15,216 research outputs found

### Strong Phases in the Decays B to D Pi

The observed strong phase difference of 30^{o} between I=(3/2) and I=(1/2)
final states for the decay B to D Pi is analyzed in terms of rescattering like
D^{∗}Pi to D Pi, etc. It is concluded that for the decay B^{o}to D^{+}
Pi^{-} the strong phase is only about 10^{o}. Implications for the
determination of sin(2 Beta + gamma) are discussed.Comment: 4 pages (includes 1 reference page

### Internal Oscillations of a Dark-Bright Soliton in a Harmonic Potential

We investigate the dynamics of a dark-bright soliton in a harmonic potential
using a mean-field approach via coupled nonlinear Schr\"odinger equations
appropriate to multicomponent Bose-Einstein condensates. We use a modified
perturbed dynamical variational Lagrangian approximation, where the
perturbation is due to the trap, taken as a Thomas-Fermi profile. The
wavefunction ansatz is taken as the correct hyperbolic tangent and secant
solutions in the scalar case for the dark and bright components of the soliton,
respectively. We also solve the problem numerically with psuedo-spectral
Runge-Kutta methods. We find, analytically and numerically, for weak trapping
the internal modes are nearly independent of center of mass motion of the
dark-bright soliton. In contrast, in tighter traps the internal modes couple
strongly to the center of mass motion, showing that for dark-bright solitons in
a harmonic potential the center of mass and relative degrees of freedom are not
independent. This result is robust against noise in the initial condition and
should, therefore, be experimentally observable.Comment: 12 pages, 11 figure

### Scattering of a dark-bright soliton by an impurity

We study the dynamics of a dark-bright soliton interacting with a fixed
impurity using a mean-field approach. The system is described by a vector
nonlinear Schrodinger equation (NLSE) appropriate to multicomponent
Bose-Einstein condensates. We use the variational approximation, based on
hyperbolic functions, where we have the center of mass of the two components to
describe the propagation of the dark and bright components independently.
Therefore, it allows the dark-bright soliton to oscillate. The fixed local
impurity is modeled by a delta function. Also, we use perturbation methods to
derive the equations of motion for the center of mass of the two components.
The interaction of the dark-bright soliton with a delta function potential
excites different modes in the system. The analytical model capture two of
these modes: the relative oscillation between the two components and the
oscillation in the widths. The numerical simulations show additional internal
modes play an important role in the interaction problem. The excitation of
internal modes corresponds to inelastic scattering. In addition, we calculate
the maximum velocity for a dark-bright soliton and find it is limited to a
value below the sound speed, depending on the relative number of atoms present
in the bright soliton component and excavated by the dark soliton component,
respectively. Above a critical value of the maximum velocity, the two
components are no longer described by one center of mass variable and develop
internal oscillations, eventually breaking apart when pushed to higher
velocities. This effect limits the incident kinetic energy in scattering
studies and presents a smoking gun experimental signal.Comment: 10 pages, 10 figure

### Dynamics of Vector Solitons in Bose-Einstein Condensates

We analyze the dynamics of two-component vector solitons, namely
bright-in-dark solitons, via the variational approximation in Bose-Einstein
condensates. The system is described by a vector nonlinear Schr\"odinger
equation appropriate to multi-component Bose-Einstein condensates (BECs). The
variational approximation is based on hyperbolic secant (hyperbolic tangent)
for the bright (dark) component, which leads to a system of coupled ordinary
differential equations for the evolution of the ansatz parameters. We obtain
the oscillation dynamics of two-component dark-bright vector solitons.
Analytical calculations are performed for same-width components in the vector
soliton and numerical calculations extend the results to arbitrary widths. We
calculate the binding energy of the system and find it proportional to the
intercomponent coupling interaction, and numerically demonstrate the break up
or unbinding of a dark-bright soliton. Our calculations explore observable
eigenmodes, namely the internal oscillation eigenmode and the Goldstone
eigenmode. We find analytically that the density of the bright component is
required to be less than the density of the dark component in order to find the
internal oscillation eigenmode of the vector soliton and support the existence
of the dark-bright soliton. This outcome is confirmed by numerical results.
Numerically, we find that the oscillation frequency is amplitude independent.
For dark-bright vector solitons in $^{87}$Rb we find that the oscillation
frequency range is 90 to 405 Hz, and therefore observable in multi-component
BEC experiments.Comment: 11 pages, 9 figures, 1 table, 1 appendi

### Non-Hamiltonian Kelvin wave generation on vortices in Bose-Einstein condensates

Ultra-cold quantum turbulence is expected to decay through a cascade of
Kelvin waves. These helical excitations couple vorticity to the quantum fluid
causing long wavelength phonon fluctuations in a Bose-Einstein condensate. This
interaction is hypothesized to be the route to relaxation for turbulent tangles
in quantum hydrodynamics. The local induction approximation is the lowest order
approximation to the Biot-Savart velocity field induced by a vortex line and,
because of its integrability, is thought to prohibit energy transfer by Kelvin
waves. Using the Biot-Savart description, we derive a generalization to the
local induction approximation which predicts that regions of large curvature
can reconfigure themselves as Kelvin wave packets. While this generalization
preserves the arclength metric, a quantity conserved under the Eulerian flow of
vortex lines, it also introduces a non-Hamiltonian structure on the geometric
properties of the vortex line. It is this non-Hamiltonian evolution of
curvature and torsion which provides a resolution to the missing Kelvin wave
motion. In this work, we derive corrections to the local induction
approximation in powers of curvature and state them for utilization in vortex
filament methods. Using the Hasimoto transformation, we arrive at a nonlinear
integro-differential equation which reduces to a modified nonlinear
Schr\"odinger type evolution of the curvature and torsion on the vortex line.
We show that this modification seeks to disperse localized curvature profiles.
At the same time, the non-Hamiltonian break in integrability bolsters the
deforming curvature profile and simulations show that this dynamic results in
Kelvin wave propagation along the dispersive vortex medium.Comment: 22 pages, 7 figure

### Finite Temperature Matrix Product State Algorithms and Applications

We review the basic theory of matrix product states (MPS) as a numerical
variational ansatz for time evolution, and present two methods to simulate
finite temperature systems with MPS: the ancilla method and the minimally
entangled typical thermal state method. A sample calculation with the
Bose-Hubbard model is provided.Comment: 13 pages, 4 figure

### The nonlinear Dirac equation in Bose-Einstein condensates: Vortex solutions and spectra in a weak harmonic trap

We analyze the vortex solution space of the $(2 +1)$-dimensional nonlinear
Dirac equation for bosons in a honeycomb optical lattice at length scales much
larger than the lattice spacing. Dirac point relativistic covariance combined
with s-wave scattering for bosons leads to a large number of vortex solutions
characterized by different functional forms for the internal spin and overall
phase of the order parameter. We present a detailed derivation of these
solutions which include skyrmions, half-quantum vortices, Mermin-Ho and
Anderson-Toulouse vortices for vortex winding $\ell = 1$. For $\ell \ge 2$ we
obtain topological as well as non-topological solutions defined by the
asymptotic radial dependence. For arbitrary values of $\ell$ the
non-topological solutions are bright ring-vortices which explicitly demonstrate
the confining effects of the Dirac operator. We arrive at solutions through an
asymptotic Bessel series, algebraic closed-forms, and using standard numerical
shooting methods. By including a harmonic potential to simulate a finite trap
we compute the discrete spectra associated with radially quantized modes. We
demonstrate the continuous spectral mapping between the vortex and free
particle limits for all of our solutions.Comment: 37 pages, 15 figure

### Spatial Dependence of Entropy in Trapped Ultracold Bose Gases

We find a new physical regime in the trapped Bose-Hubbard Hamiltonian using
time-evolving block decimation. Between Mott-insulating and superfluid phases,
the latter induced by trap compression, a spatially self-organized state
appears in which non-local entropy signals entanglement between spatially
distant superfluid shells. We suggest a linear rather than harmonic potential
as an ideal way to observe such a self-organized system. We also explore both
quantum information and thermal entropies in the superfluid regime, finding
that while the former follows the density closely the latter can be strongly
manipulated with the mean field.Comment: 5 pages, 4 figure

### The nonlinear Dirac equation in Bose-Einstein condensates: Superfluid fluctuations and emergent theories from relativistic linear stability equations

We present the theoretical and mathematical foundations of stability analysis
for a Bose-Einstein condensate (BEC) at Dirac points of a honeycomb optical
lattice. The combination of s-wave scattering for bosons and lattice
interaction places constraints on the mean-field description, and hence on
vortex configurations in the Bloch-envelope function near the Dirac point. A
full derivation of the relativistic linear stability equations (RLSE) is
presented by two independent methods to ensure veracity of our results.
Solutions of the RLSE are used to compute fluctuations and lifetimes of vortex
solutions of the nonlinear Dirac equation, which include Mermin-Ho and
Anderson-Toulouse skyrmions, with lifetime $\approx 4$ seconds. Beyond vortex
stabilities the RLSE provide insight into the character of collective
superfluid excitations, which we find to encode several established theories of
physics. In particular, the RLSE reduce to the Andreev equations, in the
nonrelativistic and semiclassical limits, the Majorana equation, inside vortex
cores, and the Dirac-Bogoliubov-de Gennes equations, when nearest-neighbor
interactions are included. Furthermore, by tuning a mass gap, relative
strengths of various spinor couplings, for the small and large quasiparticle
momentum regimes, we obtain weak-strong Bardeen-Cooper-Schrieffer
superconductivity, as well as fundamental wave equations such as Schr\"odinger,
Dirac, Klein-Gordon, and Bogoliubov-de Gennes equations. Our results apply
equally to a strongly spin-orbit coupled BEC in which the Laplacian
contribution can be neglected.Comment: 43 pages, 10 figure

### Non-Hamiltonian Dynamics of Quantized Vortices in Bose-Einstein Condensates

The dynamics of quantized vortices in weakly interacting superfluids are
often modeled by a nonlinear Schr\"odinger equation. In contrast, we show that
quantized vortices in fact obey a non-Hamiltonian evolution equation, which
enhances dispersion along the vortex line while introducing a gain mechanism.
This allows the vortex medium to support a helical shock front propagating
ahead of a dissipative soliton. This dynamic relaxes localized curvature events
into Kelvin wave packets. Consequently, a beyond local induction model provides
a pathway for decay in low-temperature quantum turbulence.Comment: 6 pages, 4 figure

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