3,494 research outputs found
Robustness of adiabatic passage trough a quantum phase transition
We analyze the crossing of a quantum critical point based on exact results
for the transverse XY model. In dependence of the change rate of the driving
field, the evolution of the ground state is studied while the transverse
magnetic field is tuned through the critical point with a linear ramping. The
excitation probability is obtained exactly and is compared to previous studies
and to the Landau-Zener formula, a long time solution for non-adiabatic
transitions in two-level systems. The exact time dependence of the excitations
density in the system allows to identify the adiabatic and diabatic regions
during the sweep and to study the mesoscopic fluctuations of the excitations.
The effect of white noise is investigated, where the critical point transmutes
into a non-hermitian ``degenerate region''. Besides an overall increase of the
excitations during and at the end of the sweep, the most destructive effect of
the noise is the decay of the state purity that is enhanced by the passage
through the degenerate region.Comment: 16 pages, 15 figure
Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme
Here we present well-posedness results for first order stochastic
differential inclusions, more precisely for sweeping process with a stochastic
perturbation. These results are provided in combining both deterministic
sweeping process theory and methods concerning the reflection of a Brownian
motion. In addition, we prove convergence results for a Euler scheme,
discretizing theses stochastic differential inclusions.Comment: 30 page
Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group
A useful concept for finding numerically the dominant correlations of a given
ground state in an interacting quantum lattice system in an unbiased way is the
correlation density matrix. For two disjoint, separated clusters, it is defined
to be the density matrix of their union minus the direct product of their
individual density matrices and contains all correlations between the two
clusters. We show how to extract from the correlation density matrix a general
overview of the correlations as well as detailed information on the operators
carrying long-range correlations and the spatial dependence of their
correlation functions. To determine the correlation density matrix, we
calculate the ground state for a class of spinless extended Hubbard models
using the density matrix renormalization group. This numerical method is based
on matrix product states for which the correlation density matrix can be
obtained straightforwardly. In an appendix, we give a detailed tutorial
introduction to our variational matrix product state approach for ground state
calculations for 1- dimensional quantum chain models. We show in detail how
matrix product states overcome the problem of large Hilbert space dimensions in
these models and describe all techniques which are needed for handling them in
practice.Comment: 50 pages, 34 figures, to be published in New Journal of Physic
Density Matrix Renormalization Group study on incommensurate quantum Frenkel-Kontorova model
By using the density matrix renormalization group (DMRG) technique, the
incommensurate quantum Frenkel-Kontorova model is investigated numerically. It
is found that when the quantum fluctuation is strong enough, the
\emph{g}-function featured by a saw-tooth map in the depinned state will show a
different kind of behavior, similar to a standard map, but with reduced
magnitude. The related position correlations are studied in details, which
leads to a potentially interesting application to the recently well-explored
phase transitions in cold atoms loaded in optical lattices.Comment: 11 figures, submitted to Phys. Rev.
Quantum computing with a single molecular ensemble and a Cooper pair box
We propose to encode quantum information in rotational excitations in a
molecular ensemble. Using a stripline cavity field for quantum state transfer
between the molecular ensemble and a Cooper pair box two-level system, our
proposal offers a linear scaling of the number of qubits in our register with
the number of rotationally excited states available in the molecules.Comment: 4 pages, 3 figures Minor corrections from reviewing proces
A discrete contact model for crowd motion
The aim of this paper is to develop a crowd motion model designed to handle
highly packed situations. The model we propose rests on two principles: We
first define a spontaneous velocity which corresponds to the velocity each
individual would like to have in the absence of other people; The actual
velocity is then computed as the projection of the spontaneous velocity onto
the set of admissible velocities (i.e. velocities which do not violate the
non-overlapping constraint). We describe here the underlying mathematical
framework, and we explain how recent results by J.F. Edmond and L. Thibault on
the sweeping process by uniformly prox-regular sets can be adapted to handle
this situation in terms of well-posedness. We propose a numerical scheme for
this contact dynamics model, based on a prediction-correction algorithm.
Numerical illustrations are finally presented and discussed.Comment: 22 page
A variational method based on weighted graph states
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a
class of states which is suitable as a variational set to find ground states in
spin systems of arbitrary spatial dimension and with long-range entanglement.
Here, we continue the exposition of our technique, extend from spin 1/2 to
higher spins and use the boson Hubbard model as a non-trivial example to
demonstrate our scheme.Comment: 36 pages, 13 figure
Transport of interface states in the Heisenberg chain
We demonstrate the transport of interface states in the one-dimensional
ferromagnetic Heisenberg model by a time dependent magnetic field. Our analysis
is based on the standard Adiabatic Theorem. This is supplemented by a numerical
analysis via the recently developed time dependent DMRG method, where we
calculate the adiabatic constant as a function of the strength of the magnetic
field and the anisotropy of the interaction.Comment: minor revision, final version; 13 pages, 4 figure
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