- Person
- Lev Landau
- Lived
- 1908–1968
- Field
- Theoretical Physics
- From
- Soviet
The story
Lev Landau was a prodigy. Born in Baku in 1908 to Jewish parents, an oil engineer father and a doctor mother, he had mastered calculus by the age of thirteen and entered Baku University at fourteen. In 1924 he moved to Leningrad, then the main centre of Soviet physics. He later recalled the ecstasy of reading the papers by Werner Heisenberg and Erwin Schrödinger that announced the birth of quantum mechanics, and his first scientific paper, on the spectra of diatomic molecules, was published in 1926 when he was an eighteen-year-old undergraduate.
Ordinary quantum mechanics describes a system by a single state, a wavefunction. But real systems are often part of something larger, entangled with their surroundings, and then no single wavefunction can describe the part on its own. Landau was troubled by exactly this problem. In 1927, the year he graduated, he published The Problem of Damping in Wave Mechanics, his first paper on quantum theory, in which he introduced a new mathematical object to describe such a subsystem.
That object is now called the density matrix. The Hungarian-American mathematician John von Neumann introduced the same idea, more systematically, in the same year, motivated by quantum statistics and the theory of measurement, and the two are credited as independent co-discoverers. The name 'density' came a few years later, when Paul Dirac used the operator in 1931 to calculate the electron density in atoms.
The density matrix became one of the fundamental tools of quantum theory. It can represent mixed states, in which a system's preparation is uncertain, as well as parts of entangled systems. Landau went on to apply quantum ideas across almost every branch of physics.
Today the density matrix is used throughout quantum statistical mechanics and quantum chemistry, in the study of open quantum systems and decoherence, and in quantum information science, where it is essential for describing the fragile qubits of quantum computers.
Why it matters
The density matrix is essential to modern quantum technologies, from lasers to quantum computers.
About Lev Landau
Baku-born prodigy who founded the great Soviet school of theoretical physics, survived Stalin’s prison, explained superfluid helium and won the 1962 Nobel Prize.
More about Lev Landau
- Lev Landau predicted a strange way plasma waves fadeIn 1946 Lev Landau predicted that waves in a plasma can lose energy without any collisions, an effect confirmed experimentally in 1964 and now called Landau damping.
- Lev Landau explained frictionless superfluid heliumLev Landau explained why liquid helium flows without friction below 2.17 K, introducing phonons and 'rotons'; it won him the 1962 Nobel Prize in Physics.
- Landau's Fermi liquid theory explains metalsIn 1956 Lev Landau introduced Fermi liquid theory, explaining why electrons in metals and atoms in liquid helium-3 behave almost like free particles.
- The Ginzburg–Landau theory explains superconductorsLev Landau and Vitaly Ginzburg created the Ginzburg–Landau theory of superconductivity, work that helped win Ginzburg and Landau's student Abrikosov the 2003 Nobel Prize.
- Landau levels underpin the quantum Hall effectIn 1930 Lev Landau showed that electrons in a magnetic field occupy discrete energy levels, now called Landau levels, key to explaining the quantum Hall effect.
- Landau and Lifshitz wrote physics' great textbook seriesWith his student Evgeny Lifshitz, Lev Landau began the ten-volume Course of Theoretical Physics, still used by graduate physics students worldwide.
- Landau's 'Theoretical Minimum' trained a generationLev Landau's famous 'Theoretical Minimum' exams, passed by only 43 candidates from 1934 to 1961, created the Soviet Union's greatest school of theoretical physics.
- Landau's theory explains how matter changes stateLev Landau's theory of second-order phase transitions introduced the 'order parameter', still a broad and powerful framework for how matter changes state.
Sources
- Lev Landau Wikipedia
- Lev Davidovich Landau MacTutor History of Mathematics, University of St Andrews
- Density matrix Wikipedia
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