اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA periodic orbit formula for quantum reactions through transition states
226
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this letter these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.
قيم البحث
اقرأ أيضاً
The transformation of a system from one state to another is often mediated by a bottleneck in the systems phase space. In chemistry these bottlenecks are known as emph{transition states} through which the system has to pass in order to evolve from re
actants to products. The chemical reactions are usually associated with configurational changes where the reactants and products states correspond, e.g., to two different isomers or the undissociated and dissociated state of a molecule or cluster. In this letter we report on a new type of bottleneck which mediates emph{kinetic} rather than configurational changes. The phase space structures associated with such emph{kinetic transition states} and their dynamical implications are discussed for the rotational vibrational motion of a triatomic molecule. An outline of more general related phase space structures with important dynamical implications is given.
We provide a dynamical interpretation of the recently identified `roaming mechanism for molecular dissociation reactions in terms of geometrical structures in phase space. These are NHIMs (Normally Hyperbolic Invariant Manifolds) and their stable/uns
table manifolds that define transition states for ion-molecule association or dissociation reactions. The associated dividing surfaces rigorously define a roaming region of phase space, in which both reactive and nonreactive trajectories can be trapped for arbitrarily long times.
Unlike random potentials, quasi-periodic modulation can induce localisation-delocalisation transitions in one dimension. In this article, we analyse the implications of this for symmetry breaking in the quasi-periodically modulated quantum Ising chai
n. Although weak modulation is irrelevant, strong modulation induces new ferromagnetic and paramagnetic phases which are fully localised and gapless. The quasi-periodic potential and localised excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models with exponents of $ u=1^{+}$, and $zapprox 1.9$, $Delta_sigma approx 0.16$, $Delta_gammaapprox 0.63$ (up to logarithmic corrections). Technically, the clean Ising transition is destabilized by logarithmic wandering of the local reduced couplings. We conjecture that the wandering coefficient $w$ controls the universality class of the quasi-periodic transition and show its stability to smooth perturbations that preserve the quasi-periodic structure of the model.
This paper presents an {it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where non-interacting particle
s move on a spatially periodic lattice, and collide elastically with fixed scatterers. The second class are periodic systems where $N$ particles interact with each other, and one of them is a tracer particle which diffuses among the cells of the lattice. We assume that, in either case, the dynamics of the system is deterministic and hyperbolic, with positive Lyapunov exponents. This work extends methods originally developed for a chaotic two-dimensional model of diffusion, the multi-baker map, to higher dimensional, continuous time dynamical systems appropriate for systems with one or more moving particles. Here we express the rate of entropy production in terms of hydrodynamic measures that are determined by the fractal properties of microscopic hydrodynamic modes that describe the slowest decay of the system to an equilibrium state.
Unstable periodic orbits (UPOs) are a valuable tool for studying chaotic dynamical systems. They allow one to extract information from a system and to distill its dynamical structure. We consider here the Lorenz 1963 model with the classic parameters
value and decompose its dynamics in terms of UPOs. We investigate how a chaotic orbit can be approximated in terms of UPOs. At each instant, we rank the UPOs according to their proximity to the position of the orbit in the phase space. We study this process from two different perspectives. First, we find that, somewhat unexpectedly, longer period UPOs overwhelmingly provide the best local approximation to the trajectory, even if our UPO-detecting algorithm severely undersamples them. Second, we construct a finite-state Markov chain by studying the scattering of the forward trajectory between the neighbourhood of the various UPOs. Each UPO and its neighbourhood are taken as a possible state of the system. We then study the transitions between the different states. Through the analysis of the subdominant eigenvectors of the corresponding stochastic matrix we provide a novel interpretation of the mixing processes occurring in the system by taking advantage of the concept of quasi-invariant sets.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
