Theoretical_Physics

The topologist Danny Calegari discusses the inevitability of disappointment in math, and how to learn from it.

Black holes are intriguing astronomical objects that have a gravitational pull so strong that it prevents any object and even light from escaping. While black holes have been the topic of numerous astrophysical ...

Optical neural networks, which use photons instead of electrons, have advantages over traditional systems. They also face major obstacles.

Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here, we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of noncommuting observables. Our hierarchy is built on the state polynomial optimization framework, also known as scalar extension. The hierarchy is complete in the sense that it converges to tight uncertainty relations. We improve upon upper bounds for all 1292 additive uncertainty relations on up to nine operators for which a tight bound is not known. The bounds are dimension-free and depend entirely on the algebraic relations among the operators. The techniques apply to a range of scenarios, including Pauli, Heisenberg-Weyl, and fermionic operators, and generalize to higher order moments and multiplicative uncertainty relations.

By making use of randomness, a team has created a simple algorithm for estimating large numbers of distinct objects in a stream of data.

چکیده: اختلاف ها در باره نظریه کوانتومی از ابتدای پیدایش بسیار زیاد بوده است. اما امروزه می توان گفت که توافق خوبی وجود دارد که مکانیک کوانتومی در مبانی خود دارای یک مشکل جدی است. این مشکل « مسئله اندازه گیری» نام دارد. به این ترتیب می توان گفت که تفسیرهای مختلف نظریه های جایگزینی هستند که سعی می کنند این مشکل را برطرف کنند. در این ارائه مروری بر این مسئله و رویکردهای مختلف برای حل آن خواهیم داشت.

Mathematicians have disproved a major conjecture about the relationship between curvature and shape.

Chae's analyses on GAIA observations of wide binary stars have fortified the paradigm of extended gravity with particular attention to MOND-like theories. We recall that, starting from the origin...