5,380 research outputs found
A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions
We study a matrix product state (MPS) algorithm to approximate excited states
of translationally invariant quantum spin systems with periodic boundary
conditions. By means of a momentum eigenstate ansatz generalizing the one of
\"Ostlund and Rommer [1], we separate the Hilbert space of the system into
subspaces with different momentum. This gives rise to a direct sum of effective
Hamiltonians, each one corresponding to a different momentum, and we determine
their spectrum by solving a generalized eigenvalue equation. Surprisingly, many
branches of the dispersion relation are approximated to a very good precision.
We benchmark the accuracy of the algorithm by comparison with the exact
solutions of the quantum Ising and the antiferromagnetic Heisenberg spin-1/2
model.Comment: 13 pages, 11 figures, 5 table
On Kostant's partial order on hyperbolic elements
We study Kostant's partial order on the elements of a semisimple Lie group in
relations with the finite dimensional representations. In particular, we prove
the converse statement of [3, Theorem 6.1] on hyperbolic elements.Comment: 7 page
The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
We study families H_n of 1D quantum spin systems, where n is the number of
spins, which have a spectral gap \Delta E between the ground-state and
first-excited state energy that scales, asymptotically, as a constant in n. We
show that if the ground state |\Omega_m> of the hamiltonian H_m on m spins,
where m is an O(1) constant, is locally the same as the ground state
|\Omega_n>, for arbitrarily large n, then an arbitrarily good approximation to
the ground state of H_n can be stored efficiently for all n. We formulate a
conjecture that, if true, would imply our result applies to all noncritical 1D
spin systems. We also include an appendix on quasi-adiabatic evolutions.Comment: 9 pages, 1 eps figure, minor change
Information theoretic treatment of tripartite systems and quantum channels
A Holevo measure is used to discuss how much information about a given POVM
on system is present in another system , and how this influences the
presence or absence of information about a different POVM on in a third
system . The main goal is to extend information theorems for mutually
unbiased bases or general bases to arbitrary POVMs, and especially to
generalize "all-or-nothing" theorems about information located in tripartite
systems to the case of \emph{partial information}, in the form of quantitative
inequalities. Some of the inequalities can be viewed as entropic uncertainty
relations that apply in the presence of quantum side information, as in recent
work by Berta et al. [Nature Physics 6, 659 (2010)]. All of the results also
apply to quantum channels: e.g., if \EC accurately transmits certain POVMs,
the complementary channel \FC will necessarily be noisy for certain other
POVMs. While the inequalities are valid for mixed states of tripartite systems,
restricting to pure states leads to the basis-invariance of the difference
between the information about contained in and .Comment: 21 pages. An earlier version of this paper attempted to prove our
main uncertainty relation, Theorem 5, using the achievability of the Holevo
quantity in a coding task, an approach that ultimately failed because it did
not account for locking of classical correlations, e.g. see [DiVincenzo et
al. PRL. 92, 067902 (2004)]. In the latest version, we use a very different
approach to prove Theorem
Resonance Damping in Ferromagnets and Ferroelectrics
The phenomenological equations of motion for the relaxation of ordered phases
of magnetized and polarized crystal phases can be developed in close analogy
with one another. For the case of magnetized systems, the driving magnetic
field intensity toward relaxation was developed by Gilbert. For the case of
polarized systems, the driving electric field intensity toward relaxation was
developed by Khalatnikov. The transport times for relaxation into thermal
equilibrium can be attributed to viscous sound wave damping via
magnetostriction for the magnetic case and electrostriction for the
polarization case.Comment: 5 pages no figures ReVTeX
Operator monotones, the reduction criterion and the relative entropy
We introduce the theory of operator monotone functions and employ it to
derive a new inequality relating the quantum relative entropy and the quantum
conditional entropy. We present applications of this new inequality and in
particular we prove a new lower bound on the relative entropy of entanglement
and other properties of entanglement measures.Comment: Final version accepted for publication, added references in reference
[1] and [13
Deconstructing Fahr's disease/syndrome of brain calcification in the era of new genes
Introduction
There are now a number genes, known to be associated with familial primary brain calcification (PFBC), causing the so called ‘Fahr's’ disease or syndrome. These are SCL20A2, PDGFB, PDGFRB and XPR1. In this systematic review, we analyse the clinical and radiological features reported in genetically confirmed cases with PFBC. We have additionally reviewed pseudohypoparathyroidism which is a close differential diagnosis of PFBC in clinical presentation and is also genetically determined.
Methods
We performed a Medline search, from 1st Jan 2012 through to 7th November 2016, for publications with confirmed mutations of SCL20A2, PDGFB, PDGFRB, and XPR1 and found twenty papers with 137 eligible cases. A second search was done for publications of cases with Pseudohypoparathyroidism or pseudopseudohypoparathyroidism, and found 18 publications with 20 eligible cases.
Results
SLC20A2 was the most common gene involved with 75 out of 137 cases included with PFBC (55%) followed by PDGFB (31%) and PDGFRB (11%). Statistically significant correlation was found between the presence of parkinsonism with SLC20A2 mutations, headache in PDGFB and generalised tonic-clonic seizures in patients with pseudohypoparathyroidism.
Conclusion
We combine statistical analysis and clinical inference to suggest a diagnostic algorithm based on the observations in this study to help with investigation of a patient with neurological features and brain calcification
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