8,158 research outputs found
Non-equilibrium dynamics of the Bose-Hubbard model: A projection operator approach
We study the phase diagram and non-equilibrium dynamics, both subsequent to a
sudden quench of the hopping amplitude and during a ramp
with ramp time , of the Bose-Hubbard model at zero temperature using a
projection operator formalism which allows us to incorporate the effects of
quantum fluctuations beyond mean-field approximations in the strong coupling
regime. Our formalism yields a phase diagram which provides a near exact match
with quantum Monte Carlo results in three dimensions. We also compute the
residual energy , the superfluid order parameter , the equal-time
order parameter correlation function , and the wavefunction overlap
which yields the defect formation probability during non-equilibrium
dynamics of the model. We find that , , and do not exhibit the
expected universal scaling. We explain this absence of universality and show
that our results compare well with recent experiments.Comment: Replaced with the accepted version, added one figure. 4 pages, 4
figures, to appear in Phys. Rev. Let
A projection operator approach to the Bose-Hubbard model
We develop a projection operator formalism for studying both the zero
temperature equilibrium phase diagram and the non-equilibrium dynamics of the
Bose-Hubbard model. Our work, which constitutes an extension of Phys. Rev.
Lett. {\bf 106}, 095702 (2011), shows that the method provides an accurate
description of the equilibrium zero temperature phase diagram of the
Bose-Hubbard model for several lattices in two- and three-dimensions (2D and
3D). We show that the accuracy of this method increases with the coordination
number of the lattice and reaches to within 0.5% of quantum Monte Carlo
data for lattices with . We compute the excitation spectra of the bosons
using this method in the Mott and the superfluid phases and compare our results
with mean-field theory. We also show that the same method may be used to
analyze the non-equilibrium dynamics of the model both in the Mott phase and
near the superfluid-insulator quantum critical point where the hopping
amplitude and the on-site interaction satisfy . In
particular, we study the non-equilibrium dynamics of the model both subsequent
to a sudden quench of the hopping amplitude and during a ramp from to
characterized by a ramp time and exponent : . We compute the wavefunction overlap , the
residual energy , the superfluid order parameter , the equal-time
order parameter correlation function , and the defect formation
probability for the above-mentioned protocols and provide a comparison of
our results to their mean-field counterparts. We find that , , and do
not exhibit the expected universal scaling. We explain this absence of
universality and show that our results for linear ramps compare well with the
recent experimental observations.Comment: v2; new references and new sections adde
Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder
We study the non-equilibrium slow dynamics for the Kitaev model both in the
presence and the absence of disorder. For the case without disorder, we
demonstrate, via an exact solution, that the model provides an example of a
system with an anisotropic critical point and exhibits unusual scaling of
defect density and residual energy for a slow linear quench. We provide
a general expression for the scaling of () generated during a slow
power-law dynamics, characterized by a rate and exponent ,
from a gapped phase to an anisotropic quantum critical point in dimensions,
for which the energy gap for momentum
components () and for the rest components
() with : ().
These general expressions reproduce both the corresponding results for the
Kitaev model as a special case for and and the well-known
scaling laws of and for isotropic critical points for . We also
present an exact computation of all non-zero, independent, multispin
correlation functions of the Kitaev model for such a quench and discuss their
spatial dependence. For the disordered Kitaev model, where the disorder is
introduced via random choice of the link variables in the model's
Fermionic representation, we find that and () for a slow linear quench ending in the gapless
(gapped) phase. We provide a qualitative explanation of such scaling.Comment: 10 pages, 11 Figs. v
Semiclassical Spectrum of Small Bose-Hubbard Chains: A Normal Form Approach
We analyze the spectrum of the 3-site Bose-Hubbard model with periodic
boundary conditions using a semiclassical method. The Bohr-Sommerfeld
quantization is applied to an effective classical Hamiltonian which we derive
using resonance normal form theory. The derivation takes into account the 1:1
resonance between frequencies of a linearized classical system, and brings
nonlinear terms into a corresponding normal form. The obtained expressions
reproduce the exact low-energy spectrum of the system remarkably well even for
a small number of particles N corresponding to fillings of just two particles
per site. Such small fillings are often used in current experiments, and it is
inspiring to get insight into this quantum regime using essentially classical
calculations.Comment: Minor corrections to the coefficients of the effective Hamiltonian in
Eqs 14,15,18,19. Figs 1,2 are slightly modified, correspondingl
Where does the gas fueling star formation in BCGs originate?
We investigate the relationship between X-ray cooling and star formation in
brightest cluster galaxies (BCGs). We present an X-ray spectral analysis of the
inner regions, 10-40 kpc, of six nearby cool core clusters (z<0.35) observed
with Chandra ACIS. This sample is selected on the basis of the high star
formation rate (SFR) observed in the BCGs. We restrict our search for cooling
gas to regions that are roughly cospatial with the starburst. We fit single-
and multi-temperature mkcflow models to constrain the amount of isobarically
cooling intracluster medium (ICM). We find that in all clusters, below a
threshold temperature ranging between 0.9 and 3 keV, only upper limits can be
obtained. In four out of six objects, the upper limits are significantly below
the SFR and in two, namely A1835 and A1068, they are less than a tenth of the
SFR. Our results suggests that a number of mechanisms conspire to hide the
cooling signature in our spectra. In a few systems the lack of a cooling
signature may be attributed to a relatively long delay time between the X-ray
cooling and the star burst. However, for A1835 and A1068, where the X-ray
cooling time is shorter than the timescale of the starburst, a possible
explanation is that the region where gas cools out of the X-ray phase extends
to very large radii, likely beyond the core of these systems.Comment: to appear in A&
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