466 research outputs found
Model for monitoring of a charge qubit using a radio-frequency quantum point contact including experimental imperfections
The extension of quantum trajectory theory to incorporate realistic
imperfections in the measurement of solid-state qubits is important for quantum
computation, particularly for the purposes of state preparation and
error-correction as well as for readout of computations. Previously this has
been achieved for low-frequency (dc) weak measurements. In this paper we extend
realistic quantum trajectory theory to include radio frequency (rf) weak
measurements where a low-transparency quantum point contact (QPC), coupled to a
charge qubit, is used to damp a classical oscillator circuit. The resulting
realistic quantum trajectory equation must be solved numerically. We present an
analytical result for the limit of large dissipation within the oscillator
(relative to the QPC), where the oscillator slaves to the qubit. The rf+dc mode
of operation is considered. Here the QPC is biased (dc) as well as subjected to
a small-amplitude sinusoidal carrier signal (rf). The rf+dc QPC is shown to be
a low-efficiency charge-qubit detector, that may nevertheless be higher than
the dc-QPC (which is subject to 1/f noise).Comment: 12 pages, 2 colour figures. v3 is published version (minor changes
since v2
A counterexample to well-posedness of entropy solutions to the compressible Euler system
We deal with entropy solutions to the Cauchy problem for the isentropic
compressible Euler equations in the space-periodic case. In more than one space
dimension, the methods developed by De Lellis-Sz\'ekelyhidi enable us to show
failure of uniqueness on a finite time-interval for entropy solutions starting
from any continuously differentiable initial density and suitably constructed
bounded initial linear momenta.Comment: 29 page
Thermodynamically Stable One-Component Metallic Quasicrystals
Classical density-functional theory is employed to study finite-temperature
trends in the relative stabilities of one-component quasicrystals interacting
via effective metallic pair potentials derived from pseudopotential theory.
Comparing the free energies of several periodic crystals and rational
approximant models of quasicrystals over a range of pseudopotential parameters,
thermodynamically stable quasicrystals are predicted for parameters approaching
the limits of mechanical stability of the crystalline structures. The results
support and significantly extend conclusions of previous ground-state
lattice-sum studies.Comment: REVTeX, 13 pages + 2 figures, to appear, Europhys. Let
Scanning Quantum Decoherence Microscopy
The use of qubits as sensitive magnetometers has been studied theoretically
and recent demonstrated experimentally. In this paper we propose a
generalisation of this concept, where a scanning two-state quantum system is
used to probe the subtle effects of decoherence (as well as its surrounding
electromagnetic environment). Mapping both the Hamiltonian and decoherence
properties of a qubit simultaneously, provides a unique image of the magnetic
(or electric) field properties at the nanoscale. The resulting images are
sensitive to the temporal as well as spatial variation in the fields created by
the sample. As an example we theoretically study two applications of this
technology; one from condensed matter physics, the other biophysics. The
individual components required to realise the simplest version of this device
(characterisation and measurement of qubits, nanoscale positioning) have
already been demonstrated experimentally.Comment: 11 pages, 5 low quality (but arXiv friendly) image
Dual-probe decoherence microscopy: Probing pockets of coherence in a decohering environment
We study the use of a pair of qubits as a decoherence probe of a non-trivial
environment. This dual-probe configuration is modelled by three
two-level-systems which are coupled in a chain in which the middle system
represents an environmental two-level-system (TLS). This TLS resides within the
environment of the qubits and therefore its coupling to perturbing fluctuations
(i.e. its decoherence) is assumed much stronger than the decoherence acting on
the probe qubits. We study the evolution of such a tripartite system including
the appearance of a decoherence-free state (dark state) and non-Markovian
behaviour. We find that all parameters of this TLS can be obtained from
measurements of one of the probe qubits. Furthermore we show the advantages of
two qubits in probing environments and the new dynamics imposed by a TLS which
couples to two qubits at once.Comment: 29 pages, 10 figure
Displacement field and elastic constants in non-ideal crystals
In this work a periodic crystal with point defects is described in the
framework of linear response theory for broken symmetry states using
correlation functions and Zwanzig-Mori equations. The main results are
microscopic expressions for the elastic constants and for the coarse-grained
density, point-defect density, and displacement field, which are valid in real
crystals, where vacancies and interstitials are present. The coarse-grained
density field differs from the small wave vector limit of the microscopic
density. In the long wavelength limit, we recover the phenomenological
description of elasticity theory including the defect density.Comment: Phys Rev. B, in print (2010
Disease Knowledge Transfer across Neurodegenerative Diseases
We introduce Disease Knowledge Transfer (DKT), a novel technique for
transferring biomarker information between related neurodegenerative diseases.
DKT infers robust multimodal biomarker trajectories in rare neurodegenerative
diseases even when only limited, unimodal data is available, by transferring
information from larger multimodal datasets from common neurodegenerative
diseases. DKT is a joint-disease generative model of biomarker progressions,
which exploits biomarker relationships that are shared across diseases. Our
proposed method allows, for the first time, the estimation of plausible,
multimodal biomarker trajectories in Posterior Cortical Atrophy (PCA), a rare
neurodegenerative disease where only unimodal MRI data is available. For this
we train DKT on a combined dataset containing subjects with two distinct
diseases and sizes of data available: 1) a larger, multimodal typical AD (tAD)
dataset from the TADPOLE Challenge, and 2) a smaller unimodal Posterior
Cortical Atrophy (PCA) dataset from the Dementia Research Centre (DRC), for
which only a limited number of Magnetic Resonance Imaging (MRI) scans are
available. Although validation is challenging due to lack of data in PCA, we
validate DKT on synthetic data and two patient datasets (TADPOLE and PCA
cohorts), showing it can estimate the ground truth parameters in the simulation
and predict unseen biomarkers on the two patient datasets. While we
demonstrated DKT on Alzheimer's variants, we note DKT is generalisable to other
forms of related neurodegenerative diseases. Source code for DKT is available
online: https://github.com/mrazvan22/dkt.Comment: accepted at MICCAI 2019, 13 pages, 5 figures, 2 table
Sensitivity and back-action in charge qubit measurements by a strongly coupled single-electron transistor
We consider charge-qubit monitoring (continuous-in-time weak measurement) by
a single-electron transistor (SET) operating in the sequential-tunneling
regime. We show that commonly used master equations for this regime are not of
the Lindblad form that is necessary and sufficient for guaranteeing valid
physical states. In this paper we derive a Lindblad-form master equation and a
corresponding quantum trajectory model for continuous measurement of the charge
qubit by a SET. Our approach requires that the SET-qubit coupling be strong
compared to the SET tunnelling rates. We present an analysis of the quality of
the qubit measurement in this model (sensitivity versus back-action).
Typically, the strong coupling when the SET island is occupied causes
back-action on the qubit beyond the quantum back-action necessary for its
sensitivity, and hence the conditioned qubit state is mixed. However, in one
strongly coupled, asymmetric regime, the SET can approach the limit of an ideal
detector with an almost pure conditioned state. We also quantify the quality of
the SET using more traditional concepts such as the measurement time and
decoherence time, which we have generalized so as to treat the strongly
responding regime.Comment: About 11 pages, 6 figures. Changes in v2: we made general
improvements to the manuscript including, but not limited to(!), the removal
of one reference, and modification of the footnote
The density functional theory of classical fluids revisited
We reconsider the density functional theory of nonuniform classical fluids
from the point of view of convex analysis. From the observation that the
logarithm of the grand-partition function is a convex
functional of the external potential it is shown that the Kohn-Sham free
energy is a convex functional of the density . and constitute a pair of Legendre transforms and each
of these functionals can therefore be obtained as the solution of a variational
principle. The convexity ensures the unicity of the solution in both cases. The
variational principle which gives as the maximum of a
functional of is precisely that considered in the density functional
theory while the dual principle, which gives as the maximum of
a functional of seems to be a new result.Comment: 10 page
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