Tuesday, March 30, 2010

An equation you should know

Next month I am going to India to speak at a School and Conference on “Emergent Properties and Novel Behavior at the Nanoscale” organised by I2CAM and the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR) in Bangalore.

In the school I will give a one hour long lecture. Here is the abstract I have submitted. Any feedback welcome. Some related material is discussed in this talk I gave last year in the Black Forest.

Quantum design principles for functional electronic materials

In a complex material how does one optimise the quantum efficiency of the transition
between two different quantum states when there are many alternative transitions available to a system?

Regardless of whether or not it is explicitly stated this is the question which is at the heart of a wide range of research. Prominent examples include understanding biomolecular function, designing organic photovoltaic cells, and catalysis.

I will discuss how this optimisation problem involves a subtle interplay between quantum coherence and decoherence induced by the system environment. The essential physics involved can be understood in terms of the spin-boson model which describes two quantum states which are coupled to one another with an environment which is modelled by a collection of an infinite number of harmonic oscillators.

Qualitatively different dynamics occurs depending on the relative magnitude of the key energy and time scales in the problem: the thermal energy, energy difference between the two states (epsilon), the coupling of the two states (and the associated Rabi frequency), the reorganisation energy of the environment, and the typical relaxation time of the environment.

Perhaps it is not appreciated enough that for most systems of interest all of these energy scales are well-characterised.

The incoherent "classical" regime of the spin-boson model gives a simple expression for the transition rate which is the same as the Marcus-Hush expression for the electron-transfer rate. I consider this is one of the most important equations in chemical physics and particularly for the understanding and design of functional materials.

I will discuss several important applications of this equation.

1) A design principle:
The rate is a maximum for a specific non-zero value of the coupling to the environment where epsilon equals the reorganisation energy.

2) The temperature dependence of the charge mobility in molecular materials.
[This is the same expression as given by small polaron theory].

3) Forster resonant energy transfer between chromophores.

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