A Gauge-Invariant Geometric Phase for Electrons in a One-Dimensional Periodic Lattice

Here the notion of geometric phase acquired by an electron in a one-dimensional periodic lattice as it traverses the Bloch band is carefully studied. Such a geometric phase is useful in characterizing the topological properties and the electric polarization of the periodic system. An expression for this geometric phase was first provided by Zak, in a celebrated work three decades ago. Unfortunately, Zak’s expression suffers from two shortcomings: its value depends upon the choice of origin of the unit cell, and is gauge dependent. Upon careful investigation of the time evolution of the system, here we find that the system displays cyclicity in a generalized sense wherein the physical observables return in the course of evolution, rather than the density matrix. Recognition of this generalized cyclicity paves the way for a correct and consistent expression for the geometric phase in this system, christened as Pancharatnam-Zak phase. Pancharatnam-Zak geometric phase does not suffer from the shortcomings of Zak’s expression, and correctly classifies the Bloch bands of the lattice. A naturally filled band extension of the Pancharatnam-Zak phase is also constructed and studied.

Comprehensive evaluation of key management hierarchies for outsourced data

Key management is an essential component of a cryptographic access control system with a large number of resources.It manages the secret keys assigned to the system entities in such a way that only authorized users can access a resource.Read access control allows read access of a resource by the authorized users and disallows others.An important objective of a key management is to reduce the secret key storage with each authorized user.To this end,there exist two prominent types of key management hierarchy with single key storage per user used for read access control in data outsourcing scenario:user-based and resource-based.In this work,we analyze the two types of hierarchy with respect to static hierarchy characteristics and dynamic operations such as adding or revoking user authorization.Our analysis shows that the resource-based hierarchies can be a better candidate which is not given equal emphasis in the literature.A new heuristic for minimizing the key management hierarchy is introduced that makes it practical in use even for a large number of users and resources.The performance evaluation of dynamic operations such as adding or revoking a user’s read subscription is shown experimentally to support our analytical results.

Comprehensive evaluation of key management hierarchies for outsourced data

Key management is an essential component of a cryptographic access control system with a large number of resources.It manages the secret keys assigned to the system entities in such a way that only authorized users can access a resource.Read access control allows read access of a resource by the authorized users and disallows others.An important objective of a key management is to reduce the secret key storage with each authorized user.To this end,there exist two prominent types of key management hierarchy with single key storage per user used for read access control in data outsourcing scenario:user-based and resource-based.In this work,we analyze the two types of hierarchy with respect to static hierarchy characteristics and dynamic operations such as adding or revoking user authorization.Our analysis shows that the resource-based hierarchies can be a better candidate which is not given equal emphasis in the literature.A new heuristic for minimizing the key management hierarchy is introduced that makes it practical in use even for a large number of users and resources.The performance evaluation of dynamic operations such as adding or revoking a user’s read subscription is shown experimentally to support our analytical results.