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Topic: Adiabatic approximation

	(Q-5) The Atomic Nucleus and Bohr's model of the Atom
		The lack of constancy may be attributed to the fact that the tension in the string in any swing does not vary symmetrically--a small asymmetry is added by the fact the string is constantly being shortened, but slowing down the pull greatly reduces the asymmetry and its accumulated effects.
		Adiabatic invariants occur in all sorts of periodic motions, including Kepler motion, which was taken as the model of the motion of an electron around the nucleus.
		Adiabatic invariants again attracted attention in the 1950s, in the study of the motion of ions and electrons in rarefied plasmas.
	www.phy6.org /stargaze/Q5.htm (1714 words)

	Born-Oppenheimer approximation - Wikipedia, the free encyclopedia
		The Born-Oppenheimer approximation, also known as the adiabatic approximation, is a technique used in quantum chemistry and condensed matter physics in order to de-couple the motion of nuclei and electrons (i.e.
		The Born-Oppenheimer approximation is commonly confused with the Born-Oppenheimer representation.
		The Born-Oppenheimer approximation consists in replacing the electronic molecular Hamiltonian in the molecular Hamiltonian by its eigenvalues (which are adiabatically dependent on the molecular geometry) called in this context potential energy surfaces.
	en.wikipedia.org /wiki/Born-Oppenheimer_approximation (522 words)

	Born's Adiabatic method
		In the Born adiabatic approximation, the right hand side of (2.8), i.e.
		The validity of the Born-Oppenheimer approximation is dependent on the smallness of the expansion parameter
		Hence both the Born-Oppenheimer and the Born Adiabatic approximation fail to describe even qualitative characteristics of the muonic molecule, such as the number of the bound states [
	musr.physics.ubc.ca /theses/Fujiwara/node28.html (337 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		A few milestones in the history of the adiabatic theorem were the following: Kato \cite{k} proved the theorem for Hamiltonians with a non-degenerate eigenvalue separated from the rest of the spectrum, without any assumption on the nature of the rest of the spectrum.
		Subsequent works on the exponential accuracy of the adiabatic approximation have been performed by Nenciu \cite{n4} who proved the existence of ``superadiabatic evolution operators,'' {\it i.e.}, exponentially accurate approximations of the evolution generated by (\ref{schro}).
		Exponential accuracy of the adiabatic theorem was also tackled using powerful pseudo-differential operator techniques by Sj\"ostrand \cite{sj} and by Martinez \cite{m} who studied the exponential decay rate of the transition probability as a function of the parameters of the problem using this method.
	www.ma.utexas.edu /mp_arc/papers/01-288 (2847 words)

	Macroscopic: Adiabatic and diabatic states in the Born-Oppenheimer approximation = MACRO-m3c-diab
		In order to describe the forces, defined by the states of the valence electrons, the states have to be given in an appropriate representation: adiabatic or a diabatic.
		This approximation, which is also known as the adiabatic approximation, is based on the enormous mass difference between light and therefore very mobile, electrons, and the heavy slow nuclei.
		With this representation in the adiabatic states, equation 0.11 for the nuclear motion reduces to
	www.science.uva.nl /projects/commphys/papers/thesisfh/MESO/MAm3c_diab.html (639 words)

	Adiabatic and Diabatic Surfaces - Potential Energy Surfaces
		Avoided crossings are typical of adiabatic surfaces and arise because the adiabatic electronic states corresponding to the surfaces are often mixtures of two simple molecular orbital (i.e., covalent) or valence bond (i.e., ionic) electronic structures (cf.
		If the nuclei have sufficient velocity, then the Born-Oppenheimer approximation breaks down and the nuclei may effectively “ignore” the gap in the avoided crossing and simply cross over to the other adiabatic surface, adopting that configuration.
		Adiabatic surfaces are shown in (a), the diabatic diagonal elements H
	www.chm.bris.ac.uk /webprojects2002/grant/webcomp/a-diabatic.html (249 words)

	How good is the frozen-halo approximation when there is core absorption ? (Site not responding. Last check: 2007-10-26)
		Qualitative estimates for the range validity of the adiabatic approximation have been obtained [2], which take into consideration the mean breakup energies of the projectile that contribute to the elastic scattering.
		Explicit expressions have been obtained [3] for the leading non-adiabatic corrections to the elastic scattering matrix in a model in which the interaction of the valence nucleons with the target is neglected.
		We derive a new estimate for the accuracy of the adiabatic approximation when the valence-target interaction is neglected and there is strong core absorption.
	www.ph.surrey.ac.uk /scnp/talks/halo02/summers (317 words)

	Moshe Shapiro's Group Home Page (Site not responding. Last check: 2007-10-26)
		The slowly varying continuum approximation (SVCA) leading to ''direct" dissociation is considered first, and criteria for its range of validity are established.
		Next, the primitive WKB approximation and the Uniform WKB approximation are discussed.
		The matrix describing the system is diagonalized for all times; the approximation holds if the diagonalizing matrix is slowly varying with time.
	www.weizmann.ac.il /chemphys/Shapiro_group/cr-above.html (347 words)

	Plasma theories [Oulu]
		In addition, a very useful approximate way to describe the dynamics of a plasma is to consider that the motions of the plasma particles are governed by the applied external fields plus the macroscopic average internal fields, smoothed in space and time, due to presence and motion of all plasma particles.
		Because the thermal conductivity is thus zero, the plasma is non-viscous and, consequently, the non-diagonal terms of the pressure dyad are all equal to zero.
		The energy equation reduces to the adiabatic equation (warm plasma model is also called the adiabatic approximation).
	www.oulu.fi /~spaceweb/textbook/theories.html (988 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		We propose a new complete adiabatic approximant constructed from the energy and flux functions so that, effectively the approximation corresponds to the dynamics where there are no missing post-Newtonian terms in the acceleration.
		We compare the overlaps of the standard and complete adiabatic templates with the exact waveform in the adiabatic approximation of a test-mass motion in the Schwarzschild spacetime for the LIGO VIRGO and the Advanced LIGO noise spectra.
		It is found that the complete adiabatic approximants lead to a remarkable improvement in the effectualness at PN order smaller than 3PN, while standard approximants of order greater or equal to than 3PN perform as well as the complete approximants for the construction of effectual templates.
	www.iap.fr /ActivitesScientifiques/SeminairesEtColloques/SeminairesGRECO/2005/iyer.html (222 words)

	Post adiabatic atomic dynamics -- speculations for future work (Site not responding. Last check: 2007-10-26)
		The calculations and discussion of the preceding sections has been based on the adiabatic approximation (that the electrons are always in their instantaneous ground state determined by the external potential (eg the atomic nuclei), and that the forces ``felt" by the nuclei arose from the instantaneous electronic structure of the system.
		This approach was formulated to model the dynamical response of a system to light (in which the simplest model of light-solid interactions would just involve promotions of electrons to low-lying conduction states), but the formalism is similar (and much simpler) for the case of purely phonon-induced level crossings as in our problem.
		It is possible in fact that the adiabatic approximation may often be satisfactory for this kind of problem, but the question has not yet been properly investigated because of difficulties with post-adiabatic calculations.
	www.phy.ohiou.edu /~drabold/serge/node62.html (425 words)

	mca-adiabatic (Site not responding. Last check: 2007-10-26)
		Its basic use in physics is to simplify complex analyses by justifying the neglect of certain possible (but hard to calculate) interactions as being almost certainly too small to make a noticeable difference in the final answer (the adiabatic approximation).
		Moreover, and this goes beyond and adds to the separability of timescales guaranteed by the adiabatic principle, we are buffered from fast, small-scale events, like ionization of individual atoms in our bodies or even errors in gene transcription, by longer term regulatory and self-correcting processes typical of the intermediate scales of autopoietic or self-organizing systems.
		The adiabatic principle has exceptions, and one of these is fundamental to human social organization.
	www-personal.umich.edu /~jaylemke/webs/time/mca-adiabatic.htm (485 words)

	Theses from Uppsala University : 5893 - Open Quantum Systems
		The effects of open system evolution on single particle interferometry, quantum computation, and the adiabatic approximation are investigated.
		In both the global and local search case the asymptotic time-complexity of the ideal closed case is preserved, as long as the Hamiltonian dynamics is present.
		Adiabatic evolution: We generalize the adiabatic approximation to the case of open quantum systems in the joint limit of slow change and weak open system disturbances.
	publications.uu.se /theses/abstract.xsql?dbid=5893 (491 words)

	WebCalendar (Site not responding. Last check: 2007-10-26)
		Description: Abstract: The standard adiabatic approximation to phasing of gravitational waves from inspiralling compact binaries uses the post-Newtonian expansions of the binding energy and gravitational wave flux both truncated at the same relative post-Newtonian order.
		Motivated by the eventual need to go beyond the adiabatic approximation we must view the problem as the dynamics of the binary under conservative post-Newtonian forces and gravitational radiation damping.
		We compare the overlaps of the standard and complete adiabatic approximant templates with the exact waveforms (in the adiabatic approximation) for a test-particle orbiting a Schwarzschild fl hole.
	www.jncasr.ac.in /Basc/day.php?date=20050119 (233 words)

	JCE 2001 (78) 401 [Mar] Investigating the Adiabatic Approximation in Quantum Mechanics through the Analysis of Two ...
		The nature of the adiabatic approximation is investigated.
		This approximation is at the center of the Born-Oppenheimer approximation, commonly employed in the construction of molecular potentials.
		Next, a numerical and analytical application of the adiabatic approximation to systems comprising two coupled harmonic oscillators is described.
	jchemed.chem.wisc.edu /Journal/issues/2001/Mar/abs401.html (274 words)

	non-adiabatic transitions, outline
		In a zero-order approximation, nuclei in a molecule may be considered as "frozen", and diagonalization of the electronic Hamiltonian yields a set of corresponding eigenvalues, which depend parametrically on the (fixed) positions of nuclei, and are frequently called the adiabatic potential energy surface (PES).
		It may, however, be violated when the energy splitting between adiabatic PESs are comparable to or smaller than the corresponding non-adiabatic couplings, and, therefore, the latter cannot be accounted perturbatively.
		However, the separate consideration of adiabatic dynamics and non-adiabatic transitions is of limited use for reactions in condensed phase.
	www.mpibpc.gwdg.de /groups/troe/neufeld/outline2.html (993 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		The small parameter that governs the approximation is the usual Born--Oppenheimer expansion parameter $\epsilon$, where $\epsilon^4$ is the ratio of the electron mass divided by the mean nuclear mass.
		The approximate solutions we construct agree with exact solutions up to errors whose norms are bounded by $\ds C\,\exp\left(\,-\gamma/\epsilon^2\,\right)$, for some $C$ and $\gamma>0$, under analyticity assumptions on the electron Hamiltonian.
		We estimate adiabatic error terms by using Nenciu's approach in the $w$ variable and Cauchy estimates in the $t$ variable.
	www.ma.utexas.edu /mp_arc/papers/00-209 (4320 words)

	Writing a scientific document
		However the authors have forgotten to include a very valuable piece of information, which was the value of the measured formation rate, being two orders of magnitude larger than the theoretical prediction.
		The Coulomb capture of negative muons by hydrogen atoms in the non-adiabatic close-coupling approximation
		We present some results obtained within the non-adiabatic close-coupling approximation for Coulomb capture during collisions of slow negative muons with hydrogen atoms.
	clio.neutron.kth.se /phd_program/Manual.html (1490 words)

	Many Body 1 (Site not responding. Last check: 2007-10-26)
		However, the adiabatic apporximation can be violated leading to decoherence, and with very important consequences in physics, chemistry and biology.
		The corresponding approximate evolution equations, going beyond the traditional Born-Oppenheimer approximation, have been been derived rigorously only recently, the relevance of QC is by no means limited to the biological applications.
		The effective one particle states are known as quasi-particles, and the main approximation method is known by its acronym GWA.
	www.tcd.ie /Physics/People/Donal.MacKernan/Many_Body_1.html (888 words)

	[No title]
		] The approximation that the pressure and density of gas in a star are related by the adiabatic law.
		] A plot of the speed of sound as a function of the speed of flow for the adiabatic flow of a gas, which forms one quadrant of an ellipse.
		The final and initial temperature in an adiabatic, Carnot cycle.
	www.accessscience.com /Dictionary/A/A11/DictA11.html (2036 words)

	Monte Carlo hyperspherical description of cluster excited states
		Though a variety of approaches can be used to calculate ground state properties, widely applicable methods for the calculation of excited state energies and wave functions of many-body systems are still lacking.
		The J=0 many-body Schrödinger equation for the nuclear coordinates is solved numerically by combining Monte Carlo methods with the adiabatic hyperspherical approximation.
		Adopting the adiabatic approximation is motivated by the following two main arguments.
	jrm.phys.ksu.edu /Data/abstracts/Monte_Carlo_hyperspherical_description_of_cluster_excited_states.html (672 words)

	[No title]
		Our analysis shows that the double detector array is insufficient to provide the photon counting capability for effective nondeterministic nonlinear transformations, and we determine the gate fidelity for both photon counting methods as a function of detector efficiencies.
		For this reason, approximations are used to simulate the master equation which are more numerically tractable to solve.
		This paper analyses four approximations: The standard adiabatic approximation; a more sophisticated adiabatic approximation (not used before); a secular approximation; and a fully quantum dressed-state approximation.
	www.physics.uq.edu.au /qonews/010502.txt (1314 words)

	PJCh - Vol. 72 No. 7S, 1998 - pp 1283-1869
		The linear energy deposition, or stopping power, of materials for swift ions is determined, at the level of the first Born approximation, by the generalized oscillator strength distribution of the target.
		Adiabatic separations of the vibrational motions are used to simplify the calculation of the bound and quasi-bound levels close to the dissociation limit.
		We have approximately determined the radius of convergence of the Amos-Musher perturbation theory applied to the hydrogen molecule at nuclear separations ranging from 3 to 12 bohr.
	malina.ichf.edu.pl /pjch/pj-1998/pj07s98.htm (7183 words)

	George A. Hagedorn
		Hagedorn and Robinson: Approximate Rydberg States of the Hydrogen Atom that are Concentrated near Kepler Orbits.
		Hagedorn and Joye: Elementary Exponential Error Estimates for the Adiabatic Approximation.
		Hagedorn, Rousse, and Jilcott: The AC Stark Effect, Time-Independent Born-Oppenheimer Approximation, and Franck-Condon Factors.
	www.math.vt.edu /people/hagedorn (306 words)

	A
		adiabatic capture + global centrifugal sudden approximation (theory for association and ion-molecule reactions without energetic barriers) - T. Stoecklin, C.E. Dateo, and D.C. Clary, J.
		adiabatic capture + partial centrifugal sudden approximation (theory for association and ion-molecule reactions without energetic barriers) - T. Stoecklin, C.E. Dateo, and D.C. Clary, J.
		(1) asymptotic distorted wave (2) (rotationally-)adiabatic-distorted-wave (approximation for reactive scattering calculations) - J.N.L. Connor, in The Theory of Chemical Reaction Dynamics, edited by D.C. Clary, (D. Reidel, Dordrecht, 1986), p.
	www.iupac.org /reports/1996/6802brown/a.html (658 words)

	Self-Consistent Proteomic Field Theory of Stochastic Gene Switches -- Walczak et al. 88 (2): 828 -- Biophysical Journal
		The self-consistent approximation is a crude one, since in the
		prove to be a poor approximation to describe the state of the
		Comparison of probability distributions obtained by exactly solving the steady-state equations in the SCPF approximations with analogous Poissonian distributions (C and D).
	www.biophysj.org /cgi/content/full/88/2/828 (7272 words)

	Additional Publications of Sigurd Y. Larsen (Site not responding. Last check: 2007-10-26)
		I. adiabatic effective potentials for three particles with delta-function interactions", W. Gibson, S.
		"Asymptotic behavior of the eigenpotentials in the hyperspherical adiabatic approximation", M. Fabre de la Ripelle and S.
		"Behaviour of adiabatic potentials in the scattering of three particles", A. Klemm and S.
	www.temple.edu /physics/faculty/larsen_p2.html (318 words)

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