at depths of between 3 and 15 km

Purinergic junctional transmission and propagation of calcium waves in cultured spinal cord microglial networks

In order to elucidate the mechanisms of purinergic transmission of calcium (Ca(2 + )) waves between microglial cells, we have employed micro-photolithographic methods to form discrete patterns of microglia that allow quantitative measurements of Ca(2 + ) wave propagation. Microglia were confined to lanes 20–100 [Formula: see text] wide and Ca(2 + ) waves propagated from a point of mechanical stimulation, with a diminution in amplitude, for about 120 [Formula: see text]. The number of cells participating in propagation also decreased over this distance. Ca(2 + ) waves could propagate across a cell-free lane from one microglia lane to another if this distance of separation was less than about 60 [Formula: see text] , indicating that propagation involved diffusion of a chemical transmitter. This transmitter was identified as ATP since all Ca(2 + ) wave propagation was blocked by the purinoceptor antagonist suramin, which blocks P2Y(2) and P2Y(12) at relatively low concentrations. Antibodies to P2Y(12) showed these at very high density compared with P2Y(2), indicating a role for P2Y(12) receptors. These observations were quantitatively accounted for by a model in which the main determinants are the diffusion of ATP released from a stimulated microglial cell and differences in the dissociation constant of the purinoceptors on the microglial cells

Discrete interband mutual focusing in nonlinear photonic lattices

We study nonlinear coupling of mutually incoherent beams associated with different Floquet-Bloch waves in a one-dimensional optically-induced photonic lattice. We demonstrate experimentally how such interactions lead to asymmetric mutual focusing and, for waves with opposite diffraction properties, to simultaneous focusing and defocusing as well as discreteness-induced beam localization and reshaping effects.Comment: 8 pages, 6 figures. To download the associated .avi movie, go to http://www.rsphysse.anu.edu.au/~crr124/mut_focus

Reflection of a Lieb-Liniger wave packet from the hard-wall potential

Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N particles, can be found by solving an $N$-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta.Comment: revised version, improved notation, Fig. 5 adde