1,450 research outputs found
Semiclassical Phase Reduction Theory for Quantum Synchronization
We develop a general theoretical framework of semiclassical phase reduction
for analyzing synchronization of quantum limit-cycle oscillators. The dynamics
of quantum dissipative systems exhibiting limit-cycle oscillations are reduced
to a simple, one-dimensional classical stochastic differential equation
approximately describing the phase dynamics of the system under the
semiclassical approximation. The density matrix and power spectrum of the
original quantum system can be approximately reconstructed from the reduced
phase equation. The developed framework enables us to analyze synchronization
dynamics of quantum limit-cycle oscillators using the standard methods for
classical limit-cycle oscillators in a quantitative way. As an example, we
analyze synchronization of a quantum van der Pol oscillator under harmonic
driving and squeezing, including the case that the squeezing is strong and the
oscillation is asymmetric. The developed framework provides insights into the
relation between quantum and classical synchronization and will facilitate
systematic analysis and control of quantum nonlinear oscillators.Comment: 20 pages, 5 figure
Finite-Size Scaling for Quantum Criticality above the Upper Critical Dimension: Superfluid-Mott-Insulator Transition in Three Dimensions
Validity of modified finite-size scaling above the upper critical dimension
is demonstrated for the quantum phase transition whose dynamical critical
exponent is . We consider the -component Bose-Hubbard model, which is
exactly solvable and exhibits mean-field type critical phenomena in the
large- limit. The modified finite-size scaling holds exactly in that limit.
However, the usual procedure, taking the large system-size limit with fixed
temperature, does not lead to the expected (and correct) mean-field critical
behavior due to the limited range of applicability of the finite-size scaling
form. By quantum Monte Carlo simulation, it is shown that the same holds in the
case of N=1.Comment: 18 pages, 4 figure
Direct mapping of the finite temperature phase diagram of strongly correlated quantum models
Optical lattice experiments, with the unique potential of tuning interactions
and density, have emerged as emulators of nontrivial theoretical models that
are directly relevant for strongly correlated materials. However, so far the
finite temperature phase diagram has not been mapped out for any strongly
correlated quantum model. We propose a remarkable method for obtaining such a
phase diagram for the first time directly from experiments using only the
density profile in the trap as the input. We illustrate the procedure
explicitly for the Bose Hubbard model, a textbook example of a quantum phase
transition from a superfluid to a Mott insulator. Using "exact" quantum Monte
Carlo simulations in a trap with up to bosons, we show that kinks in the
local compressibility, arising from critical fluctuations, demarcate the
boundaries between superfluid and normal phases in the trap. The temperature of
the bosons in the optical lattice is determined from the density profile at the
edge. Our method can be applied to other phase transitions even when reliable
numerical results are not available.Comment: 12 pages, 5 figure
Reply to Comment on "Quantum Phase Transition of Randomly-Diluted Heisenberg Antiferromagnet on a Square Lattice"
This is a reply to the comment by A. W. Sandvik (cond-mat/0010433) on our
paper Phys. Rev. Lett. 84, 4204 (2000). We show that his data do not conflict
with our data nor with our conclusions.Comment: RevTeX, 1 page; Revised versio
Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results
A strong-coupling expansion for the Green's functions, self-energies and
correlation functions of the Bose Hubbard model is developed. We illustrate the
general formalism, which includes all possible inhomogeneous effects in the
formalism, such as disorder, or a trap potential, as well as effects of thermal
excitations. The expansion is then employed to calculate the momentum
distribution of the bosons in the Mott phase for an infinite homogeneous
periodic system at zero temperature through third-order in the hopping. By
using scaling theory for the critical behavior at zero momentum and at the
critical value of the hopping for the Mott insulator to superfluid transition
along with a generalization of the RPA-like form for the momentum distribution,
we are able to extrapolate the series to infinite order and produce very
accurate quantitative results for the momentum distribution in a simple
functional form for one, two, and three dimensions; the accuracy is better in
higher dimensions and is on the order of a few percent relative error
everywhere except close to the critical value of the hopping divided by the
on-site repulsion. In addition, we find simple phenomenological expressions for
the Mott phase lobes in two and three dimensions which are much more accurate
than the truncated strong-coupling expansions and any other analytic
approximation we are aware of. The strong-coupling expansions and scaling
theory results are benchmarked against numerically exact QMC simulations in two
and three dimensions and against DMRG calculations in one dimension. These
analytic expressions will be useful for quick comparison of experimental
results to theory and in many cases can bypass the need for expensive numerical
simulations.Comment: 48 pages 14 figures RevTe
- …