Adiabatic Condition for Nonlinear Systems

doi:10.1103/PHYSREVLETT.98.050406

Title: Adiabatic Condition for Nonlinear Systems

Full Record
Other Related Research

Abstract

The adiabatic approximation is an important concept in quantum mechanics. In linear systems, the adiabatic condition is derived with the help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a procedure that breaks down in the presence of nonlinearity. Using an explicit example relevant to photoassociation of atoms into diatomic molecules, we demonstrate that the proper way to derive the adiabatic condition for nonlinear mean-field (or classical) systems is through a linearization procedure, using which an analytic adiabatic condition is obtained for the nonlinear model under study.

Authors:

Pu Han ^[1]; Maenner, Peter; Ling, Hong Y. ^[2]; Zhang Weiping ^[3]

Department of Physics and Astronomy, and Rice Quantum Institute, Rice University, Houston, Texas 77251-1892 (United States)
Department of Physics and Astronomy, Rowan University, Glassboro, New Jersey, 08028-1700 (United States)
Key Laboratory of Optical and Magnetic Resonance Spectroscopy (Ministry of Education), Department of Physics, East China Normal University, Shanghai 200062 (China)

Publication Date:: Fri Feb 02 00:00:00 EST 2007

OSTI Identifier:: 20955409

Resource Type:: Journal Article

Resource Relation:: Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevLett.98.050406; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ADIABATIC APPROXIMATION; EIGENSTATES; EIGENVALUES; HAMILTONIANS; MEAN-FIELD THEORY; NONLINEAR PROBLEMS; QUANTUM MECHANICS

Citation Formats


                    Pu Han, Maenner, Peter, Ling, Hong Y., and Zhang Weiping. Adiabatic Condition for Nonlinear Systems.  United States: N. p., 2007. 
        Web.  doi:10.1103/PHYSREVLETT.98.050406.

Copy to clipboard


                    Pu Han, Maenner, Peter, Ling, Hong Y., & Zhang Weiping. Adiabatic Condition for Nonlinear Systems.  United States.  doi:10.1103/PHYSREVLETT.98.050406.

Copy to clipboard


                    Pu Han, Maenner, Peter, Ling, Hong Y., and Zhang Weiping. Fri .  
        "Adiabatic Condition for Nonlinear Systems".  United States.  
        doi:10.1103/PHYSREVLETT.98.050406.

Copy to clipboard


                    
@article{osti_20955409,

  title        = {Adiabatic Condition for Nonlinear Systems},

  author       = {Pu Han and Maenner, Peter and Ling, Hong Y. and Zhang Weiping},

  abstractNote = {The adiabatic approximation is an important concept in quantum mechanics. In linear systems, the adiabatic condition is derived with the help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a procedure that breaks down in the presence of nonlinearity. Using an explicit example relevant to photoassociation of atoms into diatomic molecules, we demonstrate that the proper way to derive the adiabatic condition for nonlinear mean-field (or classical) systems is through a linearization procedure, using which an analytic adiabatic condition is obtained for the nonlinear model under study.},

  doi          = {10.1103/PHYSREVLETT.98.050406},

  journal      = {Physical Review Letters},

  number       = 5,

  volume       = 98,

  place        = {United States},

  year         = {Fri Feb 02 00:00:00 EST 2007},

  month        = {Fri Feb 02 00:00:00 EST 2007}

}

Copy to clipboard

Journal Article:

DOI: 10.1103/PHYSREVLETT.98.050406

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Adiabatic evolution in nonlinear systems with degeneracy

Journal Article Zhou Xiangfa ; Zhang Yongsheng ; Zhou Zhengwei ; ... - Physical Review. A

We propose a general description of adiabatic evolution of degenerate quantum systems in both linear and nonlinear cases. We derive the effective evolution equations of the considered system. For nondegenerate cases, we obtain a generalized Berry's phase for nonlinear systems. For linear cases, the equations reduce to the Wilczek-Zee dynamics in degenerate quantum systems, where non-Abelian adiabatic connections appear. The method can be used to study the coherent atom-molecule transition in ultracold quantum gases with degeneracy and is consistent with quantized treatment.
DOI: 10.1103/PHYSREVA.81.043614
TIME EVOLUTION OF THE THREE-DIMENSIONAL ACCRETION FLOWS: EFFECTS OF THE ADIABATIC INDEX AND OUTER BOUNDARY CONDITION

Journal Article Janiuk, Agnieszka ; Sznajder, Maciej ; Moscibrodzka, Monika ; ... - Astrophysical Journal

We study a slightly rotating accretion flow onto a black hole, using the fully three-dimensional (3D) numerical simulations. We consider hydrodynamics of an inviscid flow, assuming a spherically symmetric density distribution at the outer boundary and a small, latitude-dependent angular momentum. We investigate the role of the adiabatic index and gas temperature, and the flow behavior due to non-axisymmetric effects. Our 3D simulations confirm axisymmetric results: the material that has too much angular momentum to be accreted forms a thick torus near the equator, and the mass accretion rate is lower than the Bondi rate. In our previous study ofmore »« less
DOI: 10.1088/0004-637X/705/2/1503
Necessary condition for the quantum adiabatic approximation

Journal Article Boixo, S. ; Somma, R. D. - Physical Review. A

A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a minimum time proportional to the ratio of the length of the eigenstate path to the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We also give a necessary condition for the adiabatic approximation that depends on local properties of the path, which is appropriate when the gap varies.
DOI: 10.1103/PHYSREVA.81.032308
Adiabatic condition and the quantum hitting time of Markov chains

Journal Article Krovi, Hari ; University of Connecticut, Storrs, Connecticut 06269 ; Ozols, Maris ; ... - Physical Review. A

We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P{sup '} where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP{sup '} and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markovmore »« less
DOI: 10.1103/PHYSREVA.82.022333
Semiclassical modelling of finite-pulse effects on non-adiabatic photodynamics via initial condition filtering: The predissociation of NaI as a test case

Journal Article Martínez-Mesa, Aliezer ; Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm ; Saalfrank, Peter - Journal of Chemical Physics

Femtosecond-laser pulse driven non-adiabatic spectroscopy and dynamics in molecular and condensed phase systems continue to be a challenge for theoretical modelling. One of the main obstacles is the “curse of dimensionality” encountered in non-adiabatic, exact wavepacket propagation. A possible route towards treating complex molecular systems is via semiclassical surface-hopping schemes, in particular if they account not only for non-adiabatic post-excitation dynamics but also for the initial optical excitation. One such approach, based on initial condition filtering, will be put forward in what follows. As a simple test case which can be compared with exact wavepacket dynamics, we investigate the influencemore »« less
DOI: 10.1063/1.4919780

Similar Records