Constraints on scattering amplitudes in multistate LandauZener theory
Abstract
Here, we derive a set of constraints, which we will call hierarchy constraints, on scattering amplitudes of an arbitrary multistate LandauZener model (MLZM). The presence of additional symmetries can transform such constraints into nontrivial relations between elements of the transition probability matrix. This observation can be used to derive complete solutions of some MLZMs or, for models that cannot be solved completely, to reduce the number of independent elements of the transition probability matrix.
 Authors:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of California, Berkeley, CA (United States)
 Wayne State Univ., Detroit, MI (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1346843
 Alternate Identifier(s):
 OSTI ID: 1341911
 Report Number(s):
 LAUR1626921
Journal ID: ISSN 24699926; PLRAAN; TRN: US1700911
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review A
 Additional Journal Information:
 Journal Volume: 95; Journal Issue: 1; Journal ID: ISSN 24699926
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Mathematics; Material Science; Quantum Algebra, Nonadiabatic Transition, Scattering Theory
Citation Formats
Sinitsyn, Nikolai A., Lin, Jeffmin, and Chernyak, Vladimir Y. Constraints on scattering amplitudes in multistate LandauZener theory. United States: N. p., 2017.
Web. doi:10.1103/PhysRevA.95.012140.
Sinitsyn, Nikolai A., Lin, Jeffmin, & Chernyak, Vladimir Y. Constraints on scattering amplitudes in multistate LandauZener theory. United States. doi:10.1103/PhysRevA.95.012140.
Sinitsyn, Nikolai A., Lin, Jeffmin, and Chernyak, Vladimir Y. Mon .
"Constraints on scattering amplitudes in multistate LandauZener theory". United States.
doi:10.1103/PhysRevA.95.012140. https://www.osti.gov/servlets/purl/1346843.
@article{osti_1346843,
title = {Constraints on scattering amplitudes in multistate LandauZener theory},
author = {Sinitsyn, Nikolai A. and Lin, Jeffmin and Chernyak, Vladimir Y.},
abstractNote = {Here, we derive a set of constraints, which we will call hierarchy constraints, on scattering amplitudes of an arbitrary multistate LandauZener model (MLZM). The presence of additional symmetries can transform such constraints into nontrivial relations between elements of the transition probability matrix. This observation can be used to derive complete solutions of some MLZMs or, for models that cannot be solved completely, to reduce the number of independent elements of the transition probability matrix.},
doi = {10.1103/PhysRevA.95.012140},
journal = {Physical Review A},
number = 1,
volume = 95,
place = {United States},
year = {Mon Jan 30 00:00:00 EST 2017},
month = {Mon Jan 30 00:00:00 EST 2017}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Cited by: 3works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Fourstate nonstationary models in multistate LandauZener theory
A dynamic fourstate system is considered within the context of multistate LandauZener theory. It is shown that the theory accounts very well for the timedependent state populations and final transition probabilities even in cases when multiple crossings appear in close vicinity of each other. This is also true for multiple paths systems when the phases are appropriately accounted for. It is found that transitions may take place also between diabatic states that do not couple directly and that the dynamics of such crossings may be accurately described within the multichannel LandauZener theory. 
Analytical results for statetostate transition probabilities in the multistate LandauZener model by nonstationary perturbation theory
Multistate generalizations of LandauZener model are studied by summing entire series of perturbation theory. A technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. Expressions for some statetostate transition probabilities are derived in degenerate cases. 
Solvable multistate model of LandauZener transitions in cavity QED
We consider the model of a single optical cavity mode interacting with twolevel systems (spins) driven by a linearly timedependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of LandauZener (LZ) transitions leads to coflips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.Cited by 6