Asymptotics of natural and artificial atoms in strong magnetic fields

Elliott H. Lieb; Jan Philip Solovej; Jakob Yngvason

doi:10.1007/3-540-27056-6_13

Asymptotics of natural and artificial atoms in strong magnetic fields

Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Magnetic fields in terrestrial experiments have only tiny effects on the ground-state properties of conventional atoms. The reason is that the natural atomic unit for magnetic field strength, B⁰ = m² e ³ c/h = 2.35 x 10⁵ Tesla, is enormous compared with laboratory fields, which are seldom larger than 10 T. Here m denotes the electron mass, e the elementary charge, and h and c have their usual meaning. The unit B₀ is the field strength B at which the magnetic length lb = (hc/(eB))^1/2 (∼ cyclotron radius for an electron in the lowest Landau level) is equal to the Bohr radius a₀ = h/(me²). Equivalently, at B = B₀ the Landau energy hω_B with ω_b - eB/(mc) the cyclotron frequency, becomes equal to the Rydberg energy e²/a₀. For B B₀ distortions of ground-state wave functions and energy level shifts due to the magnetic field will therefore be small, and their standard treatment by means of perturbation theory is completely adequate.

Original language	English (US)
Title of host publication	The Stability of Matter
Subtitle of host publication	From Atoms to Stars: Fourth Edition
Publisher	Springer Berlin Heidelberg
Pages	147-169
Number of pages	23
ISBN (Print)	3540420835, 9783540222125
DOIs	https://doi.org/10.1007/3-540-27056-6_13
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Access to Document

10.1007/3-540-27056-6_13

Cite this

@inbook{fa6b3d1d1c734f868a03fe6e811994de,

title = "Asymptotics of natural and artificial atoms in strong magnetic fields",

abstract = "Magnetic fields in terrestrial experiments have only tiny effects on the ground-state properties of conventional atoms. The reason is that the natural atomic unit for magnetic field strength, B0 = m2 e 3 c/h = 2.35 x 105 Tesla, is enormous compared with laboratory fields, which are seldom larger than 10 T. Here m denotes the electron mass, e the elementary charge, and h and c have their usual meaning. The unit B0 is the field strength B at which the magnetic length lb = (hc/(eB))1/2 (∼ cyclotron radius for an electron in the lowest Landau level) is equal to the Bohr radius a0 = h/(me2). Equivalently, at B = B0 the Landau energy hωB with ωb - eB/(mc) the cyclotron frequency, becomes equal to the Rydberg energy e2/a0. For B B0 distortions of ground-state wave functions and energy level shifts due to the magnetic field will therefore be small, and their standard treatment by means of perturbation theory is completely adequate.",

author = "Lieb, {Elliott H.} and Solovej, {Jan Philip} and Jakob Yngvason",

year = "2005",

doi = "10.1007/3-540-27056-6_13",

language = "English (US)",

isbn = "3540420835",

pages = "147--169",

booktitle = "The Stability of Matter",

publisher = "Springer Berlin Heidelberg",

}

TY - CHAP

T1 - Asymptotics of natural and artificial atoms in strong magnetic fields

AU - Lieb, Elliott H.

AU - Solovej, Jan Philip

AU - Yngvason, Jakob

PY - 2005

Y1 - 2005

N2 - Magnetic fields in terrestrial experiments have only tiny effects on the ground-state properties of conventional atoms. The reason is that the natural atomic unit for magnetic field strength, B0 = m2 e 3 c/h = 2.35 x 105 Tesla, is enormous compared with laboratory fields, which are seldom larger than 10 T. Here m denotes the electron mass, e the elementary charge, and h and c have their usual meaning. The unit B0 is the field strength B at which the magnetic length lb = (hc/(eB))1/2 (∼ cyclotron radius for an electron in the lowest Landau level) is equal to the Bohr radius a0 = h/(me2). Equivalently, at B = B0 the Landau energy hωB with ωb - eB/(mc) the cyclotron frequency, becomes equal to the Rydberg energy e2/a0. For B B0 distortions of ground-state wave functions and energy level shifts due to the magnetic field will therefore be small, and their standard treatment by means of perturbation theory is completely adequate.

AB - Magnetic fields in terrestrial experiments have only tiny effects on the ground-state properties of conventional atoms. The reason is that the natural atomic unit for magnetic field strength, B0 = m2 e 3 c/h = 2.35 x 105 Tesla, is enormous compared with laboratory fields, which are seldom larger than 10 T. Here m denotes the electron mass, e the elementary charge, and h and c have their usual meaning. The unit B0 is the field strength B at which the magnetic length lb = (hc/(eB))1/2 (∼ cyclotron radius for an electron in the lowest Landau level) is equal to the Bohr radius a0 = h/(me2). Equivalently, at B = B0 the Landau energy hωB with ωb - eB/(mc) the cyclotron frequency, becomes equal to the Rydberg energy e2/a0. For B B0 distortions of ground-state wave functions and energy level shifts due to the magnetic field will therefore be small, and their standard treatment by means of perturbation theory is completely adequate.

UR - http://www.scopus.com/inward/record.url?scp=84892310508&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892310508&partnerID=8YFLogxK

U2 - 10.1007/3-540-27056-6_13

DO - 10.1007/3-540-27056-6_13

M3 - Chapter

AN - SCOPUS:84892310508

SN - 3540420835

SN - 9783540222125

SP - 147

EP - 169

BT - The Stability of Matter

PB - Springer Berlin Heidelberg

ER -

Asymptotics of natural and artificial atoms in strong magnetic fields

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this