This award supports theoretical research and education on the role of fluctuations in various physical contexts. Fluctuations, whether of quantum, thermal, or non-equilibrium origin, are an inherent part of physical matter. Constraining these fluctuations by boundaries, geometry or topology, leads to a myriad of interactions, patterns and phases. This proposal aims at quantifying such phenomena in several contexts. Specific questions that will be addressed by the research include: (i) The forces between neutral objects are due to constrained electromagnetic fluctuations. How do these forces depend on the shapes and orientations of these objects? Can one hold an object in stable equilibrium using only such forces? (ii) How does the confinement of critical thermal fluctuations of the order parameter lead to the thinning of helium films at the onset of superfluidity? (iii) What is the role of rigidity in the melting of double-stranded polymers such as DNA? How do fluctuations soften the elasticity of polymers and sheets? (iv) What governs the distribution of escape times, from a confining interval, in a process that is slower than diffusion? Is there a common description for such processes? (iv) How can we classify and catalog entangled proteins?
Fluctuating systems are characterized by probability distribution functions. Statistical physics provides the relative weights of different configurations in equilibrium, and the time evolution of weights away from equilibrium. The methods of statistical field theory are appropriate for handling quantum fluctuations of the electromagnetic field. The Casimir force between different materials and its dependence of geometry can be obtained by constraining the fluctuations on the bodies. Transfer matrix and renormalization group methods will be used to address questions involving semi-flexible polymers. Anomalous dynamics will be studied by a combination of scaling theory, and Monte Carlo and Molecular Dynamics simulations.
Education is an important component of this award. This research project is interdisciplinary; methods from statistical physics will be applied to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web will have impact on broader scientific community. The PI will also be an organizer of a workshop at the Kavli Institute for Theoretical Physics on the subject of fluctuation?induced forces.
NONTECHNICAL SUMMARY:
This award supports theoretical research and education on the materials and physical consequences of fundamental principles of statistical physics. The research encompasses a wide range of physical systems and phenomena that are connected through the unifying question of how confinement modifies behavior and properties. The effects of confinement are an inherent part of physical systems and the effects of boundaries and geometry lead to a myriad of interactions, patterns and phases. This research quantifies such phenomena in several contexts. Varied research questions are addressed.
(i) Theoretical predictions concerning the forces between neutral objects, due to mere proximity, known as Casimir forces, are decades old, but have only recently been measured and even more recently been the subject of experiments to investigate their application in devices. This research moves from what is known for simple planar geometries to investigating how these forces depend on the shapes and orientations of the objects. Unanswered fundamental questions are taken up, such as can one hold an object in stable arrangement using only such forces? (ii) This thrust focuses on how the confinement of helium films alters their behavior from simple fluids to exhibit a variety of unusual fluid properties. Films of the element helium are essentially two dimensional liquids that exist at very low temperatures and exhibit behavior governed by quantum mechanics. (iii) A related topic is the role of confinement induced in molecules by crowding and interacting with other members of bulk collection. This aspect of the research studies the softening and elasticity of polymers and flexible sheets. In this case, confinement arises through the entanglement of long molecules.
Education is an important component of this award. This research project is interdisciplinary; methods from statistical physics will be applied to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web will have impact on broader scientific community. The PI will also be an organizer of a workshop for the broader theoretical physics community at the Kavli Institute for Theoretical Physics.
Fluctuations are ubiquitous in nature, from thermal motion of molecules in a fluid at rest, to non-equilibrium fluctuations of air in a tempest. Even the vacuum is teeming with quantum fluctuations of the electromagnetic field. Constraining these fluctuations by boundaries of different shapes or topology, leads to a myriad of interactions, patterns and phases. This NSF project explored a number of such phenomena, including: * Ordinary (uncharged) matter is held together by forces due to quantum fluctuations of charge and current. These fluctuation-induced forces at short distances are sensitive to shape, and we developed a formalism that can compute such shape dependence. In particular, we obtained forces between objects with sharp edges and tips. * Very similar methodology can be employed to compute forces exerted by molecules due to thermal (rather than quantum mechanical) fluctuations. We have shown that the force exerted by a fluctuating polymer on the tip of an atomic force microscope has a very simple form, dependent only on temperature and separation. * A prime example of non-equilibrium is provided by objects at different temperatures. This is of course a classical problem studied in elementary physics classes. However, again at close proximity, the heat transferred between the two objects can be very different- possibly thousand times larger- than obtained from classical computations due to the fluctuating fields. The formalism we developed for calculation of forces can also be adapted to compute heat transfer in these non-classical settings. * Yet another instance of non-equilibrium is a non-stationary object, such as a rotating sphere or cylinder. Classically, an isolated rotating body will maintain its rotation forever due to conservation of angular momentum. We show that an electrically neutral conductor actually slows down due to interactions with the fluctuating electromagnetic fields in the surrounding vacuum. This is tantamount to friction, with the energy lost radiated away. * Non-equilibrium processes are also at the basis of biological phenomena. It is known that the diffusion and reactions of fluctuating molecules on a membrane can lead to a dynamic form of aggregation into regular patterns. Interpreting recent experiments, we have suggested that such aggregates may form precursors to structures observed at a neural synapse. The methodology employed in tackling the diversity of problems indicated above is that of Statistical Physics. The tools of Statistical Physics provide the means of understanding how intricate and complex phenomena can emerge from interactions amongst large numbers of relatively simple ingredients. A broader impact of research supported by NSF is education and broader dissemination of the this methodology. Indeed, the research is closely linked to courses taught by the PI, which through textbooks and distribution by the web have reached a large number of students. Many of these students are engaged in interdisciplinary fields of research spanning biophysics to geophysics.
