3,049 research outputs found
Quantum Many-Body Dynamics of Dark Solitons in Optical Lattices
We present a fully quantum many-body treatment of dark solitons formed by
ultracold bosonic atoms in one-dimensional optical lattices. Using
time-evolving block decimation to simulate the single-band Bose-Hubbard
Hamiltonian, we consider the quantum dynamics of density and phase engineered
dark solitons as well as the quantum evolution of mean-field dark solitons
injected into the quantum model. The former approach directly models how one
may create quantum entangled dark solitons in experiment. While we have already
presented results regarding the latter approach elsewhere [Phys. Rev. Lett.
{\bf 103}, 140403 (2009)], we expand upon those results in this work. In both
cases, quantum fluctuations cause the dark soliton to fill in and may induce an
inelasticity in soliton-soliton collisions. Comparisons are made to the
Bogoliubov theory which predicts depletion into an anomalous mode that fills in
the soliton. Our many-body treatment allows us to go beyond the Bogoliubov
approximation and calculate explicitly the dynamics of the system's natural
orbitals.Comment: 14 pages, 11 figures -- v3 has only minor changes from v2 -- this is
the print versio
Relating the description of gluon production in pA collisions and parton energy loss in AA collisions
We calculate the classical gluon field of a fast projectile passing through a
dense medium. We show that this allows us to calculate both the initial state
gluon production in proton-nucleus collisions and the final state gluon
radiation off a hard parton produced in nucleus-nucleus collisions. This
unified description of these two phenomena makes the relation between the
saturation scale and the transport coefficient more transparent.
Also, we discuss the validity of the eikonal approximation for gluon
propagation inside the nucleus in proton-nucleus collisions at RHIC energy.Comment: 18 pages, 3 figure
Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential
We consider dynamics of Bose-Einstein condensates with long-range attractive
interaction proportional to and arbitrary angular dependence. It is
shown exactly that collapse of Bose-Einstein condensate without contact
interactions is possible only for . Case is critical and requires
number of particles to exceed critical value to allow collapse. Critical
collapse in that case is strong one trapping into collapsing region a finite
number of particles.
Case is supercritical with expected weak collapse which traps rapidly
decreasing number of particles during approach to collapse. For
singularity at is not strong enough to allow collapse but attractive
interaction admits stable self-trapping even in absence of external
trapping potential
An all-optical event horizon in an optical analogue of a Laval nozzle
Exploiting the fact that light propagation in defocusing nonlinear media can
mimic the transonic flow of an equivalent fluid, we demonstrate experimentally
the formation of an all-optical event horizon in a waveguide structure akin to
a hydrodynamic Laval nozzle. The analogue event horizon, which forms at the
nozzle throat is suggested as a novel platform for analogous gravity
experiments
On integration of some classes of dimensional nonlinear Partial Differential Equations
The paper represents the method for construction of the families of
particular solutions to some new classes of dimensional nonlinear
Partial Differential Equations (PDE). Method is based on the specific link
between algebraic matrix equations and PDE. Admittable solutions depend on
arbitrary functions of variables.Comment: 6 page
Weak Wave Turbulence Scaling Theory for Diffusion and Relative Diffusion in Turbulent Surface Waves
We examine the applicability of the weak wave turbulence theory in explaining
experimental scaling results obtained for the diffusion and relative diffusion
of particles moving on turbulent surface waves. For capillary waves our
theoretical results are shown to be in good agreement with experimental
results, where a distinct crossover in diffusive behavior is observed at the
driving frequency. For gravity waves our results are discussed in the light of
ocean wave studies.Comment: 5 pages; for related work visit http://www.imedea.uib.es/~victo
Cosmology and the Korteweg-de Vries Equation
The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has
played a fundamental role in diverse branches of mathematical and theoretical
physics. In the present paper, we consider its significance to cosmology. It is
found that the KdV equation arises in a number of important scenarios,
including inflationary cosmology, the cyclic universe, loop quantum cosmology
and braneworld models. Analogies can be drawn between cosmic dynamics and the
propagation of the solitonic wave solution to the equation, whereby quantities
such as the speed and amplitude profile of the wave can be identified with
cosmological parameters such as the spectral index of the density perturbation
spectrum and the energy density of the universe. The unique mathematical
properties of the Schwarzian derivative operator are important to the analysis.
A connection with dark solitons in Bose-Einstein condensates is briefly
discussed.Comment: 7 pages; References adde
Collinear Photon Emission from the Quark-Gluon Plasma: The Light-Cone Path Integral Formulation
We give a simple physical derivation of the photon emission rate from the
weakly coupled quark-gluon plasma connected with the collinear processes and . The analysis is based on the light-cone
path integral approach to the induced radiation. Our results agree with that by
Arnold, Moore and Yaffe obtained using the real-time thermal perturbation
theory. It is demonstrated that the solution of the AMY integral equation is
nothing but the time-integrated Green's function of the light-cone path
integral approach written in the momentum representation.Comment: 12 pages, 2 figure
Stability of Bose-Einstein Condensates Confined in Traps
Bose-Einstein condensation has been realized in dilute atomic vapors. This
achievement has generated immerse interest in this field. Presented is a review
of recent theoretical research into the properties of trapped dilute-gas
Bose-Einstein condensates. Among them, stability of Bose-Einstein condensates
confined in traps is mainly discussed. Static properties of the ground state
are investigated by use of the variational method. The anlysis is extended to
the stability of two-component condensates. Time-development of the condensate
is well-described by the Gross-Pitaevskii equation which is known in nonlinear
physics as the nonlinear Schr\"odinger equation. For the case that the
inter-atomic potential is effectively attractive, a singularity of the solution
emerges in a finite time. This phenomenon which we call collapse explains the
upper bound for the number of atoms in such condensates under traps.Comment: 74 pages with 12 figures, submitted to the review section of
International Journal of Modern Physics
Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
Analytic-bilinear approach for construction and study of integrable
hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice
hierarchies are considered. This approach allows to represent generalized
hierarchies of integrable equations in a condensed form of finite functional
equations. Generalized hierarchy incorporates basic hierarchy, modified
hierarchy, singularity manifold equation hierarchy and corresponding linear
problems. Different levels of generalized hierarchy are connected via
invariants of Combescure symmetry transformation. Resolution of functional
equations also leads to the -function and addition formulae to it.Comment: 43 pages, Late
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