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The Quantum Schur Transform: Theory and Implementations

The quantum Schur transform is a unitary change of basis from the computational product basis to the so-called Schur basis, a basis labeled by the irreducible representations of the symmetric and unitary groups, based on the Schur-Weyl duality in the group representation theory. The latter basis is called the Schur basis. The quantum Schur transform […]

Mahn-Soo Choi, Korea University
Events & Courses

Wolfram Neural Networks Boot Camp; January 5–16

Learn to apply AI and deep learning to text, image, audio and video analysis; build and train your own neural net models. This two-week online boot camp is for anyone who wants to develop proficiency in neural networks and explore ways to apply AI and make use of LLMs.

Wolfram U
Wolfram Community

Hyperbolic Spin Liquids

Hyperbolic lattices present a unique opportunity to venture beyond the conventional paradigm of crystalline many-body physics and explore correlated phenomena in negatively curved space. As a theoretical benchmark for such investigations, we extend Kitaev’s spin-1/2 honeycomb model to hyperbolic lattices and exploit their non-Euclidean space-group symmetries to solve the model exactly. In this Wolfram Mathematica notebook, we first show how to construct Kitaev models on hyperbolic lattices. Subsequently, we demonstrate how to use hyperbolic band theory to obtain the ground-state phase diagram on one of them and study the phases therein. In particular, we study the exotic compressible spin liquid with low-energy density of states dominated by non-Abelian Bloch states of Majorana fermions appearing for isotropic couplings which develops into a gapped chiral spin liquid under a time-reversal-breaking perturbation.

Patrick M. Lenggenhager, Max Planck Institute for the Physics of Complex Systems
Wolfram Community

Enhanced Geneva Mechanism Animation: A Detailed and Complex 3D Representation

An advanced 3D animation of the Geneva mechanism, significantly enhancing the design of a previous, more simplified version. While the earlier animation utilized basic geometric forms like cylinders and triangular prisms, this new version introduces detailed and intricate shapes, resulting in a more realistic and visually complex representation. The animation includes refined components such as the Geneva wheel, lock wheel and driving pin, all modeled with precision. Interactive controls for parameters like the number of slots, pin radius and rotation angle provide users with the ability to explore and analyze the mechanism’s functionality dynamically. This improved animation serves as a valuable resource for engineering studies and enthusiasts interested in Geneva mechanisms.

David Balandra, Honeywell
Events & Courses

Daily Study Group: Neural Networks for AI; October 27-31

Perfect for anyone new to the world of AI or those looking to further their understanding, this Daily Study Group provides an introduction to neural networks and their application in AI using Wolfram Language. Join the Wolfram U team and a cohort of fellow learners in exploring fundamental concepts such as embeddings, network architecture and training processes. Gain hands-on experience with the Wolfram Neural Net Framework.

Wolfram U
Products

From MRI to Model: In Silico Medicine with Wolfram Language

In silico medicine, particularly through the use of finite element simulations, is revolutionizing patient-specific healthcare, especially in the musculoskeletal system. By creating detailed computational models of individual anatomy, finite element analysis enables precise simulation of biomechanical behavior under various conditions. This approach allows for personalized treatment strategies, offering predictive insights into how specific interventions—such as surgeries, prosthetics or rehabilitation plans—might affect the patient’s musculoskeletal health. Unlike traditional experiments such as in vivo or in vitro, in silico medicine refers to simulations where the experimental environment is recreated within the processor.
Alessandro Mastrofini, Bioengineering Application Developer Intern, Algorithms R&D
Computation & Analysis

How Long to Boil an Egg? FEM Modeling with Wolfram Language

It’s time to answer the question on any breakfast-lover’s mind: “How long do I boil an egg?” While it seems so simple—place an egg in boiling water and wait—it would be remiss to say a fully hard-boiled egg is the only way to enjoy a delightful protein boost. We can use the finite element method (FEM) to simulate the conditions of an egg in water and find the ideal temperature and duration for the perfect egg by assessing temperature changes within the egg itself. We can then predict how long it takes to reach various consistencies, such as a runny yolk or a crumbly, fully set yolk.

Ricardo López, et al.
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