Understanding the sorption kinetics of nanoporous systems is crucial for the development and design of novel porous materials for practical applications. Here, using a porous coordination polymer/quartz crystal microbalance (PCP/QCM) hybrid device, we investigate the desorption of various vapor molecules featuring different degrees of intermolecular (hydrogen bonding) or molecule-framework interactions. Our findings reveal that strong intermolecular interactions lead to the desorption process proceeding via an unprecedented metastable state, wherein the guest molecules are clustered within the pores, causing the desorption rate to be temporarily slowed. The results demonstrate the considerable impact of the chemical nature of an adsorbate on the kinetics of desorption, which is also expected to influence the efficiency of certain processes, such as desorption by gas purge.

We show that the quantum single particle motion on a one-dimensional line with Fülöp-Tsutsui point interactions exhibits characteristics usually associated with nonintegrable systems both in bound state level statistics and scattering amplitudes. We argue that this is a reflection of the underlying stochastic dynamics which persists in classical domain. The advancement in nano-engineering in the last decade has brought novel incentives to the study of low-dimensional quantum systems with geometrically designed forms that have no counterpart in nature. The quantum graph, which is a generic one-dimensional model of nano-device composed of quantum wires, represents one of such systems [1,2]. The interest to the quantum graph is enhanced with its possibility to emulate the two-dimensional system of quantum billiard [3], whose solution has required rather extensive numerical treatments. It is therefore quite appropriate, at this point, to investigate generic aspects and general features of quantum graphs ahead of detailed studies of specific models of nano-devices.In a parallel development, quantum graphs have been used as a tractable model for the study of quantum chaos, or the irregular aspects of quantum dynamics occurring as quantum manifestations of classically chaotic systems [4,5]. Naturally, it is expected that random quantum graphs, which are complex networks of quantum lines, would result in the universal quantum fluctuation that has been associated to the quantum chaotic dynamics [6,7]. It has been revealed, however, that no real complex network is required for the irregular quantum dynamics to present itself. A very simple version of the quantum graph, the star graph, which is a quantum graph with many lines connected at a single node, has been shown to display the characteristics associated to partial quantum chaos in an analytical semiclassical study [8]. A natural question to be asked is whether we can further simplify the model of quantum chaos to the point of solvability.In this article, we consider one of the simplest possible quantum graph which is made up solely of nodes with two connected lines with the special property for the nodes called scale invariance. The resulting system amounts to a single one-dimensional line with number of scale invariant point interactions. We show that the system has elementary analytical scattering matrices and also elementary analytical eigenvalue equation, yet displays full characteristics of irregular quantum dynamics, both in scattering amplitudes and in bound state level statistics.We discuss the implication of the results, and look into the apparent contradiction of the appearance of the quantum chaos in a seemingly integrable, solvable conservative one-dimensional system. We consider a quantum particle, constrained to move on a one-dimensional line with N point-like defects [9] whose locations are given by x = s i with i = 1, 2, ..N (FIG. 1). The Hamiltonian of the system is given, in appropriately rescaled unit, by

We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schrödinger equation with energy rescaled by the billiard dimension.As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature.

We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wave functions approximate solutions of the Schrödinger equation with energy rescaled by the billiard dimension.As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature.