Three-dimensional analytical infinite order sudden quantum theory for triatomic photodissociation: Dependence on initial rotational and vibrational state and on thermal averages for NOCl dissociation on T1(1 3A″) surface

Our previously developed analytical infinite order sudden quantum theory of triatomic photodissociation is generalized to compute fragment internal energy distributions when the initial triatomic rotational state has K ≠ 0. The dependence of product rotational energy distributions on initial rotational and vibrational state is illustrated through model computations for the direct NOCl photodissociation from the ground to the T1(1 3A″) potential energy surface. The calculations consider all J,K ≤ 9 and employ a repulsive potential that is fit to ab initio computations. Comparisons of fragment rotational distributions with previous semiclassical approximations further elucidate the role of the mapping of the initial state bending wave function onto the fragment rotational distributions and the influence of parent rotations on this mapping. The infinite order sudden quantum-mechanical distributions exhibit a more complex structure, but upon thermal averaging they are already transformed at T = 3 K into fairly broad rotational distributions. The present theory readily permits the calculations of energy distributions for initial states of high J and K. © 1994 American Institute of Physics.Fil:Grinberg, H. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Three-dimensional analytical infinite order sudden quantum theory for triatomic indirect photodissociation processes

Our previously developed analytical infinite order sudden (IOS) quantum theory of triatomic photodissociation is extended to describe indirect photodissociation processes through a real or virtual intermediate state. The theory uses the IOS approximation for the dynamics in the final dissociative channels and an Airy function approximation for the continuum states. These approximations enable us to evaluate the multi-dimensional non-separable transition amplitudes analytically (as one-dimensional quadratures), despite the different natural coordinates for the initial bound, the intermediate resonant, and the final dissociative states. The fragment internal energy distributions are described as a function of the initial and final quantum states and the photon excitation energy. The theory readily permits the evaluation of rotational distributions for high values of the total angular momentum J in the initial bound molecular state, a feature that would be very difficult with close-coupled methods. In paper II we apply the theory to describe the photofragment yield spectrum of NOCl in the region of the T1(13A″)→S0(11A′) transition. © 1997 American Institute of Physics.Fil:Grinberg, H. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Surface Polymer Network Model and Effective Membrane Curvature Elasticity

A microscopic model of a surface polymer network - membrane system is introduced, with contact polymer surface interactions that can be either repulsive or attractive and sliplinks of functionality four randomly distributed over the supporting membrane surface anchoring the polymers to it. For the supporting surface perturbed from a planar configuration and a small relative number of surface sliplinks, we investigate an expansion of the free energy in terms of the local curvatures of the surface and the surface density of sliplinks, obtained through the application of the Balian - Bloch - Duplantier multiple surface scattering method. As a result, the dependence of the curvature elastic modulus, the Gaussian modulus as well as of the spontaneous curvature of the "dressed" membrane, ~{\sl i.e.} polymer network plus membrane matrix, is obtained on the mean polymer bulk end to end separation and the surface density of sliplinks.Comment: 15 pages with one included compressed uuencoded figure

Screening of Hydrodynamic Interactions in Semidilute Polymer Solutions: A Computer Simulation Study

We study single-chain motion in semidilute solutions of polymers of length N = 1000 with excluded-volume and hydrodynamic interactions by a novel algorithm. The crossover length of the transition from Zimm (short lengths and times) to Rouse dynamics (larger scales) is proportional to the static screening length. The crossover time is the corresponding Zimm time. Our data indicate Zimm behavior at large lengths but short times. There is no hydrodynamic screening until the chains feel constraints, after which they resist the flow: "Incomplete screening" occurs in the time domain.Comment: 3 figure

Fermi's golden rule and exponential decay as a RG fixed point

We discuss the decay of unstable states into a quasicontinuum using models of the effective Hamiltonian type. The goal is to show that exponential decay and the golden rule are exact in a suitable scaling limit, and that there is an associated renormalization group (RG) with these properties as a fixed point. The method is inspired by a limit theorem for infinitely divisible distributions in probability theory, where there is a RG with a Cauchy distribution, i.e. a Lorentz line shape, as a fixed point. Our method of solving for the spectrum is well known; it does not involve a perturbation expansion in the interaction, and needs no assumption of a weak interaction. We use random matrices for the interaction, and show that the ensemble fluctuations vanish in the scaling limit. Thus the limit is the same for every model in the ensemble with probability one.Comment: 20 pages, 1 figur

Self-intersection local times of random walks: Exponential moments in subcritical dimensions

Fix $p>1$, not necessarily integer, with $p(d-2)<d$. We study the $p$-fold self-intersection local time of a simple random walk on the lattice $\Z^d$ up to time $t$. This is the $p$-norm of the vector of the walker's local times, $\ell_t$. We derive precise logarithmic asymptotics of the expectation of $\exp\{\theta_t \|\ell_t\|_p\}$ for scales $\theta_t>0$ that are bounded from above, possibly tending to zero. The speed is identified in terms of mixed powers of $t$ and $\theta_t$, and the precise rate is characterized in terms of a variational formula, which is in close connection to the {\it Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation principle for $\|\ell_t\|_p/(t r_t)$ for deviation functions $r_t$ satisfying t r_t\gg\E[\|\ell_t\|_p]. Informally, it turns out that the random walk homogeneously squeezes in a $t$-dependent box with diameter of order $\ll t^{1/d}$ to produce the required amount of self-intersections. Our main tool is an upper bound for the joint density of the local times of the walk.Comment: 15 pages. To appear in Probability Theory and Related Fields. The final publication is available at springerlink.co

Effects of a nanoscopic filler on the structure and dynamics of a simulated polymer melt and the relationship to ultra-thin films

We perform molecular dynamics simulations of an idealized polymer melt surrounding a nanoscopic filler particle to probe the effects of a filler on the local melt structure and dynamics. We show that the glass transition temperature $T_g$ of the melt can be shifted to either higher or lower temperatures by appropriately tuning the interactions between polymer and filler. A gradual change of the polymer dynamics approaching the filler surface causes the change in the glass transition. We also find that while the bulk structure of the polymers changes little, the polymers close to the surface tend to be elongated and flattened, independent of the type of interaction we study. Consequently, the dynamics appear strongly influenced by the interactions, while the melt structure is only altered by the geometric constraints imposed by the presence of the filler. Our findings show a strong similarity to those obtained for ultra-thin polymer films (thickness $\lesssim 100$ nm) suggesting that both ultra-thin films and filled-polymer systems might be understood in the same context

Diffusion in Stationary Flow from Mesoscopic Non-equilibrium Thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic theory and projector operator techniques. That equation exhibits violation of the fluctuation dissipation-theorem. By implementing the hydrodynamic regime described by the first moments of the non-equilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose, makes it applicable to more complex situations, often encountered in problems of soft condensed matter, in which not only one but more degrees of freedom are coupled to a non-equilibrium bath.Comment: 10 pages, accepted in Phys. Rev.

Diffusion in Stationary Flow from Mesoscopic Non-equilibrium Thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic theory and projector operator techniques. That equation exhibits violation of the fluctuation dissipation-theorem. By implementing the hydrodynamic regime described by the first moments of the non-equilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose, makes it applicable to more complex situations, often encountered in problems of soft condensed matter, in which not only one but more degrees of freedom are coupled to a non-equilibrium bath.Comment: 10 pages, accepted in Phys. Rev.

A Quantum-mechanical Approach for Constrained Macromolecular Chains

Many approaches to three-dimensional constrained macromolecular chains at thermal equilibrium, at about room temperatures, are based upon constrained Classical Hamiltonian Dynamics (cCHDa). Quantum-mechanical approaches (QMa) have also been treated by different researchers for decades. QMa address a fundamental issue (constraints versus the uncertainty principle) and are versatile: they also yield classical descriptions (which may not coincide with those from cCHDa, although they may agree for certain relevant quantities). Open issues include whether QMa have enough practical consequences which differ from and/or improve those from cCHDa. We shall treat cCHDa briefly and deal with QMa, by outlining old approaches and focusing on recent ones.Comment: Expands review published in The European Physical Journal (Special Topics) Vol. 200, pp. 225-258 (2011