Related papers: Geometric Phases and Mielnik's Evolution Loops
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…
Many intracellular processes continue to oscillate during the cell cycle. Although it is not well-understood how they are affected by discontinuities in the cellular environment, the general assumption is that oscillations remain robust…
We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over $Z_2$). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study…
Evolution of systems in which Hamiltonians are generators of gauge transformations is a notion that requires more structure than the canonical theory provides. We identify and study this additional structure in the framework of relational…
A monitored quantum system undergoing a cyclic evolution of the parameters governing its Hamiltonian accumulates a geometric phase that depends on the quantum trajectory followed by the system on its evolution. The phase value will be…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting…
We investigate the evolution of a state which is dominated by a finite-dimensional non-Hermitian time-dependent Hamiltonian operator with a nondegenerate spectrum by using a biorthonormal approach. The geometric phase between any two…
In a quantum system initially in the n-th eigenstate, an adiabatic evolution of the Hamiltonian ensures that the system remains in the corresponding instantaneous eigenstate while acquiring a phase factor. This phase has two components: one…
I argue that certain bosonic insulator-superfluid phase transitions as an interaction constant varies are driven by emergent geometric properties of insulating states. The {\em renormalized} chemical potential and distribution of disordered…
Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at…
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…
The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the…
We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution…
We derive an elegant solution for a two-level system evolving adiabatically under the influence of a driving field with a time-dependent phase, which includes open system effects such as dephasing and spontaneous emission. This solution,…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…