Bloch oscillations in one-dimensional solids and solitary wave packets

Journal Article · Sun Sep 01 04:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526825· OSTI ID:5404294

Luban, M

We derive the exact solution of a single-band time-dependent Schroedinger equation for an electron in an idealized one-dimensional periodic solid in the presence of a constant uniform electric field. We show that all wave functions are necessarily periodic in time. This result is the fully quantum-mechanical analog of the well-known Bloch oscillations predicted by quasiclassical dynamics. Our method of solution consists of mapping the electron Schroedinger equation to the exactly solvable problem of a quantum planar rotor in the eikonal limit subject to an arbitrary angular and time-dependent external potential. The time periodicity of the electron wave functions is due to the fact that all of the rotor wave functions have the form of solitary wave packets.

• Research Organization: Ames Laboratory, United States Department of Energy and Department of Physics, Iowa State University, Ames, Iowa 50011
• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 5404294
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:9; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

656000* -- Condensed Matter Physics
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
BLOCH THEORY
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FUNCTIONS
LEPTONS
MECHANICS
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICS
POTENTIALS
QUANTUM MECHANICS
QUASI PARTICLES
SCHROEDINGER EQUATION
SOLID STATE PHYSICS
SOLITONS
TIME DEPENDENCE
VARIATIONS
WAVE EQUATIONS
WAVE FUNCTIONS