# Adiabatic perturbation theory in quantum dynamics

@inproceedings{Teufel2003AdiabaticPT, title={Adiabatic perturbation theory in quantum dynamics}, author={Stefan Teufel}, year={2003} }

Introduction.- First-order adiabatic theory.- Space-adiabatic perturbation theory.- Applications and extensions.- Quantum dynamics in periodic media.- Adiabatic decoupling without spectral gap.- Pseudodifferential operators.- Operator-valued Weyl calculus for tau-equivariant symbols.- Related approaches.- List of symbols.- References.- Index.

## 363 Citations

Adiabatic Ensemble Control of a Continuum of Quantum Systems

- MathematicsSIAM J. Control. Optim.
- 2018

The technique is based on adiabatic approximation theory and on the presence of curves of conical eigenvalue intersections of the controlled Hamiltonian and shows that the assumptions guaranteeing ensemble controllability are structurally stable with respect to perturbations of the parametrized family of systems.

Appearance of gauge fields and forces beyond the adiabatic approximation

- Physics
- 2010

We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered…

Precise Coupling Terms in Adiabatic Quantum Evolution

- Physics, Mathematics
- 2005

Abstract.It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the…

High-fidelity adiabatic quantum computation via dynamical decoupling

- Physics, Computer Science
- 2012

Numerical results demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding which allows computation to proceed alongside decoupled, can dramatically enhance the fidelity of adiabatic quantum computation in spite of decoherence.

Recent Results on Non--Adiabatic Transitions in Quantum Mechanics

- Physics, Mathematics
- 2005

We review mathematical results concerning exponentially small corrections to adiabatic approximations and Born–Oppenheimer approximations.

Tosio Kato’s work on non-relativistic quantum mechanics: part 1

- Mathematics, Physics
- 2018

We review the work of Tosio Kato on the mathematics of non-relativistic quantum mechanics and some of the research that was motivated by this. Topics in this first part include analytic and…

Ensemble control of parameter-dependent quantum systems by adiabatic evolution

- Physics2017 IEEE 56th Annual Conference on Decision and Control (CDC)
- 2017

This work considers the problem of controlling a parameter-dependent family of quantum systems by a single vector-valued control law by exploiting adiabatic approximation and conically connected spectra for the controlled Hamiltonian and recovers the celebrated counterintuitive solution.

Weakly Nonlinear Time-Adiabatic Theory

- Physics, Mathematics
- 2014

We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schrödinger equations in which either the nonlinear…

Tosio Kato’s work on non-relativistic quantum mechanics: part 2

- Physics
- 2018

We review the work of Tosio Kato on the mathematics of non-relativistic quantum mechanics and some of the research that was motivated by this. Topics in this second part include absence of embedded…

Space-adiabatic perturbation theory

- Physics, Mathematics
- 2002

3.1 Almost invariant subspaces
3.2 Mapping to the reference space
3.3 Effective dynamics
3.3.1 Expanding the effective Hamiltonian
3.4 Semiclassical limit for effective…

## References

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Adiabatic Theorem without a Gap Condition

- Physics, Mathematics
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Abstract:We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional…

Space-adiabatic perturbation theory

- Physics, Mathematics
- 2002

3.1 Almost invariant subspaces
3.2 Mapping to the reference space
3.3 Effective dynamics
3.3.1 Expanding the effective Hamiltonian
3.4 Semiclassical limit for effective…

Superadiabatic evolution and adiabatic transition probability between two nondegenerate levels isolated in the spectrum

- Physics
- 1993

During the last years several theoretical and experimental works have been devoted to different aspects of the adiabatic regime of quantum dynamics. We consider here two aspects of this physically…

Realizing Holonomic Constraints in Classical and Quantum Mechanics

- Mathematics, Physics
- 1999

Abstract: We consider the problem of constraining a particle to a smooth compact submanifold Σ of configuration space using a sequence of increasing potentials. We compare the classical and quantum…

Precise Coupling Terms in Adiabatic Quantum Evolution: The Generic Case

- Physics
- 2005

For multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. Based on…