Differential Representations of SO（4） Dynamical Group

In this paper we present systematic differential representations for the dynamical group SO（4）. These representations include the left and the right differential representations and the left and the right adjoint differential representations in both the group parameter space and its coset spaces. They are the generalization of the differential representations of the SO（3） rotation group in the Euler angles. These representations may find their applications in the study of the physical systems with SO（4） dynamical symmetry.     

How should complexity scale with system size?

We study how statistical complexity depends on the system size and how the complexity of the whole system relates to the complexity of its subsystems. We study this size dependence for two well-known complexity measures, the excess entropy of Grassberger and the neural complexity introduced by Tononi, Sporns and Edelman. We compare these results to properties of complexity measures that one might wish to impose when seeking an axiomatic characterization. It turns out that those two measures do not satisfy all those requirements, but a renormalized version of the TSE-complexity behaves reasonably well.     

On explicit free field realization of current algebras

We construct the explicit free field representations of the current algebras so(2n)_k, so(2n+1)_k and sp(2n)_k for a generic positive integer n and an arbitrary level k. The corresponding energy–momentum tensors and screening currents of the first kind are also given in terms of free fields.     

Angle of incidence effects in a molecular solid

We investigate the influence of the angle of incidence on the sputter yield when bombarding molecular solid, benzene, with C₆₀. Our simulations show that at normal incidence, essentially all of the projectile energy is deposited into the substrate within ∼2.5 nm of the surface. However, at 75° incident angle, only 35% of the projectile energy is deposited within a depth of less than 1.5 nm of the surface while 65% of the projectile energy is reflected. Therefore, important aspects of the collision process which are dependent upon energy deposition, such as sputter yield, ejection depth, and molecule dissociation, may change as the incident angle changes.     

The dynamics of random interfaces in phase transitions

A review is given of recent developments involving the dynamics of random interfaces formed in the evolution of metastable and unstable systems. Topics which are discussed include interface growth and nonequilibrium dynamical scaling. The possibility of there being dynamical universality classes in first-order phase transitions is also discussed. There are a large number of systems of experimental interest which include binary alloys, binary fluids, and polymer mixtures. Other systems studied by computer simulation include the kinetic Ising, Potts, andZ _N models.Work supported by NSF grant No. DMR-8013700.     

Eigenvalues and eigenfunctions of the Fokker-Planck equation for the extremely underdamped Brownian motion in a double-well potential

The eigenvalues and eigenfunctions of the Fokker-Planck equation describing the extremely underdamped Brownian motion in a symmetric double-well potential are investigated. By transforming the Fokker-Planck equation to energy and position coordinates and by performing a suitable averaging over the position coordinate, a differential equation depending only on energy is derived. For finite temperatures this equation is solved by numerical integration, whereas in the weak-noise limit an analytic result for the lowest nonzero eigenvalue is obtained. Furthermore, by using a boundary-layer theory near the critical trajectory, the correction term to the zero-friction-limit result is found.     

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.     

Alteration of skin light-scattering and absorption properties by application of sunscreen nanoparticles: A Monte Carlo study

We report about the results of our investigations on the alteration of optical properties of the superficial layer of human skin at four UV range wavelengths, 310, 318, 360 and 400 nm, by application of 35-200 nm-sized particles of titanium dioxide (TiO₂), silicon (Si) and zinc oxide (ZnO). The theoretical study based on combination of the Mie theory and Monte Carlo simulations reveals the optimal sizes of the nanoparticles minimizing the light transmittance for the considered wavelengths.     

An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.