DISSIPATION IN QUANTUM MECHANICS THE TWO-LEVEL SYSTEM

Journal Article · Sun Sep 15 04:00:00 EDT 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.131.2827· OSTI ID:4648350

Senitzky, I R

The study of a two-level system (TLS) coupled to a loss mechanism (LM), the fluctuations of which are taken into account, is motivated by relating the problem to spinlattice relaxation, radiation damping. and Brownian motion A TLS of the electric dipole type (coupled to the LM through one variable only) is discussed first. The problem is formulated in terms of the Pauli spin matrices, and the Langevin equations for Brownian motion of a TLS are derived. Their solution---- made possible by taking expectation values in LM space---contains the Weisskopf-Wigner exponential decay formula of radiation theory, as well as a second-order shift in frequency of the TLS produced by the (nondispersive) LM. A driving force is added to the problem and expressions are obtained for a driven lossy TLS of the electric dipole type. The same analysis is applied to a TLS of the magnetic dipole type and differential equations for the spin matrices, for which the expectation values in LM space have been taken, are obtained. Taking expectation values in TLS space converts these equations into the Bloch equations. Unlike the electric dipole case, no frequency shift is piesent. (auth)

• Research Organization: Army Electronics Research and Development Lab., Fort Monmouth, N.J.
• NSA Number: NSA-17-036858
• OSTI ID: 4648350
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 131; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BLOCH EQUATIONS
BROWNIAN MOVEMENT
COLLISIONS
COUPLING
DECAY
DIFFERENTIAL EQUATIONS
DIFFUSION
DIPOLES
ELECTRIC MOMENTS
ENERGY LEVELS
EQUATIONS
EXPECTATION VALUE
FREQUENCY
INTERACTIONS
LANGEVIN EQUATION
LANGEVIN THEORY
LATTICES
LOSSES
MAGNETIC MOMENTS
MAGNETIC RESONANCE
MATHEMATICS
MATRICES
MOLECULES
MOTION
NUCLEAR MAGNETIC RESONANCE
PHYSICS
POWER
QUANTUM MECHANICS
RADIATIONS
RELAXATION
SLOWDOWN
SPECTRAL SHIFT
SPIN
VARIATIONS