The momentum distribution (MD) dynamics of a Tonks-Girardeau (TG) gas is studied in the context of Bragg reflections of a many-body wave packet. We find strong suppression of a Bragg reflection peak for a large and dense TG wave packet; our observation illustrates the dependence of the MD on the interactions and wave function symmetry. The MD is calculated from the reduced single-particle density matrix (RSPDM). We develop a method for calculating the RSPDM of a TG gas, which is operative for a large number of particles, and does not depend on the external potential and the state of the system. The method is based on a formula expressing the RSPDM via a dynamically evolving single-particle basis.

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, Eint ∝ t −3 .

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We develop a graphical user interface method, ColorHOR, for fast computational identification of HORs in a given genomic sequence, without requiring a priori information on the composition of the genomic sequence. ColorHOR is based on an extension of the key-string algorithm and provides a color representation of the order and orientation of HORs. For the key string, we use a robust 6 bp string from a consensus alpha satellite and its representative nature is tested. ColorHOR algorithm provides a direct visual identification of HORs (direct and/or reverse complement). In more detail, we first illustrate the ColorHOR results for human chromosome 1. Using ColorHOR we determine for the first time the HOR annotation of the GenBank sequence of the whole human genome. In addition to some HORs, corresponding to those determined previously biochemically, we find new HORs in chromosomes 4, 8, 9, 10, 11 and 19. For the first time, we determine exact consensus lengths of HORs in 10 chromosomes. We propose that the HOR assignment obtained by using ColorHOR be included into the GenBank database.

Exact solutions of the Schrödinger 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 Schrödinger 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.HD-THEP-07-26 Nonequilibrium phenomena in quantum many-body systems are among the most fundamental and intriguing phenomena in physics. One-dimensional (1D) interacting Bose gases provide a unique opportunity to study such phenomena. In some cases, the models describing these systems [1,2,3] allow to determine exact timedependent solutions of the Schrödinger equation [4,5] providing insight beyond various approximations, which is particularly important in strongly correlated regimes. These 1D systems are experimentally realized with atoms tightly confined in effectively 1D waveguides [6,7,8], where nonequilibrium dynamics is considerably affected by the kinematic restrictions of the geometry [8], while quantum effects are enhanced [9,10,11]. Today, experiments have the possibility to explore 1D Bose gases for various interaction strengths, from the Lieb-Liniger (LL) gas with finite coupling [6,8] up to the so-called TonksGirardeau (TG) regime of "impenetrable-core" bosons [7,8]. However, most theoretical studies of the exact time-dependence address the TG regime (see, e.g., Refs. [4,12,13,14,15,16,17,18]). In this limit, the complex many-body problem is considerably simplified due to the Fermi-Bose mapping property [4] where dynamics follows a set of uncoupled single-particle (SP) Schrödinger equations [4]. It is therefore desirable to employ an efficient method for calculating the time-evolution of a LL gas with finite interaction strength.In 1963, Lieb and Liniger [1] presented, on the basis of the Bethe ansatz, a solution for a homogeneous Bose gas with (repulsive) δ-function interactions, for arbitrary interaction strength c; periodic boundary conditions were imposed. This system was analyzed by McGuire on an infinite line with attractive interactions [3]. The renewed interest in 1D Bose gases stimulated recent studies of static LL wave functions [19,20,21] including a LL gas in box confinement [21]. Besides the wave functions, the correlations of a LL system with finite coupling [22,23,24,25,26,27,28,29,30,31] provide a link to many observables and were analyzed by using various techniques, including the inverse scattering method [24,25,30,31]

We propose a scheme for observing dark stationary waves in a Tonks-Girardeau (TG) gas. The scheme is based on parity-selective dynamical "evaporation" of the gas via a time-dependent potential, which excites the gas from its ground state towards a desired specially-tailored many-body state. These excitations of the TG gas are analogous to linear partially coherent nondiffracting beams in optics, as evident from the mapping between the quantum dynamics of the TG gas and the propagation of incoherent light in one-dimensional linear photonic structures. Trapped bose gases confined to one-dimensional (1D) geometry are highly attractive for studying quantum many-body dynamics because pertinent models yield exact solutions [1,2,3,4], these regimes are experimentally accessible [5,6,7,8], and quantum effects are enhanced [9,10,11]. Tonks-Girardeau (TG) gas is a system of 1D bosons with "impenetrable core" repulsive interactions [1]. In the fashion of the Pauli exclusion principle, "impenetrable cores" prevent bosons to occupy the same position in space, which causes TG gas to exhibit fermionic properties. This similarity is manifested in the mapping between 1D noninteracting fermions and TG bosons [1,4]. From the properties of atomic interactions in tight atomic waveguides [9] it follows that the TG regime can be reached at low temperatures, low linear densities or stronger effective interactions [9,10,11]. The experimental realizations of the TG gas in 2004 [6,7] boosted the physical relevance of the model. A recent experiment has demonstrated that such gas does not relax to the thermodynamic equilibrium even after numerous collisions [8], due to the integrability of the underlying model. This work inspired a theoretical study of 1D "impenetrable core" bosons on a lattice, which suggested that the system can undergo irreversible relaxation to a steady state carrying more memory of the initial conditions than the usual thermodynamic equilibrium [12]. Some aspects of the TG quantum dynamics have been studied theoretically within the context of so-called "dark solitons" [4,13], matter-wave interference [14], 1D expansion [15,16], irregular dynamics [17], and coherent states [18]. In this work, we study the dynamical tailoring of the TG gas via a time-dependent potential to produce dark stationary states, as well as point out the relation between TG dynamics and the propagation of incoherent light in linear photonic structures.The Fermi-Bose mapping [1,4], applicable both in the static [1] and time-dependent case [4], prescribes the construction of the exact many-body wavefunction of the TG gas from single-particle (SP) wavefunctions, which obey a set of uncoupled linear SP Schrödinger equations. In Ref.[4] Girardeau and Wright discuss the dynamics of the TG gas within the context of dark solitons [19,20,21,22]. Dark solitons are fundamental nonlinear excitations, which have been studied theoretically within the nonlinear mean-field theories applicable for weakly interacting gases [19,21,22], and observed experimentally i...

We predict the existence of lattice solitons made of incoherent white light: lattice solitons made of light originating from an ordinary incandescent light bulb. We find that the intensity structure and spatial power spectra associated with different temporal frequency constituents of incoherent white-light lattice solitons (IWLLSs) arrange themselves in a characteristic fashion, with the intensity structure more localized at higher frequencies, and the spatial power spectrum more localized at lower frequencies; the spatial correlation distance is larger at lower frequency constituents of IWLLSs. This characteristic shape of incoherent white-light lattice solitons reflects the fact that diffraction is stronger for lower temporal frequency constituents, while higher frequencies experience stronger effective nonlinearity and deeper lattice structure.

We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one-and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. We compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.