Jul 19, 2013
Kubo response theory applied to memristive, memcapacitive and meminductive systems
Memristors, memcapacitors and meminductors – collectively called memelements – are attracting considerable attention from scientists and engineers, but they are also erroneously assumed to be new circuit elements. Using Kubo response theory it can be shown that resistors, capacitors and inductors with memory emerge naturally in the response of systems subjected to external perturbations.
This is even more so in systems of nanoscale dimensions where the dynamics of a few atoms may affect the whole structure dramatically. As such, some degree of memory in the response of the system to external fields is always present. This also shows that ideal resistors, capacitors and inductors are just circuit theory idealizations of actual properties of real systems, being a good representation of such properties only within a range of experimental conditions (for example, within certain intervals of amplitudes and frequencies). It also shows that memristive, memcapacitive and meminductive systems are simply resistors, capacitors and inductors, respectively, whose memory is made more apparent under certain experimental conditions.
In a recent study, researchers in the US demonstrate that memory, whether volatile or non-volatile, is a consequence of the fact that no condensed matter system, which is ultimately comprised of electrons and ions, can respond instantaneously to external perturbations.
Old theories never die
To show this explicitly, Di Ventra and Pershin used a well-known theory that goes back to the 1950s, introduced by Kubo to study the response of a given system to any external perturbation. Using this theory the two scientists highlight the generality of response functions with memory. And, as a simple consequence of this, they find that diverging and non-crossing input–output curves of all memory elements are physically possible in both quantum and classical regimes. For similar reasons, memcapacitances and meminductances can acquire negative values at certain times during dynamics, while memristive systems – being always passive dissipative devices – can only have non-negative values of resistance at any given time.
Don’t be fooled by ideals
When the memristance originates only from the charge that flows through the system (ideal memristors) the situation is even trickier: unavoidable fluctuations will ultimately destroy the memory state – a stochastic catastrophe – the Landauer principle of minimal energy dissipated per logic operation is violated, and some other important limitations hold. This is true for ideal memcapacitors and meminductors as well. All these considerations are very important when one simulates systems and complex circuits with memelements.
The researchers presented their work in the journal Nanotechnology 24 255201
About the author
Massimiliano Di Ventra is professor of physics at the University of California, San Diego. His research interests include the theory of electronic and transport properties of nanoscale systems, non-equilibrium statistical mechanics, DNA sequencing/polymer dynamics in nanochannels, and memory effects in nanostructures for applications in unconventional computing and biophysics. His group's website is http://www.physics.ucsd.edu/~diventra/. Yuriy Pershin is assistant professor at the University of South Carolina and his research interests span broad areas of nanotechnology, including the physics of nanostructures with memory, spintronic, and biophysical properties. More information about his research can be found at http://www.physics.sc.edu/~pershin/.