arXiv subjects

Biswash Ghimire

Publications and source records attributed to Biswash Ghimire.

2 recordsLinked to original sources

arXiv2022

Quantum Grid States and Hybrid Graphs

Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement properties of grid states are adapted to these interpretations. These additional classes of grid states are shown to exhibit rich entanglement properties, including bound entanglement. Further, we introduce graphical techniques to construct bound entangled states in a modular fashion. We also extend the grid states model to hypergraphs. Our work, on one hand, opens up possibilities for constructing additional families of mixed quantum states in the grid state model. On the other hand, it can serve as an instrument for investigating entanglement problems from a graph theory perspective.

quant-ph↗

arXiv2014

Edge Corrections to Electromagnetic Casimir Energies From General-Purpose Mathieu Function Routines

Scattering theory methods make it possible to calculate the Casimir energy of a perfectly conducting elliptic cylinder opposite a perfectly conducting plane in terms of Mathieu functions. In the limit of zero radius, the elliptic cylinder becomes a finite-width strip, which allows for the study of edge effects. However, existing packages for computing Mathieu functions are insufficient for this calculation, because none can compute Mathieu functions of both the first and second kind for complex arguments. To address this shortcoming, we have written a general purpose Mathieu function package, based on algorithms developed by Alhargan [1,2]. We use these routines to find edge corrections to the proximity force approximation for the Casimir energy of a perfectly conducting strip opposite a perfectly conducting plane.

quant-ph↗