6,662 research outputs found
Quantum Entanglement in Heisenberg Antiferromagnets
Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is
investigated using the concurrence measure. For a nondegenerate S=0 ground
state, a simple formula relates the concurrence to the diagonal correlation
function. The concurrence length is seen to be extremely short. A few finite
clusters are studied numerically, to see the trend in higher dimensions. It is
argued that nearest-neighbour concurrence is zero for triangular and Kagome
lattices. The concurrences in the maximal-spin states are explicitly
calculated, where the concurrence averaged over all pairs is larger than the
S=0 states.Comment: 7 pages, 3 figure
Optimal query complexity for estimating the trace of a matrix
Given an implicit matrix with oracle access for any
, we study the query complexity of randomized algorithms for
estimating the trace of the matrix. This problem has many applications in
quantum physics, machine learning, and pattern matching. Two metrics are
commonly used for evaluating the estimators: i) variance; ii) a high
probability multiplicative-approximation guarantee. Almost all the known
estimators are of the form for being i.i.d. for some special distribution.
Our main results are summarized as follows. We give an exact characterization
of the minimum variance unbiased estimator in the broad class of linear
nonadaptive estimators (which subsumes all the existing known estimators). We
also consider the query complexity lower bounds for any (possibly nonlinear and
adaptive) estimators: (1) We show that any estimator requires
queries to have a guarantee of variance at most
. (2) We show that any estimator requires
queries to achieve a
-multiplicative approximation guarantee with probability at
least . Both above lower bounds are asymptotically tight.
As a corollary, we also resolve a conjecture in the seminal work of Avron and
Toledo (Journal of the ACM 2011) regarding the sample complexity of the
Gaussian Estimator.Comment: full version of the paper in ICALP 201
Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay
We study, analytically and numerically, the stability of quantum motion for a
classically chaotic system. We show the existence of different regimes of
fidelity decay which deviate from Fermi Golden rule and Lyapunov decay.Comment: 5 pages, 5 figure
Domain Wall Resistance in Perpendicular (Ga,Mn)As: dependence on pinning
We have investigated the domain wall resistance for two types of domain walls
in a (Ga,Mn)As Hall bar with perpendicular magnetization. A sizeable positive
intrinsic DWR is inferred for domain walls that are pinned at an etching step,
which is quite consistent with earlier observations. However, much lower
intrinsic domain wall resistance is obtained when domain walls are formed by
pinning lines in unetched material. This indicates that the spin transport
across a domain wall is strongly influenced by the nature of the pinning.Comment: 9 pages, 3 figure
Short time decay of the Loschmidt echo
The Loschmidt echo measures the sensitivity to perturbations of quantum
evolutions. We study its short time decay in classically chaotic systems. Using
perturbation theory and throwing out all correlation imposed by the initial
state and the perturbation, we show that the characteristic time of this regime
is well described by the inverse of the width of the local density of states.
This result is illustrated and discussed in a numerical study in a
2-dimensional chaotic billiard system perturbed by various contour deformations
and using different types of initial conditions. Moreover, the influence to the
short time decay of sub-Planck structures developed by time evolution is also
investigated.Comment: 7 pages, 7 figures, published versio
Entanglement in spin-1/2 dimerized Heisenberg systems
We study entanglement in dimerized Heisenberg systems. In particular, we give
exact results of ground-state pairwise entanglement for the four-qubit model by
identifying a Z_2 symmetry. Although the entanglements cannot identify the
critical point of the system, the mean entanglement of nearest-neighbor qubits
really does, namely, it reaches a maximum at the critical point.Comment: Four pages, three figures, accepted in Communications in Theoretical
Physic
Double-layer-gate architecture for few-hole GaAs quantum dots
We report the fabrication of single and double hole quantum dots using a double-layer-gate design on an undoped accumulation mode AlxGa1-xAs/GaAs heterostructure. Electrical transport measurements of a single quantum dot show varying addition energies and clear excited states. In addition, the two-level-gate architecture can also be configured into a double quantum dot with tunable inter-dot coupling
An Integrated Physiological Model of the Lung Mechanics and Gas Exchange Using Electrical Impedance Tomography in the Analysis of Ventilation Strategies in ARDS Patients
Mouloud Denai, M. Mahfouf, A. Wang, D. A. Linkens, and G. H. Mills, 'An Integrated Physiological Model of the Lung Mechanics and Gas Exchange Using Electrical Impedance Tomography in the Analysis of Ventilation Strategies in ARDS Patients'. Paper presented at the 3rd International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2010), 20 - 23 January 2010, Valencia, Spain.Peer reviewedFinal Published versio
Large Scale Spectral Clustering Using Approximate Commute Time Embedding
Spectral clustering is a novel clustering method which can detect complex
shapes of data clusters. However, it requires the eigen decomposition of the
graph Laplacian matrix, which is proportion to and thus is not
suitable for large scale systems. Recently, many methods have been proposed to
accelerate the computational time of spectral clustering. These approximate
methods usually involve sampling techniques by which a lot information of the
original data may be lost. In this work, we propose a fast and accurate
spectral clustering approach using an approximate commute time embedding, which
is similar to the spectral embedding. The method does not require using any
sampling technique and computing any eigenvector at all. Instead it uses random
projection and a linear time solver to find the approximate embedding. The
experiments in several synthetic and real datasets show that the proposed
approach has better clustering quality and is faster than the state-of-the-art
approximate spectral clustering methods
Time Evolution of Two-Level Systems Driven by Periodic Fields
In this paper we study the time evolution of a class of two-level systems
driven by periodic fields in terms of new convergent perturbative expansions
for the associated propagator U(t). The main virtue of these expansions is that
they do not contain secular terms, leading to a very convenient method for
quantitatively studying the long-time behaviour of that systems. We present a
complete description of an algorithm to numerically compute the perturbative
expansions. In particular, we applied the algorithm to study the case of an
ac-dc field (monochromatic interaction), exploring various situations and
showing results on (time-dependent) observable quantities, like transition
probabilities. For a simple ac field, we analised particular situations where
an approximate effect of dynamical localisation is exhibited by the driven
system. The accuracy of our calculations was tested measuring the unitarity of
the propagator U(t), resulting in very small deviations, even for very long
times compared to the cycle of the driving field.Comment: 1 table, 5 figures. Version 2 contains minor correction
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