Adiabatic theorem for the time-dependent wave operator

Viennot, David; Jolicard, Georges; Killingbeck, J; Perrin, Marie‐Yvonne

doi:10.1103/physreva.71.052706

Cited by 8 publications

(11 citation statements)

References 22 publications

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“…The important fact is that the Berry phenomenon involves two ingredients, the time-dependent projector P (t) sited in the base space, and the time-dependent phase (or unitary matrix) associated with the horizontal lift sited in the total space of the bundle. In [8] we proved that the wave operator is a succession of instantaneous Bloch wave operators at the adiabatic limit, demonstrating in this way that the wave operator is rigorously related to spectral projectors at the adiabatic limit. This result is related to the behaviour of the wave operator treatment in the projector space, but it does not elucidate the relationship between the wave operator and the Berry phase.…”

Section: Introductionmentioning

confidence: 65%

“…U T (s) is the evolution operator and T (s) = U T (s)(P (0)U T (s)P (0)) −1 is the time-dependent wave operator. The conjectured result (12) was actually later demonstrated (in [8]). This expression reveals that the adiabatic limit of the wave operator is a pure stationary operator without any rapid phase terms, by contrast with the equivalent adiabatic limit of the wavefunction, which includes both dynamical and Berry phases.…”

Section: A Review Of the Wave Operator Theorymentioning

confidence: 70%

“…The efficiency of the wave operator theory for the description of adiabatic processes has been revealed in a previous paper [8], which introduced an adiabatic theorem for the timedependent wave operator. This theorem identifies the adiabatic active subspace at t = 0 with the wave operator active subspace.…”

Section: Introductionmentioning

confidence: 99%

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Berry phase and time-dependent wave operators

Viennot¹,

Jolicard²,

Killingbeck³

2006

J. Phys. A: Math. Gen.

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The present paper analyses the relation between the theory of the timedependent wave operator and the Berry phase concept. It is proved that the wave operator approach is consistent with the non-adiabatic (Aharonov-Anandan) Berry phase, given that the wave operator and the parallel transport commute. It is then demonstrated that the non-Abelian Aharonov-Anandan phase can be calculated by working inside a reduced active space in the framework of wave operator theory. Finally an adiabatic transport formula is derived in the wave operator context and the influence of this effective Hamiltonian theory on the Berry phase is analysed. The theoretical results concerning the non-adiabatic Berry phase are confirmed numerically by considering a photodissociation process in the framework of the generalized Floquet theory.

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Section: Introductionmentioning

confidence: 65%

Section: A Review Of the Wave Operator Theorymentioning

confidence: 70%

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Berry phase and time-dependent wave operators

Viennot¹,

Jolicard²,

Killingbeck³

2006

J. Phys. A: Math. Gen.

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“…A direct consequence is that the adiabatic limit of the time-dependent wave operator is given by a succession of instantaneous Bloch wave operators 31 .…”

Section: Stationary and Dynamic Treatments For Adiabatic Processementioning

confidence: 99%

Constrained adiabatic trajectory method: A global integrator for explicitly time-dependent Hamiltonians

Leclerc

Jolicard

Viennot

et al. 2012

The Journal of Chemical Physics

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The constrained adiabatic trajectory method (CATM) is reexamined as an integrator for the Schrödinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent or explicitly time-dependent Hamiltonians. The emphasis is put on adiabatic processes and within this adiabatic framework the interdependence between the CATM, the wave operator, the Floquet, and the (t, t') theories is presented in detail. Two points are then more particularly analyzed and illustrated by a numerical calculation describing the H(2)(+) ion submitted to a laser pulse. The first point is the ability of the CATM to dilate the Hamiltonian spectrum and thus to make the perturbative treatment of the equations defining the wave function possible, possibly by using a Krylov subspace approach as a complement. The second point is the ability of the CATM to handle extremely complex time-dependencies, such as those which appear when interaction representations are used to integrate the system.

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“…The eigenstates evolve periodically in time with frequency   . The wave packet consists of a linear combination of stationary vibrational states with energy proportional to n i e  , where t    , and n  is the associated vibrational eigenvalue [47,48]. Tuning the chirp parameter allows us to control the angular momentum of the wave packet and thus its deconstructive interference and transport through a conical intersection.…”

Section: Introductionmentioning

confidence: 99%

Molecular level crossing and the geometric phase effect from the optical Hanle perspective

Glenn

Dantus²

2016

Phys. Rev. A

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Level-crossing spectroscopy involves lifting the degeneracy of an excited state and using the interference of two nearly degenerate levels to measure the excited state lifetime. Here we use the idea of interference between different pathways to study the momentum-dependent wave packet lifetime due an excited state level-crossing (conical intersection) in a molecule. Changes in population from the wave packet propagation are reflected in the detected fluorescence. We use a chirped pulse to control the wave packet momentum. Changing the chirp rate affects the transition to the lower state through the conical intersection. It also affects the interference of different pathways in the upper electronic state, due to the geometric phase acquired. Increasing the chirp rate decreases the coherence of the wave packet in the upper electronic state. This suggests that there is a finite momentum dependent lifetime of the wave packet through the level-crossing as function of chirp. We dub this lifetime the wave packet momentum lifetime. : 33.15.Hp, 32.50.+d, 33.80.Be, 78.20.Bh, 42.65.Re ( b ). When both levels are nearly degenerate and excited simultaneously, the fluorescence is proportional to   2 ab AA  . Resonance occurs when the magnetic field is zero and increasing the magnetic field strength partially destroys the coherence. Thus, the absolute radiative lifetime can be measured by detecting the fluorescence as a function magnetic field strength, without any knowledge of the density of the emitters [13]. Electronic level-crossings (conical intersections) occur in nearly all molecules and are responsible for many excitedstate chemical processes [2][3][4][14][15][16]. The isomerization PACS

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Adiabatic theorem for the time-dependent wave operator

Cited by 8 publications

References 22 publications

Berry phase and time-dependent wave operators

Berry phase and time-dependent wave operators

Constrained adiabatic trajectory method: A global integrator for explicitly time-dependent Hamiltonians

Molecular level crossing and the geometric phase effect from the optical Hanle perspective

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