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Register a new userQuantum Carpets made simple
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Authors
I. Marzoli
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We show that the concept of degeneracy is the key idea for understanding the quantum carpet woven by a particle in the box.
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We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, We observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension $D$. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as $sim 100$. We observe that our algorithm also works well for settings without a UT basis.
Molecular ferroelectrics have captured immense attention due to their superiority over inorganic oxide ferroelectrics, such as environmentally friendly, low-cost, flexible, foldable. However, the mechanisms of ferroelectric switching and phase transition for the molecular ferroelectrics are still missing, leaving the development of novel molecular ferroelectrics less efficient. In this work, we have provided a methodology combining molecular dynamics (MD) simulation on a polarized force field named polarized crystal charge (PCC) and enhanced sampling technique, replica-exchange molecular dynamics (REMD) to simulate such mechanisms. With this procedure, we have investigated a promising molecular ferroelectric material, (R)/(S)-3-quinuclidinol crystal. We have simulated the ferroelectric hysteresis loops of both enantiomers and obtained spontaneous polarization of 7/8 mu C cm-2 and a corresponding coercive electric field of 15 kV cm-1. We also find the Curie temperature as 380/385 K for ferro-/para-electric phase transition of both enantiomers. All of the simulated results are highly compatible with experimental values. Besides of that, we predict a novel Curie temperature of about 600 K. This finding is further validated by principal component analysis (PCA). Our work would significantly promote the future exploration of multifunctional molecular ferroelectrics for the next generation of intelligent devices.
We introduce the wedge diagram, an intuitive way to illustrate how cosmological models with a classical (non-singular) bounce generically resolve fundamental problems in cosmology. These include the well-known horizon, flatness, and inhomogeneity problems; the small tensor-to-scalar ratio observed in the cosmic microwave background; the low entropy at the beginning of a hot, expanding phase; and the avoidance of quantum runaway. The same diagrammatic approach can be used to compare with other cosmological scenarios.
We give a short proof of Gaos Quantum Union Bound and Gentle Sequential Measurement theorems.
Many blockchain consensus protocols have been proposed recently to scale the throughput of a blockchain with available bandwidth. However, these protocols are becoming increasingly complex, making it more and more difficult to produce proofs of their security guarantees. We propose a novel permissionless blockchain protocol OHIE which explicitly aims for simplicity. OHIE composes as many parallel instances of Bitcoins original (and simple) backbone protocol as needed to achieve excellent throughput. We formally prove the safety and liveness properties of OHIE. We demonstrate its performance with a prototype implementation and large-scale experiments with up to 50,000 nodes. In our experiments, OHIE achieves linear scaling with available bandwidth, providing about 4-10 Mbps transaction throughput (under 8-20 Mbps per-node available bandwidth configurations) and at least about 20x better decentralization over prior works.
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