Related papers: On the consistency in the adiabatic theorem and qu…
In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this…
We consider the scattering of an atom by a sequence of two near-resonant standing light waves each formed by two running waves with slightly different wave vectors. Due to opposite detunings of the two standing waves and within the rotating…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast…
We introduce the perturbative aspects of noncommutative quantum mechanics. Then we study the Berry's phase in the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics which depend on…
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
Quantum decoherence is of primary importance for relaxation to an equilibrium distribution and, accordingly, for equilibrium processes. We demonstrate how coherence breaking implies evolution to a microcanonical distribution…
We investigate the decoherence effect of a bosonic bath on the Berry phase of a spin-1/2 in a time-dependent magnetic field, without making the Markovian approximation. A two-cycle process resulting in a pure Berry phase is considered. The…
The condition for adiabatic approximation are of basic importance for the applications of the adiabatic theorem. The traditional quantitative condition was found to be necessary but not sufficient, but we do not know its physical meaning…
Finding new phase is a fundamental task in physics. Landau's theory explained the deep connection between symmetry breaking and phase transition commonly occurring in magnetic, superconducting and super uid systems. The discovery of the…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for 3D Hartree type equations with a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is…
In order to understand quantum decoherence of a quantum system due to its interaction with a large system behaving classically, we introduce the concept of adiabatic quantum entanglement based on the Born-Oppenhemeir approximation. In the…
We examine the adiabatic dynamics of a quantum system coupled to a noisy classical control field. A stochastic phase shift is shown to arise in the off-diagonal elements of the system's density matrix which can cause decoherence. We derive…
On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from the electronic structure programs. However, frequently occurring in this representation conical…
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve…
Topological phases emerge as the parameters of a quantum system vary with time. Under the adiabatic approximation, the time dependence can be eliminated, allowing the Berry topological phase to be obtained from a closed trajectory in…
A sharp definition of what "adiabatic" means is given; it is then shown that the time-dependent expectation value of a quantum-mechanical observable in the adiabatic limit can be expressed -- in many cases -- by means of the appropriate…
Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance, yet is often poorly understood. We study the dynamics of a…
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron…