Related papers: Topology hidden behind the breakdown of adiabatici…
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 results from [BeTe1] for special…
A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.
We study feedback control of classical Hamiltonian systems with the controlling parameter varying slowly in time. The control aims to change system's energy. We show that the control problems can be solved with help of an adiabatic…
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…
We give an example of a simple mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. This system is a linearized plane pendulum with…
A $\textit{shortcut to adiabaticity}$ is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
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…
Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field…
By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This…
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic…
In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $t\to \pm \infty$, the transition probabilities between adiabatic states are exponentially small. They are characterized by an…
We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems…
The time evolution of the adiabatic piston problem and the consequences of its stochastic motion are investigated. The model is a one dimensional piston of mass $M$ separating two ideal fluids made of point particles with mass $m\ll M$. For…
Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature…
We consider a periodically driven system where the high-frequency driving protocol consists of a sequence of potentials switched on and off at different instants within a period. We explore the possibility of introducing an adiabatic…
In atomic physics, adiabatic evolution is often used to achieve a robust and efficient population transfer. Many adiabatic schemes have also been implemented in optical waveguide structures. Recently there has been increasing interests in…
We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it…
Recent years have seen a growing interest in topological phases beyond the standard paradigm of gapped, isolated systems. One recent direction is to explore topological features in non-hermitian systems that are commonly used as effective…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…