Mathematical classical mechanics is underpinned by Hamiltonian flows on symplectic and more general Poisson manifolds, with conserved energy functions defining vector fields whose integrability is ...

Quantum differential operators, encompassing Schrödinger, Dirac and more general elliptic operators, serve as fundamental constructs in the mathematical description of quantum phenomena. Spectral ...

One hundred years ago on a quiet, rocky island, German physicist Werner Heisenberg helped set in motion a series of scientific developments that would touch nearly all of physics. There, Heisenberg ...

One of the most perplexing aspects of quantum mechanics is that tiny subatomic particles don't seem to "choose" a state until an outside observer measures it. The act of measurement converts all the ...

In 2022, the physics Nobel prize was awarded for experimental work showing that the quantum world must break some of our fundamental intuitions about how the universe works. Many look at those ...

Quantum mechanics is one of the most successful theories in science — and makes much of modern life possible. Technologies ranging from computer chips to medical-imaging machines rely on the ...

Quantum mechanics is simultaneously beautiful and frustrating. Its explanatory power is unmatched. Armed with the machinery of quantum theory, we have unlocked the secrets of atomic power, divined the ...

Quantum theory is often sold as a story about tiny particles, but its real disruption lands squarely on our everyday sense of what is real. At the smallest scales, the equations that power lasers, ...

A century ago, science went quantum. To celebrate, physicists are throwing a global, year-long party. In 1925, quantum mechanics, the scientific theory that describes the unintuitive rules of physics ...

Dark matter is an elusive form of matter that almost never emits, absorbs or reflects light, while only weakly interacting with regular matter. These properties make it very difficult to detect using ...

In commemoration of the 100th anniversary of modern quantum mechanics, a survey asked physicists for their takes on some hot questions in quantum theory. Reading time 4 minutes In July 1925—exactly a ...