Related papers: Eigenvalue and eigenspace anholonomies in hierarch…
In several situations, most notably when describing metastable states, a system can evolve according to an effective non hermitian Hamiltonian. To each eigenvalue of a non hermitian Hamiltonian is associated an eigenstate $\vert\phi\rangle$…
In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $\Lambda$ three-level system. They further…
A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a…
Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum…
The design of quantum control methods has been shown to greatly improve the performance of many evolving quantum technologies. To this end, the usage of adiabatic dynamics to drive quantum systems is seriously limited by the action of…
The anomalous dynamical evolution and the crossing of nonadiabatic energy levels are investigated for exactly solvable time-dependent quantum systems through a reverse-engineering scheme. By exploiting a typical driven model, we elucidate…
The adiabatic theorem states that if we prepare a quantum system in one of the instantaneous eigenstates then the quantum number is an adiabatic invariant and the state at a later time is equivalent to the instantaneous eigenstate at that…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process…
We apply the method of moving anholonomic frames in order to construct new classes of solutions of the Einstein equations on (2+1)-dimensional pseudo-Riemannian spaces. There are investigated black holes with deformed horizons and…
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…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
Transition amplitudes between instantaneous eigenstates of quantum two-level system are evaluated analytically on the basis of a new parametrization of its evolution operator, which has recently been proposed to construct exact solutions.…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…
The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…
Eigenvectors of decaying quantum systems are studied at exceptional points of the Hamiltonian. Special attention is paid to the properties of the system under time reversal symmetry breaking. At the exceptional point the chiral character of…
We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum…