Nonlocal Dynamics in Nonlinear Biomolecular and Optical Systems

The notion of nonlocality in the description of physical systems is receiving an increasing amount of interest, and with good reason. Nonlocality implies that in order to describe the physical properties of a system at a given point, one cannot simply look at the values of the variables and parameters at that very point, but it is necessary to use inputs from the rest of the domain in order to understand the situation correctly. Nonlocality has been used for a broad range of problems, from molecular systems to liquid crystals. In the present work, two quite different physical systems — a model of a DNA molecule and one of a nonlinear optical crystal — are studied within a nonlocal context. In living cells, the immensely important DNA molecule is responsible for protein processing and cell replication. Both effects require an opening of the double-stranded molecule and to facilitate this, energy localization is believed to play an important role. It is known that by introducing inhomogeneities along a model molecular chain — which could simulate the action of enzymes — localization of vibrational energy can occur and thereby facilitate DNA opening. In this work we augment a renowned existing model to include both long range dipole-dipole interaction and geometry. The geometrical features cannot be appreciated without nonlocality. With an intrinsically homogeneous molecule we are then able to observe energy localization originating only from geometrical variables through a nonlocal interaction. Nonlinear optics is a young (the laser was invented not half a century ago), but immensely progressive fields of physics with applications to ultra-fast data processing and transmissions. Already today, fiber-optical cables are used in conventional communication systems. All-optical signal processing is not yet possible, but is a main research topic as localized quantities can act as carriers of information. One possible realization of such an entity is the so-called X-wave. Nonlocality can be used to describe X-waves and like phenomena and particularly to inspire a search for X-waves in materials with anomalous dispersion as well, which is not previously predicted. Numerical examples of these are suggested in the present work.