1,086 research outputs found
Time-dependent numerical renormalization group method for multiple quenches: towards exact results for the long time limit of thermodynamic observables and spectral functions
We develop an alternative time-dependent numerical renormalization group
(TDNRG) formalism for multiple quenches and implement it to study the response
of a quantum impurity system to a general pulse. Within this approach, we
reduce the contribution of the NRG approximation to numerical errors in the
time evolution of observables by a formulation that avoids the use of the
generalized overlap matrix elements in our previous multiple-quench TDNRG
formalism [Nghiem {\em et al.,} Phys. Rev. B {\bf 89}, 075118 (2014); Phys.
Rev. B {\bf 90}, 035129 (2014)]. We demonstrate that the formalism yields a
smaller cumulative error in the trace of the projected density matrix as a
function of time and a smaller discontinuity of local observables between
quenches than in our previous approach. Moreover, by increasing the switch-on
time, the time between the first and last quench of the discretized pulse, the
long-time limit of observables systematically converges to its expected value
in the final state, i.e., the more adiabatic the switching, the more accurately
is the long-time limit recovered. The present formalism can be
straightforwardly extended to infinite switch-on times. We show that this
yields highly accurate results for the long-time limit of both thermodynamic
observables and spectral functions, and overcomes the significant errors within
the single quench formalism [Anders {\em et al.}, Phys. Rev. Lett. {\bf 95},
196801 (2005); Nghiem {\em et al.}, Phys. Rev. Lett. {\bf 119}, 156601 (2017)].
This improvement provides a first step towards an accurate description of
nonequilibrium steady states of quantum impurity systems, e.g., within the
scattering states NRG approach [Anders, Phys. Rev. Lett. {\bf 101}, 066804
(2008)].Comment: 15 pages and 10 figures; Additional figures and references added;
typos fixed; references fixe
Procyon-A and Eta-Bootis: Observational Frequencies Analyzed by the Local-Wave Formalism
In the present analysis of Procyon-A and Eta-Bootis, we use the local-wave
formalism which, despite its lack of precision inherent to any semi-analytical
method, uses directly the model profile without any modification when
calculating the acoustic mode eigenfrequencies. These two solar-like stars
present steep variations toward the center due to the convective core
stratification, and toward the surface due to the very thin convective zone.
Based on different boundary conditions, the frequencies obtained with this
formalism are different from that of the classical numerical calculation. We
point out that (1) the frequencies calculated with the local-wave formalism
seem to agree better with observational ones. All the frequencies detected with
a good confident level including those classified as 'noise' find an
identification, (2) some frequencies can be clearly identified here as
indications of the core limit.Comment: SOHO 18 / GONG 2006 / HELAS I Meetin
Quantum Algorithm For Estimating Eigenvalue
A majority of numerical scientific computation relies heavily on handling and
manipulating matrices, such as solving linear equations, finding eigenvalues
and eigenvectors, and so on. Many quantum algorithms have been developed to
advance these computational tasks, and in some cases, such as solving linear
equations, can be shown to yield exponential speedup. Here, employing the
techniques in the HHL algorithm and the ideas of the classical power method, we
provide a simple quantum algorithm for estimating the largest eigenvalue in
magnitude of a given Hermitian matrix. As in the case of the HHL algorithm, our
quantum procedure can also yield exponential speedup compared to classical
algorithms that solve the same problem. We also discuss a few possible
extensions and applications of our quantum algorithm, such as a version of a
hybrid quantum-classical Lanczos algorithm
Vegetation Change Detection in Southern California Solar Energy Developments
Change detection from satellite sensor vegetation indices (VIs) presents an opportunity to monitor trends and disturbances at the regional scale for southern California's Mojave and Lower Colorado Deserts. Renewable energy sites are being constructed in this region on public lands under the Bureau of Land Management (BLM). We have developed a framework for VI change detection over the past two decades, with initial focus on three sites, Joshua Tree National Park, Mojave National Preserve, and a proximal group of Development Focus Areas (DFAs), for comparison between protected and development-targeted lands. Three Terra MODIS VIs (normalized difference [NDVI], enhanced [EVI], soil-adjusted [SAVI]) were evaluated in the Breaks for Additive Season and Trend (BFAST) setting for the regional MODIS 250-m resolution grid to estimate significant time series shifts (breakpoints) from February 2000 to May 2018. All three VIs tended to detect the maximum number of breakpoints at a grid location, but cross-correlations with precipitation and comparison with timing of wildfire burns near the study sites for breakpoint density (proportion of area with a breakpoint) showed that NDVI had the strongest response to these major disturbances, supporting its use for subsequent analysis. Time series of NDVI breakpoint change densities for individual solar energy sites did not have a consistent vegetation response following construction. Bootstrapping showed that the DFAs had significantly larger kurtosis and variance in the positive NDVI breakpoint distribution than did the protected sites, but there was no significant difference in the negative distribution for all three sites. The inconsistent post-construction NDVI signal and the large number of breakpoints overall suggested that the largest changes in vegetation cover density were tied to seasonal precipitation amounts. The distributional results indicated that existing site-specific conditions were the main control on VI responses, given the history of human disturbances in the DFAs. Although the results do not support persistent VI disturbances resulting from recent solar energy development, continued monitoring and examination of other ecological variables and surface temperatures will be vital to the long-term protection of this desert environment
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Does a New Polyomavirus Contribute to Merkel Cell Carcinoma?
A new technique designed to hunt for non-human transcripts has identified a novel SV40-like
virus present in the majority of Merkel cell carcinomas. Here we examine what it will take to
determine whether or not this virus contributes to carcinogenesis
Does a new polyomavirus contribute to Merkel cell carcinoma?
A new polyomavirus has been discovered in Merkel cell carcinomas, but does it contribute to carcinogenesis
Quantum Algorithm for Estimating Betti Numbers Using a Cohomology Approach
Topological data analysis has emerged as a powerful tool for analyzing
large-scale data. High-dimensional data form an abstract simplicial complex,
and by using tools from homology, topological features could be identified.
Given a simplex, an important feature is so-called Betti numbers. Calculating
Betti numbers classically is a daunting task due to the massive volume of data
and its possible high-dimension. While most known quantum algorithms to
estimate Betti numbers rely on homology, here we consider the `dual' approach,
which is inspired by Hodge theory and de Rham cohomology, combined with recent
advanced techniques in quantum algorithms. Our cohomology method offers a
relatively simpler, yet more natural framework that requires exponentially less
qubits, in comparison with the known homology-based quantum algorithms.
Furthermore, our algorithm can calculate its -th Betti number up
to some multiplicative error with running time , where is the number
of -simplex. It thus works best when the -th Betti number is considerably
smaller than the number of the -simplex in the given triangulated manifold
Constant-time Quantum Algorithm for Homology Detection in Closed Curves
Given a loop or more generally 1-cycle of size L on a closed
two-dimensional manifold or surface, represented by a triangulated mesh, a
question in computational topology asks whether or not it is homologous to
zero. We frame and tackle this problem in the quantum setting. Given an oracle
that one can use to query the inclusion of edges on a closed curve, we design a
quantum algorithm for such a homology detection with a constant running time,
with respect to the size or the number of edges on the loop , requiring only
a single usage of oracle. In contrast, classical algorithm requires
oracle usage, followed by a linear time processing and can be improved to
logarithmic by using a parallel algorithm. Our quantum algorithm can be
extended to check whether two closed loops belong to the same homology class.
Furthermore, it can be applied to a specific problem in the homotopy detection,
namely, checking whether two curves are \textit{not} homotopically equivalent
on a closed two-dimensional manifold
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