39 research outputs found
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
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, .Comment: Section VI added to v2; published versio
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
-approximation ( 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 -dimensional Fourier transform as in the case
of free expansion
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
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
Analysis of copy number variation in the Abp gene regions of two house mouse subspecies suggests divergence during the gene family expansions
The Androgen-binding protein (Abp) gene region of the mouse genome contains 64 genes, some encoding pheromones that influence assortative mating between mice from different subspecies. Using CNVnator and quantitative PCR, we explored copy number variation in this gene family in natural populations of Mus musculus domesticus (Mmd) and Mus musculus musculus (Mmm), two subspecies of house mice that form a narrow hybrid zone in Central Europe. We found that copy number variation in the center of the Abp gene region is very common in wild Mmd, primarily representing the presence/absence of the final duplications described for the mouse genome. Clustering of Mmd individuals based on this variation did not reflect their geographical origin, suggesting no population divergence in the Abp gene cluster. However, copy number variation patterns differ substantially between Mmd and other mouse taxa. Large blocks of Abp genes are absent in Mmm, Mus musculus castaneus and an outgroup, Mus spretus, although with differences in variation and breakpoint locations. Our analysis calls into question the reliance on a reference genome for interpreting the detailed organization of genes in taxa more distant from the Mmd reference genome. The polymorphic nature of the gene family expansion in all four taxa suggests that the number of Abp genes, especially in the central gene region, is not critical to the survival and reproduction of the mouse. However, Abp haplotypes of variable length may serve as a source of raw genetic material for new signals influencing reproductive communication and thus speciation of mice
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 ( and ) with respect to the dark notch at ; the
correlations oscillate rather than decay as the points and are being
separated.Comment: 9 pages, 8 figure
Atomistic modeling of different loading paths in single crystal copper and aluminum
Utilizing molecular dynamics (MD) integration model we have investigated some of the relevant physical processes caused by different loading paths at the atomic level in Cu and Al monocrystal specimen. Interactions among the atoms in the bulk are modeled with the standard realistic Embedded Atom Method (EAM) potentials. MD simulation gives us the detailed information about non-equilibrium dynamics including crystal structure defects, vacancies and dislocations. In particular, we have obtained result that indicate increase in the total energy of the crystal during loading (especially cyclic) that provides us direct quantitative evidence of the metal weakening. For the basic response, we have deformed copper and aluminum single crystal according to the simple loading path and a series of multiaxial loading-paths including cyclic repetition. We compute equivalent stress-strain diagrams as well as dislocation total length vs time graphs to describe signatures of the anisotropic response of the crystal. 
Combinatorial Level Densities from a Microscopic Relativistic Structure Model
A new model for calculating nuclear level densities is investigated. The
single-nucleon spectra are calculated in a relativistic mean-field model with
energy-dependent effective mass, which yields a realistic density of
single-particle states at the Fermi energy. These microscopic single-nucleon
states are used in a fast combinatorial algorithm for calculating the
non-collective excitations of nuclei. The method, when applied to magic and
semi-magic nuclei, such as Ni, Sn and Pb, reproduces the
cumulative number of experimental states at low excitation energy, as well as
the s-wave neutron resonance spacing at the neutron binding energy.
Experimental level densities above 10 MeV are reproduced by multiplying the
non-collective level densities by a simple vibrational enhancement factor.
Problems to be solved in the extension to open-shell nuclei are discussedComment: 22 pages, 5 figures, revised version, to appear in Nucl. Phys.
Shortcuts to adiabaticity in a time-dependent box
A method is proposed to drive an ultrafast non-adiabatic dynamics of an
ultracold gas trapped in a box potential. The resulting state is free from
spurious excitations associated with the breakdown of adiabaticity, and
preserves the quantum correlations of the initial state up to a scaling factor.
The process relies on the existence of an adiabatic invariant and the inversion
of the dynamical self-similar scaling law dictated by it. Its physical
implementation generally requires the use of an auxiliary expulsive potential
analogous to those used in soliton control. The method is extended to a broad
family of many-body systems. As illustrative examples we consider the ultrafast
expansion of a Tonks-Girardeau gas and of Bose-Einstein condensates in
different dimensions, where the method exhibits an excellent robustness against
different regimes of interactions and the features of an experimentally
realizable box potential.Comment: 6 pp, 4 figures, typo in Eq. (6) fixe