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# Theoretical Physics at UVM SPS

Theoretical physicists study the mathematical models of physical entities to better describe and predict the phenomena of the surrounding world. Perhaps one of the most famous disciplines of physics (thanks to the works of such people as Einstein, Newton, and Feynman), it is also one of the most daunting. The theoretical physicist has to be both a natural scientist and a mathematician to do his/her job well. Nevertheless, despite its reputation as the most difficult disciplines, it is also the most fulfilling; to be a theoretical physicist, one studies the very fiber of the universe, and the secrets of our existence might be just a few equations away...

Below, you will find some theoretical research topics which SPS members are currently or have been engaged in.

## Nonlinear Fluctuation-Dissipation Theorem Applied to the Classical One-Component Plasma

#### Adviser: Prof. Kenneth Golden

When we introduce an external perturbation to a system (say, a bunch of particles) and wait a long time, we say that the system is in equilibrium. It is not uncommon for physical theorems to consider a system in equilibrium--it is much easier to consider such a calm, unchanging system. However, the real world isn't usually like this--a physical system usually has numerous pokes and prods which drive it out of equilibrium. A common system to consider is a classical one-component plasma, which is simply a collection of N particles with the same charge q in a uniform neutralizing background. Often called a strongly coupled coulomb system, we can introduce a perturbation very easily, by either dropping an external charge into our plasma or by simply marking one of the charges as the perturbation (i.e., by metaphorically "painting it red" and dubbing it the perturbation).

To understand such non-equilibrium plasma systems, one must utilize the fluctuation-dissipation theorem (FDT). An extension of Einstein's theory of Brownian motion as devised by Paul Langevin and later expanded upon by Ryogo Kubo, the FDT link non-equilibrium transport coefficients (density response functions, conductivities, electric susceptibilities, etc.) to equilibrium n-point correlation functions. In other words, we can utilize the FDT to understand non-equilibrium phenomena by examining equilibrium functions. However, a large problem with the conventional FDT is that it only describes the linear response of a system to an external perturbation. In the latter half of the 20th century, Dr. Kenneth Golden, with Dr. Gabor Kalman and Michael Silevitch, devised the nonlinear fluctuation dissipation theorem (NFDT) to describe the nonlinear response of the system.

It is important to note that the NFDT developed by Golden et. al. only goes to quadratic order in the dynamic case and cubic order in the static case. In 2014, Joshuah T. Heath and Prof. Golden expanded upon the original theorem by extending out to quartic order for both the static and quadratic limit. To learn more, visit Joshuah's profile page or click here to see his Bachelor's thesis in mathematics, where he outlines the derivation for the static quartic theorem, in addition to the ansantz of the general, combinatorical static hierarchy.

## Physics of Strained Graphene

#### Advisers: Prof. Valeri Kotov

Sometimes, the most amazing physics can be found in the most unexpected places. Perhaps one of the most amazing physics discoveries in the latter half of the twentieth century, graphene is simply a two-dimensional sheet of graphite--i.e., a one-atom thick sheet of carbon. Though graphene could be grown on top of other materials, it wasn't until 2004, when University of Manchester physicists Andre Geim and Kostya Novoselov extracted single-atom-thick sheets from bulk graphite using micromechanical cleavage (or the "Scotch tape" technique), that the field of graphene research kicked off. This was because of two reasons: 1) Geim and Novoselov's technique of graphene extraction was one of the first efficient, large scale methods of graphene fabrication, and 2) the technique they used provided experimental evidence of the anomalous quantum Hall effect in graphene, a phenomena which told scientists that graphene was home to massless Dirac fermions. Therefore, electrons in graphene can be treated as particles going near the speed of light, even though they move at non-relativistic speeds.

Prof. Kotov's research is concerned mostly with strained multi-layered graphene. Such a system, which is simply just a few graphene layers stacked on top of each other, are particularly interesting due to the fact that they exhibit phenomena unseen in single-layered, such as excitonic condensation, frictional Coulomb drag, or van der Waals interaction. In particular, van der Waals forces (i.e., interactions which are caused by electrical interactions between a pair (or more) of closely-spaced atoms or molecules.) might help us achieve novel quantum engineered devices unseen today. Recently, physics graduate and ex-SPS member Stephen Bristol conducted research in the effects of strain and electron-electron interactions on the van der Waals interaction in a two-layer graphene system. In the research, Stephen analyzed the effects of the van der Waals interaction under multiple axial strains of differing strengths.

## Quantum Sticking at Ultralow Energies

#### Adviser: Prof. Dennis Clougherty

Let's say we have a particle coming from infinity towards a van der Waals interaction--that is, a potential that dips down to a minimum before increasing to infinity as it nears the origin. Note that, at some large distance r from the origin, we have a potential V(r)=0. There is some probability that the particle with stay in the well, and there is some probability that the particle will bounce back. If we take the limit of the particle's energy as it goes to zero, then the sticking probability goes to one. However, this is only considering the classical case. What about in the quantum view? Interesting, if we consider the quantum case with the EXACT same potential as before, then we get the opposite outcome--that is, if we let the energy of the particle go to zero, then the sticking probability goes to ZERO! To be specific, this is because the lower energy atom has a longer quantum mechanical wavelength, and thus it will see a sharper, more square well. Thus, it at lower energy, it will experience perfect reflection.

However, there is another phenomena that reduces sticking probability besides this bizarre quantum mechanical effect: the orthogonality catastrophe. When the particle comes near a surface (say, graphene), the surface will deform. As it deforms, this will change the ground state of the atoms on the surface, which in turn (due to the great number of atoms) will make the probability of the atom sticking to the surface approach zero. In the 2012-2013 academic year, physics graduate and ex-SPS member Adam Doherty conducted research in the quantum sticking of atomic hydrogen to graphene under Prof. Dennis Clougherty. His research found that low-frequency fluctuations of the graphene membrane are extremely important for quantum sticking, and effects the sticking probability.

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Last modified August 12 2014 10:00 PM