Related papers: Topological phase effects
Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc.…
One milestone in quantum physics is Berry's seminal work [Proc.~R.~Soc.~Lond.~A \textbf{392}, 45 (1984)], in which a quantal phase factor known as geometric phase was discovered to solely depend on the evolution path in state space. Here,…
A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…
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…
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…
The evolution of a quantum system is governed by the associated Hamiltonian. A system defined by a parameter-dependent Hamiltonian acquires a geometric phase when adiabatically evolved. Such an adiabatic evolution of a system having…
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection…
By analyzing the vectorial Helmholtz equation within the thin-layer approach, we find that light acquires a novel geometrical phase, in addition to the usual one (the optical Berry phase), during the propagation along a curved path. Unlike…
The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not…
Garrison and Wright showed that upon undergoing cyclic quantum evolution a meta-stable state acquires both a geometric phase and a geometric decay probability. This is described by a complex geometric ``phase'' associated with the cyclic…
The second quantized approach to geometric phases is reviewed. The second quantization generally induces a hidden local (time-dependent) gauge symmetry. This gauge symmetry defines the parallel transport and holonomy, and thus it controls…
We investigate the geometric phase or Berry phase of adiabatic quantum evolution in the Bose-Einstein condensate (BEC) systems governed by nonlinear Gross-Pitaevskii(GP) equations. We study how this phase is modified by the nonlinearity and…
The state of a quantum system acquires a phase factor, called the geometric phase, when taken around a closed trajectory in the parameter space, which depends only on the geometry of the parameter space. Due to its sensitive nature, the…
We investigate the geometric phase or Berry phase of adiabatic quantum evolution in an atom-molecule conversion system, and find that the Berry phase in such system consists of two parts: the usual Berry connection term and a novel term…
Quantum mechanical phases arising from a periodically varying Hamiltonian are considered. These phases are derived from the eigenvalues of a stationary, ``dressed'' Hamiltonian that is able to treat internal atomic or molecular structure in…
Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase…
In quantum mechanics, a quantum wavepacket may acquire a geometrical phase as it evolves along a cyclic trajectory in parameter space. In condensed matter systems, the Berry phase plays a crucial role in fundamental phenomena such as the…
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…