51,388 research outputs found
Competing Orders in a Dipolar Bose-Fermi Mixture on a Square Optical Lattice: Mean-Field Perspective
We consider a mixture of a two-component Fermi gas and a single-component
dipolar Bose gas in a square optical lattice and reduce it into an effective
Fermi system where the Fermi-Fermi interaction includes the attractive
interaction induced by the phonons of a uniform dipolar Bose-Einstein
condensate. Focusing on this effective Fermi system in the parameter regime
that preserves the symmetry of , the point group of a square, we explore,
within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition
among density wave orderings and superfluid pairings. We construct the matrix
representation of the linearized gap equation in the irreducible
representations of . We show that in the weak coupling regime, each matrix
element, which is a four-dimensional (4D) integral in momentum space, can be
put in a separable form involving a 1D integral, which is only a function of
temperature and the chemical potential, and a pairing-specific "effective"
interaction, which is an analytical function of the parameters that
characterize the Fermi-Fermi interactions in our system. We analyze the
critical temperatures of various competing orders as functions of different
system parameters in both the absence and presence of the dipolar interaction.
We find that close to half filling, the d_{x^{2}-y^{2}}-wave pairing with a
critical temperature in the order of a fraction of Fermi energy (at half
filling) may dominate all other phases, and at a higher filling factor, the
p-wave pairing with a critical temperature in the order of a hundredth of Fermi
energy may emerge as a winner. We find that tuning a dipolar interaction can
dramatically enhance the pairings with - and g-wave symmetries but not
enough for them to dominate other competing phases.Comment: 18 pages, 9 figure
Provable Deterministic Leverage Score Sampling
We explain theoretically a curious empirical phenomenon: "Approximating a
matrix by deterministically selecting a subset of its columns with the
corresponding largest leverage scores results in a good low-rank matrix
surrogate". To obtain provable guarantees, previous work requires randomized
sampling of the columns with probabilities proportional to their leverage
scores.
In this work, we provide a novel theoretical analysis of deterministic
leverage score sampling. We show that such deterministic sampling can be
provably as accurate as its randomized counterparts, if the leverage scores
follow a moderately steep power-law decay. We support this power-law assumption
by providing empirical evidence that such decay laws are abundant in real-world
data sets. We then demonstrate empirically the performance of deterministic
leverage score sampling, which many times matches or outperforms the
state-of-the-art techniques.Comment: 20th ACM SIGKDD Conference on Knowledge Discovery and Data Minin
Spontaneous phase oscillation induced by inertia and time delay
We consider a system of coupled oscillators with finite inertia and
time-delayed interaction, and investigate the interplay between inertia and
delay both analytically and numerically. The phase velocity of the system is
examined; revealed in numerical simulations is emergence of spontaneous phase
oscillation without external driving, which turns out to be in good agreement
with analytical results derived in the strong-coupling limit. Such
self-oscillation is found to suppress synchronization and its frequency is
observed to decrease with inertia and delay. We obtain the phase diagram, which
displays oscillatory and stationary phases in the appropriate regions of the
parameters.Comment: 5 pages, 6 figures, to pe published in PR
model with Hopf term and fractional spin statistics
We reconsider the model with the Hopf term by using the
Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of the Dirac
quantization method. We also perform a semi-classical quantization of the
topological charge Q sector by exploiting the collective coordinates to
explicitly show the fractional spin statistics.Comment: 15 page
Collective phase synchronization in locally-coupled limit-cycle oscillators
We study collective behavior of locally-coupled limit-cycle oscillators with
scattered intrinsic frequencies on -dimensional lattices. A linear analysis
shows that the system should be always desynchronized up to . On the other
hand, numerical investigation for and 6 reveals the emergence of the
synchronized (ordered) phase via a continuous transition from the fully random
desynchronized phase. This demonstrates that the lower critical dimension for
the phase synchronization in this system is $d_{l}=4
Topological current of point defects and its bifurcation
From the topological properties of a three dimensional vector order
parameter, the topological current of point defects is obtained. One shows that
the charge of point defects is determined by Hopf indices and Brouwer degrees.
The evolution of point defects is also studied. One concludes that there exist
crucial cases of branch processes in the evolution of point defects when the
Jacobian .Comment: revtex,14 pages,no figur
Symmetries of SU(2) Skyrmion in Hamiltonian and Lagrangian approaches
We apply the Batalin-Fradkin-Tyutin (BFT) method to the SU(2) Skyrmion to
study the full symmetry structure of the model at the first class Hamiltonian
level. On the other hand, we also analyze the symmetry structure of the action
having the WZ term, which corresponds to this Hamiltonian, in the framework of
the Lagrangian approach. Furthermore, following the BFV formalism we derive the
BRST invariant gauge fixed Lagrangian from the above extended action.Comment: 14 pages, final revised version, to appear in Mod. Phys. Lett.
Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation
As a continuum work of Bhaumik et al who derived the common eigenvector of
the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9
(1976) 1507) we search for the simultaneous eigenvector of Q and
(ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite
entangled state representation. The differential equation is then solved in
terms of the two-variable Hermite polynomials and the formal hypergeometric
functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by
Fan and Klauder, in which the common eigenkets of Q and pair creators are
discussed
Anisotropic Cosmological Models with Energy Density Dependent Bulk Viscosity
An analysis is presented of the Bianchi type I cosmological models with a
bulk viscosity when the universe is filled with the stiff fluid
while the viscosity is a power function of the energy density, such as . Although the exact solutions are obtainable only when the
is an integer, the characteristics of evolution can be clarified for the
models with arbitrary value of . It is shown that, except for the
model that has solutions with infinite energy density at initial state, the
anisotropic solutions that evolve to positive Hubble functions in the later
stage will begin with Kasner-type curvature singularity and zero energy density
at finite past for the models, and with finite Hubble functions and
finite negative energy density at infinite past for the models. In the
course of evolution, matters are created and the anisotropies of the universe
are smoothed out. At the final stage, cosmologies are driven to infinite
expansion state, de Sitter space-time, or Friedman universe asymptotically.
However, the de Sitter space-time is the only attractor state for the
models. The solutions that are free of cosmological singularity for any finite
proper time are singled out. The extension to the higher-dimensional models is
also discussed
Exact solution of gyration radius of individual's trajectory for a simplified human mobility model
Gyration radius of individual's trajectory plays a key role in quantifying
human mobility patterns. Of particular interests, empirical analyses suggest
that the growth of gyration radius is slow versus time except the very early
stage and may eventually arrive to a steady value. However, up to now, the
underlying mechanism leading to such a possibly steady value has not been well
understood. In this Letter, we propose a simplified human mobility model to
simulate individual's daily travel with three sequential activities: commuting
to workplace, going to do leisure activities and returning home. With the
assumption that individual has constant travel speed and inferior limit of time
at home and work, we prove that the daily moving area of an individual is an
ellipse, and finally get an exact solution of the gyration radius. The
analytical solution well captures the empirical observation reported in [M. C.
Gonz`alez et al., Nature, 453 (2008) 779]. We also find that, in spite of the
heterogeneous displacement distribution in the population level, individuals in
our model have characteristic displacements, indicating a completely different
mechanism to the one proposed by Song et al. [Nat. Phys. 6 (2010) 818].Comment: 4 pages, 4 figure
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