Thursday, May 21, 2015

A novel correspondence between entropy and statistical physics

Exact correspondences between seemingly different concepts play important role in all fields of physics. An example is the fluctuation-dissipation theorem, which states that the linear response of a system to externally applied forces corresponds to the system fluctuations. 

In the last decade, the fluctuation-dissipation theorem has initiated important developments in quantum transport, quantum computation, and other similar phenomenological theories. This theorem can be extended to nonlinear responses and to full counting statistics, giving more extended sets of similar relations. 

The Shannon entropy in quantum physics is considered unphysical, or non-observable, due to its nonlinear dependence on density matrix. So is the generalized Shannon entropy, called Renyi entropies --named after the French Mathematician and Physicist Alfred Renyi

An interesting and non-trivial question is: 
Is there any relation between the flows of entropy and the physical flows? 

The answer to the question, is YES! 

A novel relation is presented in the following research article that is similar to the fluctuation-dissipation theorem in spirit and provides an exact correspondence between the flows of quantum entropy and full counting statistics of energy transfers.

By: Mohammad H. Ansari 


1- Exact correspondence between Renyi quantum entropy flows and physical flows, 
M. H. Ansari and Yu. V. Nazarov,  
To appear in Phys. Rev. B., arXiv:1502.08020

2- Renyi entropy flows from quantum heat engines, 
M. H. Ansari and Yu. V. Nazarov, Phys. Rev. B 91, 104303 (2015) arxiv:1408.3910

Monday, March 16, 2015

We understood how to measure it

A novel correspondence between entropy flow and  statistics of energy exchange was reported in this paper. This is an extension of earlier result by Levitov and Klich on how to measure entropy in systems with charge transfers.
There seems to be an exact correspondence
between Renyi entropy flow
and statistics of energy exchange. 

The situation is fairly similar to the fluctuation-dissipation theorem however the new correspondence links between the Renyi (and Shannon) entropy and physical and measurable quantities.

What is Renyi entropy?
It was proposed by Alfred Renyi in '60s as novel information measures. Shannon entropy is determined from them as an example.

Why measuring entropy? 
Information content in Renyi entropy is a key concept to establish fundamental laws of thermodynamics in small scales. It helps to understand  how to communicate information with quantum devices.

Now between two systems A and B that exchange energy, we understood how to measure the Renyi entropies.

This correspondence can serve as a fundamental approach to study a second law of thermodynamics in quantum scales (if there is any.) 

Friday, February 06, 2015

A simple phenomenology on quasiparticles

Photo: 128 qubit Rainier chip from here
A simple and phenomenological insight about how to calculate the rate of tunneling nonequilibrium quasiparticles in superconducting small islands.

M. H. Ansari, Supercond. Sci. Technol. 28, 045005 (2015).

One always blame quasiparticles for all kinds of experimental noise and poor sample properties, but there is not yet a common understanding how exactly nonequilibrium quasiparticles affect a qubit. This is partly due to lack of experimental resolution, and partly due to lack of theoretical model.

This paper addresses relevant questions for many of the on-going experiments with superconducting qubits.

The main result of this work is summarized in Fig.1c, where a "non-monotonic" behavior of the relaxation rate as function of temperature is presented. This is a consequence of the assumed phenomenological model for non-equilibrium, where a fixed non-equilibrium quasiparticle density leads to a temperature-dependent chemical potential shift, see Eq.(1). The simplicity of the model point to the possible generality of the predicted non-monotonicity.

Want to know a bit more?! Read the abstract here.
An arxiv version in here: arXiv:1303.1453

* A bit of side story:

I remember that the core idea of this work came to me when I was sitting in a ViaRail train in a cold typical Canadian Friday evening of 2013. Inside the train I did simple calculations and surprisingly saw that experimental expectations can be satisfied from simple ideas. A few weeks later the model has become ready. There was, however, a rather long delay in publishing it, which partly comes from strange situations in life. Finally I could manage an update and sent the paper to a professional journal about superconductivity on Sept 2014.

In response I received three reviews that not only helped to improve the text, but also helped to get confidence on my shaking knees when I stand up alone. Thanks Canada!

Wednesday, August 20, 2014

Quantum entropy flows - updated

Non-equilibrium quantum thermodynamics is a quite new fields in physics that surprisingly left  less explored in the last century. Recently this field is becoming active both experimentally and theoretically. 

When interaction occurs between two systems there is a flow of some conserved quantities, such as electric charge, energy etc. between the two.  Shannon entropy (as well as its generalized Renyi entropy) is a conserved quantity in a world made of subsystems A and B.  Owing to this conservation there are finite flows of entropy between A and B.

For the first time we present a consistent derivation of the flows of Shannon and Renyi entropies for a generic quantum heat engine to a probe environment kept in thermal equilibrium. The flows consist of heat flow and fictitious dissipation originating from quantum coherence. 

Rényi entropy flows from quantum heat engines
Mohammad H. Ansari, Yuli V. Nazarov

An update is that paper has been published in Phys. Rev. B 91, 104303 - doi

Tuesday, July 01, 2014

another contribution to quasiparticle poisoning

just appeared on arxiv:1406.7350 in a collaboration that connect people in Sanata Barabra, Waterloo, Kocaeli,  and Delft.

In a flux qubit, the energy spectrum versus magnetic flux must be single hyperbolic, but what is observed usually in practice is double lines.

Cooling down does not help to remove the second line but it helps only a little bit to reduce the gap between the two. Why is this so?

This paper explains that the reason is quasiparticle poisoning in the junction. These quasiparticles have nonequilibrium nature, which at higher temperature turns to the equilibrium one. We propose a detailed theory and exactly extracted the gap from a quasiparticle tunneling theory.

Previously I made 2 more contributions to the theory of qusiparticle tunneling, here arXiv:1211.4745 (published) and arxiv:1303.1453 (recently submitted for publication).

The new preprint is an experimental evidence to the problem.