Adiabatic theorem without a gap condition
Joseph E. Avron,Alexander Elgart +1 more
Reads0
Chats0
TLDR
In this paper, it was shown that the adiabatic theorem holds for the ground state of atoms in quantized radiation field without the traditional gap condition, and that the general result gives no information on the rate at which the adabiabatic limit is approached, but with additional spectral information one can also estimate this rate.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 spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate.read more
Citations
More filters
Journal ArticleDOI
Adiabatic quantum computation
Tameem Albash,Daniel A. Lidar +1 more
TL;DR: In this paper, the equivalence of the adiabatic and circuit models of quantum computation has been proved, and the placement of quantum computations in the more general classification of computational complexity theory is discussed.
Journal ArticleDOI
Nonequilibrium dynamical mean-field theory and its applications
TL;DR: In this paper, the authors discuss the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit.
Journal ArticleDOI
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
TL;DR: It is suggested that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent and this result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions.
Book
Adiabatic perturbation theory in quantum dynamics
TL;DR: First-order adiabatic theory and space-adiabatic perturbation theory were studied in this article, where the Weyl calculus for tau-equivariant symbols is used.
Proceedings ArticleDOI
Adiabatic quantum state generation and statistical zero knowledge
Dorit Aharonov,Amnon Ta-Shma +1 more
TL;DR: Adiabatic state generation (ASG) as mentioned in this paper is a quantum state generation approach based on Hamiltonians instead of unitary gates, which is equivalent in power to state generation in the standard quantum model.
References
More filters
Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Journal ArticleDOI
Quantal phase factors accompanying adiabatic changes
TL;DR: In this article, it was shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor and a general formula for γ(C) was derived in terms of the spectrum and eigen states of the Hamiltonian over a surface spanning C.
Book ChapterDOI
Quantum Mechanics of One- and Two-Electron Atoms
Hans A. Bethe,Edwin E. Salpeter +1 more
TL;DR: The theory of atoms with one or two electrons is the simplest and most completely treated field of application of quantum mechanics as mentioned in this paper, and it is one of the simplest fields of application for quantum mechanics.