Related papers: Geometric phases in discrete dynamical systems
High-fidelity quantum operations are a key requirement for fault-tolerant quantum information processing. In electron spin resonance, manipulation of the quantum spin is usually achieved with time-dependent microwave fields. In contrast to…
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…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
We study the geometric phase phenomenon in the context of the adiabatic Floquet theory (the so-called the $(t,t')$ Floquet theory). A double integration appears in the geometric phase formula because of the presence of two time variables…
We introduce the non-adiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how it could be implemented with superconducting charge qubits. While it may circumvent many of the drawbacks related to the…
We show that the definition of instantaneous eigenstate populations for a dynamical non-self-adjoint system is not obvious. The naive direct extension of the definition used for the self-adjoint case leads to inconsistencies; the resulting…
The geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schr\"{o}dinger equation. Fast oscillations are found in the non-adiabatic case. For parameter values such that the…
The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…
We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
This study explores the integration of a diffusion control parameter into the chaotic dynamics of a modified bouncing ball model. By extending beyond simple elastic collisions, the model introduces elements that affect the diffusive…
A magnetically trapped atom experiences an adiabatic geometric (Berry's) phase due to changing field direction. We investigate theoretically such an Aharonov-Bohm-like geometric phase for atoms adiabatically moving inside a storage ring as…
We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in…
Ab initio modeling of conical intersection dynamics is crucial for various photochemical, photophysical, and biological processes. However, adiabatic electronic states obtained from electronic structure computations involve random phases,…
The geometric phase acquired by the vector states under an adiabatic evolution along a noncyclic path can be calculated correctly in any instantaneous basis of a Hamiltonian that varies in time due to a time-dependent classical field.
We give sufficient conditions for asymptotic stabilization of equilibrium points and periodic orbits of a dynamical system when we add a geometric dissipation of gradient type. We also describe the domain of attraction in the case of…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a…
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled…