Related papers: Is the Adiabatic Approximation Inconsistent?
The strategy of shortcuts to adiabaticity enables us to realize adiabatic dynamics in finite time. In the counter-diabatic driving approach, an auxiliary Hamiltonian which is called the counter-diabatic Hamiltonian is appended to an…
Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a…
The adiabatic theorem is a fundamental result established in the early days of quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time…
We consider the electrons of a molecule in the adiabatic time-dependent density functional theory approximation. We establish the well-posedness of the time evolution and its linear response close to a non-degenerate ground state, and prove…
Recently, some quantum algorithms have been implemented by quantum adiabatic evolutions. In this paper, we discuss the accurate relation between the running time and the distance of the initial state and the final state of a kind of quantum…
We prove an adiabatic theorem for general densities of observables that are sums of local terms in finite systems of interacting fermions, without periodicity assumptions on the Hamiltonian and with error estimates that are uniform in the…
We consider a time-dependent small quantum system weakly coupled to an environnement, whose effective dynamics we address by means of a Lindblad equation. We assume the Hamiltonian part of the Lindbladian is slowly varying in time and the…
Artificial interface conditions parametrized by a complex number $\theta_{0}$ are introduced for 1D-Schr\"odinger operators. When this complex parameter equals the parameter $\theta\in i\R$ of the complex deformation which unveils the shape…
We extend the concept of locality to enclose a situation where a tensor-product structure for the Hilbert space is not \textit {a priori} assumed; rather, this locality is related to a given matrix representation of the Hamiltonian…
Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…
The method of adiabatic invariants for time dependent Hamiltonians is applied to a massive scalar field in a de Sitter space-time. The scalar field ground state, its Fock space and coherent states are constructed and related to the particle…
We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
Quantum adiabatic evolution, an important fundamental concept inphysics, describes the dynamical evolution arbitrarily close to the instantaneous eigenstate of a slowly driven Hamiltonian. In most systems undergoing spontaneous…
Adiabatic quantum computing is a powerful framework for state preparation, while its evolution time often scales quadratically in the inverse Hamiltonian spectral gap, leading to sub-optimal computational complexity. In this work, we…
We study the characterization of several distance problems for linear differential-algebraic systems with dissipative Hamiltonian structure. Since all models are only approximations of reality and data are always inaccurate, it is an…
Several misprints and small mistakes were in the initial version. They have been corrected. Following the recent experimental realization of synthetic gauge magnetic forces, Jean Dalibard adressed the question whether the adiabatic ansatz…
We study a nonlinear generalization of the Landau-Zener resonance-crossing problem relevant to coherent photo- and magneto-association of ultracold atoms. Due to the structure of the corresponding classical phase space, the adiabatic…
We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time…
When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion…