Related papers: Berry's phase for compact Lie groups
The Berezin quantization on a simply connected homogeneous K\"{a}hler manifold, which is considered as a phase space for a dynamical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic…
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.
The paper aims to spell out the relevance of the Berry phase in view of the question what the minimal mathematical structure is that accounts for all observable quantum phenomena. The question is both of conceptual and of ontological…
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,…
The evolution of a two level system with a slowly varying Hamiltonian, modeled as s spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a…
The presence/absence of a Berry phase depends on the topology of the manifold of dynamical Jahn-Teller potential minima. We describe in detail the relation between these topological properties and the way the lowest two adiabatic potential…
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…
In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic…
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.…
We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases -- both phases are…
In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is…
In 1984 Michael Berry discovered that an isolated eigenstate of an adiabatically changing periodic Hamiltonian $H(t)$ acquires a phase, called the Berry phase. We show that under very general assumptions the adiabatic approximation of the…
It has been recently found that the equations of motion of several semiclassical systems must take into account anomalous velocity terms arising from Berry phase contributions. Those terms are for instance responsible for the spin Hall…
We explore topological transitions in parameter space in order to enable adiabatic passages between regions adiabatically disconnected within a given parameter manifold. To this end, we study the Hamiltonian of two coupled qubits…
The adiabatic evolution of two doubly-degenerate (Kramers) levels is considered. The general five-parameter Hamiltonian describing the system is obtained and shown to be equivalent to one used in the $\Gamma_8 \otimes(\tau_2\oplus\epsilon)$…
We discuss the one-dimensional, general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form…
The Berry connection describes transformations induced by adiabatically varying Hamiltonians. We study how zero modes of the modular Hamiltonian are affected by varying the region that supplies the modular Hamiltonian. In the vacuum of a 2d…
We associate Hamiltonian homological evolutionary vector fields --which are the non-Abelian variational Lie algebroids' differentials-- with Lie algebra-valued zero-curvature representations for partial differential equations.
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…
We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that…