Mark Yakovlevich Azbel (; 12 May 1932 — 31 March 2020) was a Soviet and Israeli

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

. He was a member of the

American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of ...

. Between 1956 and 1958, he experimentally demonstrated cyclotron resonance in metals, and worked out its theoretical basis. Azbel's 1964 analysis of Bloch electrons in a magnetic field contained ideas which were prescient of both the renormalization group and (though he did not make this explicit) the possibility of a

fractal In mathematics, a fractal is a Shape, geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scale ...

that was eventually discovered by

Douglas Hofstadter Douglas Richard Hofstadter (born 15 February 1945) is an American cognitive and computer scientist whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, Strange loop, strange ...

and later called

Hofstadter's butterfly In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a Crystal structure, lattice. The fractal, self-similarity, self-similar na ...

Biography

Azbel was born in 1932, in

Kharkiv Kharkiv, also known as Kharkov, is the second-largest List of cities in Ukraine, city in Ukraine.

(at the time, in the

Ukrainian Soviet Socialist Republic The Ukrainian Soviet Socialist Republic, abbreviated as the Ukrainian SSR, UkrSSR, and also known as Soviet Ukraine or just Ukraine, was one of the Republics of the Soviet Union, constituent republics of the Soviet Union from 1922 until 1991. ...

) to a family of physicians. From 1941, aged 9 to 12, he and his family lived under wartime evacuation in (

Siberia Siberia ( ; , ) is an extensive geographical region comprising all of North Asia, from the Ural Mountains in the west to the Pacific Ocean in the east. It has formed a part of the sovereign territory of Russia and its predecessor states ...

). In 1944, the family returned to Kharkiv. In 1948 Azbel graduated from high school and in the same year entered the National University of Kharkiv. After graduation, he taught mathematics at evening school. In 1958, he defended his doctorate (Doctor of Physical and Mathematical Sciences) under the supervision of

Lev Landau Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and ma ...

and

Pyotr Kapitsa Pyotr Leonidovich Kapitsa or Peter Kapitza (, ; – 8 April 1984) was a leading Soviet physicist and Nobel laureate, whose research focused on low-temperature physics. Biography Kapitsa was born in Kronstadt, Russian Empire, to the Bessar ...

. In 1964 he began working at

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

and concurrently as a section chair at the Landau Institute for Theoretical Physics. In 1972, Azbel applied for

emigration Emigration is the act of leaving a resident country or place of residence with the intent to settle elsewhere (to permanently leave a country). Conversely, immigration describes the movement of people into one country from another (to permanentl ...

from the Soviet Union to Israel, and in 1973 (a full four years before leaving the Soviet Union) was appointed a lecturer at

Tel Aviv University Tel Aviv University (TAU) is a Public university, public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Located in northwest Tel Aviv, the university is the center of teaching and ...

, where he initially gave his lectures by telephone. Having been refused exit permission from the Soviet Union, he participated in the movement of

refusenik Refusenik (, ; alternatively spelled refusnik) was an unofficial term for individuals—typically, but not exclusively, Soviet Jews—who were denied permission to emigrate, primarily to Israel, by the authorities of the Soviet Union and oth ...

s in the USSR in the mid-seventies. Azbel finally emigrated from the USSR in 1977 and was appointed Professor at

. He lived mainly in Israel until his death in 2020.

Scientific contributions

Azbel was a theoretical physicist. His areas of study included the quantum physics of electrons in metals, and he made the first prediction of cyclotron resonance in metals, now widely known as the Azbel-Kaner resonance. In an important 1964 article, Azbel made conjectures about the nature of the Harper spectrum which contributed to the discovery of the Hofstadter butterfly in 1974.

Works

* * *

Awards and prizes

*Lomonosov Prize, 1966 *Lomonosov Prize, 1968 *Landau Prize, Israel, 1989 *Humboldt Prize, Germany, 2001

References

External links

Институт теоретической физики им. Ландау

* ttps://jewish.ru/ru/people/science/192613/ Физик, хам, антисоветчик {{DEFAULTSORT:Azbel, Mark 1932 births 2020 deaths Scientists from Kharkiv Academic staff of Moscow State University Academic staff of Tel Aviv University National University of Kharkiv alumni Soviet physicists Israeli physicists Refuseniks Kharkiv Institute of Physics and Technology people