Temperature is a quantum operator

(with Dr. Dervis Can Vural) 

S. Ghonge and D. C. Vural, J. Stat. Mech. (2018)

We proposed a thought experiment to argue that temperature must be a quantum observable and explored the theoretical and experimental consequences of this proposition.

I have written an expository article about it here: Temperature operator in quantum mechanics.

Uncovering the structure of networks

(with Dr. Dervis Vural)

S. Ghonge and D. C. Vural, Phys. Rev. E. (2017)

All our decisions and choices are affected by external factors such as advertising campaigns, opinions of our friends, or choices of the people who we admire. Innovations such as new software, new medicines or novel technologies also spread similarly. 

Often one can see processes, such as people making decisions or parts of machines failing, but we cannot see the underlying social or physical networks which lead to these phenomena.

In this work, we developed methods to infer the structure of a network by observing such processes taking place on it.

By observing when people adopt certain ideas, we can determine what social exchanges led to it. For example, we could very accurately determine which doctor is friends with which doctor only by observing when they started prescribing new drugs.

Invertibility of the almost Mathieu operator

With Dr. S. Sivananthan

The almost Mathieu operator is a tridiagonal operator, which appears as the Hamiltonian in the study of quantum Hall effect. Various studies of the measure and topology of its spectrum have been done and very interesting properties were found. However, its invertibility is still unknown.