440 research outputs found
Spectral function and quasi-particle damping of interacting bosons in two dimensions
We employ the functional renormalization group to study dynamical properties
of the two-dimensional Bose gas. Our approach is free of infrared divergences,
which plague the usual diagrammatic approaches, and is consistent with the
exact Nepomnyashchy identity, which states that the anomalous self-energy
vanishes at zero frequency and momentum. We recover the correct infrared
behavior of the propagators and present explicit results for the spectral
line-shape, from which we extract the quasi-particle dispersion and damping.Comment: 4 pages, 3 figures, revisited version, to appear as Phys. Rev. Lette
Field-induced decay dynamics in square-lattice antiferromagnet
Dynamical properties of the square-lattice Heisenberg antiferromagnet in
applied magnetic field are studied for arbitrary value S of the spin. Above the
threshold field for two-particle decays, the standard spin-wave theory yields
singular corrections to the excitation spectrum with logarithmic divergences
for certain momenta. We develop a self-consistent approximation applicable for
S >= 1, which avoids such singularities and provides regularized magnon decay
rates. Results for the dynamical structure factor obtained in this approach are
presented for S = 1 and S = 5/2.Comment: 12 pages, 11 figures, final versio
Functional renormalization for Bose-Einstein Condensation
We investigate Bose-Einstein condensation for interacting bosons at zero and
nonzero temperature. Functional renormalization provides us with a consistent
method to compute the effect of fluctuations beyond the Bogoliubov
approximation. For three dimensional dilute gases, we find an upper bound on
the scattering length a which is of the order of the microphysical scale -
typically the range of the Van der Waals interaction. In contrast to fermions
near the unitary bound, no strong interactions occur for bosons with
approximately pointlike interactions, thus explaining the high quantitative
reliability of perturbation theory for most quantities. For zero temperature we
compute the quantum phase diagram for bosonic quasiparticles with a general
dispersion relation, corresponding to an inverse microphysical propagator with
terms linear and quadratic in the frequency. We compute the temperature
dependence of the condensate and particle density n, and find for the critical
temperature T_c a deviation from the free theory, Delta T_c/T_c = 2.1 a
n^{1/3}. For the sound velocity at zero temperature we find very good agreement
with the Bogoliubov result, such that it may be used to determine the particle
density accurately.Comment: 21 pages, 16 figures. Reference adde
Collapse and revival of excitations in Bose-Einstein condensates
We study the energies and decay of elementary excitations in weakly
interacting Bose-Einstein condensates within a finite-temperature gapless
second-order theory. The energy shifts for the high-lying collective modes turn
out to be systematically negative compared with the
Hartree-Fock-Bogoliubov-Popov approximation and the decay of the low-lying
modes is found to exhibit collapse and revival effects. In addition,
perturbation theory is used to qualitatively explain the experimentally
observed Beliaev decay process of the scissors mode.Comment: 9 pages, 5 figure
Coherence time of a Bose-Einstein condensate
Temporal coherence is a fundamental property of macroscopic quantum systems,
such as lasers in optics and Bose-Einstein condensates in atomic gases and it
is a crucial issue for interferometry applications with light or matter waves.
Whereas the laser is an "open" quantum system, ultracold atomic gases are
weakly coupled to the environment and may be considered as isolated. The
coherence time of a condensate is then intrinsic to the system and its
derivation is out of the frame of laser theory. Using quantum kinetic theory,
we predict that the interaction with non-condensed modes gradually smears out
the condensate phase, with a variance growing as A t^2+B t+C at long times t,
and we give a quantitative prediction for A, B and C. Whereas the coefficient A
vanishes for vanishing energy fluctuations in the initial state, the
coefficients B and C are remarkably insensitive to these fluctuations. The
coefficient B describes a diffusive motion of the condensate phase that sets
the ultimate limit to the condensate coherence time. We briefly discuss the
possibility to observe the predicted phase spreading, also including the effect
of particle losses.Comment: 17 pages, 8 figures; typos correcte
Optically-Induced Polarons in Bose-Einstein Condensates: Monitoring Composite Quasiparticle Decay
Nonresonant light-scattering off atomic Bose-Einstein condensates (BECs) is
predicted to give rise to hitherto unexplored composite quasiparticles:
unstable polarons, i.e., local ``impurities'' dressed by virtual phonons.
Optical monitoring of their spontaneous decay can display either Zeno or
anti-Zeno deviations from the Golden Rule, and thereby probe the temporal
correlations of elementary excitations in BECs.Comment: 4 pages, 3 figure
Infrared behavior in systems with a broken continuous symmetry: classical O(N) model vs interacting bosons
In systems with a spontaneously broken continuous symmetry, the perturbative
loop expansion is plagued with infrared divergences due to the coupling between
transverse and longitudinal fluctuations. As a result the longitudinal
susceptibility diverges and the self-energy becomes singular at low energy. We
study the crossover from the high-energy Gaussian regime, where perturbation
theory remains valid, to the low-energy Goldstone regime characterized by a
diverging longitudinal susceptibility. We consider both the classical linear
O() model and interacting bosons at zero temperature, using a variety of
techniques: perturbation theory, hydrodynamic approach (i.e., for bosons,
Popov's theory), large- limit and non-perturbative renormalization group. We
emphasize the essential role of the Ginzburg momentum scale below which
the perturbative approach breaks down. Even though the action of
(non-relativistic) bosons includes a first-order time derivative term, we find
remarkable similarities in the weak-coupling limit between the classical O()
model and interacting bosons at zero temperature.Comment: v2) 19 pages, 8 figure
Quantum Fluctuations in Dipolar Bose Gases
We investigate the influence of quantum fluctuations upon dipolar Bose gases
by means of the Bogoliubov-de Gennes theory. Thereby, we make use of the local
density approximation to evaluate the dipolar exchange interaction between the
condensate and the excited particles. This allows to obtain the Bogoliubov
spectrum analytically in the limit of large particle numbers. After discussing
the condensate depletion and the ground-state energy correction, we derive
quantum corrected equations of motion for harmonically trapped dipolar Bose
gases by using superfluid hydrodynamics. These equations are subsequently
applied to analyze the equilibrium configuration, the low-lying oscillation
frequencies, and the time-of-flight dynamics. We find that both atomic magnetic
and molecular electric dipolar systems offer promising scenarios for detecting
beyond mean-field effects.Comment: Published in PR
Commensurate and incommensurate ground states of Cs_2CuCl_4 in a magnetic field
We present calculations of the magnetic ground state of Cs_2CuCl_4 in an
applied magnetic field, with the aim of understanding the commensurately
ordered state that has been discovered in recent experiments. This layered
material is a realization of a Heisenberg antiferromagnet on an anisotropic
triangular lattice. Its behavior in a magnetic field depends on field
orientation, because of weak Dzyaloshinskii-Moriya interactions.We study the
system by mapping the spin-1/2 Heisenberg Hamiltonian onto a Bose gas with hard
core repulsion. This Bose gas is dilute, and calculations are controlled, close
to the saturation field. We find a zero-temperature transition between
incommensurate and commensurate phases as longitudinal field strength is
varied, but only incommensurate order in a transverse field. Results for both
field orientations are consistent with experiment.Comment: 5 Pages, 3 Figure
Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media
We study dynamics emergent from a two-dimensional reaction--diffusion process
modelled via a finite lattice dynamical system, as well as an analogous PDE
system, involving spatially nonlocal interactions. These models govern the
evolution of cells in a bioactive porous medium, with evolution of the local
cell density depending on a coupled quasi--static fluid flow problem. We
demonstrate differences emergent from the choice of a discrete lattice or a
continuum for the spatial domain of such a process. We find long--time
oscillations and steady states in cell density in both lattice and continuum
models, but that the continuum model only exhibits solutions with vertical
symmetry, independent of initial data, whereas the finite lattice admits
asymmetric oscillations and steady states arising from symmetry-breaking
bifurcations. We conjecture that it is the structure of the finite lattice
which allows for more complicated asymmetric dynamics. Our analysis suggests
that the origin of both types of oscillations is a nonlocal reaction-diffusion
mechanism mediated by quasi-static fluid flow.Comment: 30 pages, 21 figure
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