Related papers: Modular chaos, operator algebras, and the Berry ph…
We introduce a class of topological pairing orders characterized by a half-integer pair monopole charge, leading to Berry phase enforced half-integer partial wave symmetry. This exotic spinor order emerges from pairing between Fermi…
Topological wave-packet dynamics provide a powerful framework for studying quantum transport in topological materials. However, extending this approach to non-Hermitian quantum systems presents several important challenges, primarily due to…
Majorana stars, the antipodal directions associated with the coherent states that are orthogonal to a spin state, provide a visualization and a geometric understanding of the structures of general quantum states. For example, the Berry…
The exploration of the Berry phase in classical mechanics has opened new frontiers in understanding the dynamics of physical systems, analogous to quantum mechanics. Here, we show controlled accumulation of the Berry phase in a two-level…
Taking resort to Haldane's spherical geometry we can visualize fractional quantum Hall effect on the noncommutative manifold $M_4 \times Z_N$ with $N>2$ and odd. The discrete space leads to the deformation of symplectic structure of the…
The Berry phase is a geometric phase acquired during adiabatic evolution over a closed loop in parameter space. It plays an essential role in geometric quantum gates and other phase-based protocols. In non-Hermitian systems, the Berry phase…
Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators.…
We present a reformulation of quantum adiabatic theory in terms of an emergent electromagnetic framework, emphasizing the physical consequences of geometric structures in parameter space. Contrary to conventional approaches, we demonstrate…
We consider the quantum mechanical notion of the geometrical (Berry) phase in SU(2) gauge theory, both in the continuum and on the lattice. It is shown that in the coherent state basis eigenvalues of the Wilson loop operator naturally…
Despite their apparent simplicity, coupled oscillators exhibit surprisingly complex phenomena. Two notable examples are Berry phase (a geometric or topological aspect of the oscillators' memory) and non-Hermiticity (the often…
A binary mixtures of Bose-Einstein condensate structures exhibit an incredible richness in terms of holding different kinds of phases. Depending on the ratio of the inter- and intra-atomic interactions, the transition from mixed to…
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.…
The usual, "static" version of the quantum Zeno effect consists in the hindrance of the evolution of a quantum systems due to repeated measurements. There is however a "dynamic" version of the same phenomenon, first discussed by von Neumann…
Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including…
The canonical commutation relations in quantum mechanics are not maintained in the anomalous Hall effect described by Berry's phase in the presence of the electromagnetic vector potential. To define quantum mechanical formulation, one may…
We derive closed analytical expressions for the complex Berry phase of an open quantum system in a state which is a superposition of resonant states and evolves irreversibly due to the spontaneous decay of the metastable states. The…
In these notes, we review the role of Berry phases and topology in noninteracting electron systems. Topics including the adiabatic theorem, parallel transport, and Wannier functions are reviewed, with a focus on the connection to…
The derivatives of the Berry curvature $\Omega$ and intrinsic orbital magnetic moment m in momentum space are relevant to various problems, including the nonlinear anomalous Hall effect and magneto-transport within the Boltzmann-equation…
We propose the $\mathbb{Z}_Q$ Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases for two- and three-dimensional systems. It is topologically stable for electron-electron interactions…
In this work, we develop a hybrid-order Poincar\'{e} sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincar\'{e} sphere and high-order Poincar\'{e}…