Transfer operator approach on three-dimensional quantum billiards with SO(2) symmetry.

Bogomolny's transfer operator method plays a significant role in the study of quantum chaos, along with other well known methods like Gutzwiller's trace formula and the dynamical zeta function, which generalize the Einstein-Brillouin-Keller quantization rule from integrable systems to chaotic systems. According to the theory, the Fredholm determinant of the transfer operator, defined on a Poincaré section of a classical physical system, provides a quantization condition to the energy spectrum of the corresponding quantum system. This study presents two factorization formulas, which relate different quantization conditions defined on different classical trajectory segments. These explicit relations answer the question of why all these classical quantization conditions determine exactly the same energy spectrum of the corresponding quantum systems. As an example, these formulas are illustrated in the equilateral triangular billiard.

The aim of this paper is the construction of numerical tools forthe efficient approximation of transport phenomena in non-autonomous dynamical systems.We focus on transfer operator methods which have been developed in the last yearsfor the treatment of non-autonomous dynamical systems.For instance Froyland et al. [11] proposed a methodfor the approximation of so-called coherent pairs -- these pairs of setsrepresent time-dependent slowly mixing structures -- bythresholding singular vectors of a normalized transfer operator over a fixed time-interval.In principle such transfer operator methods involve long term simulationsof trajectories on the whole state space. In our main result we showthat transport phenomena over a fixed (long) time horizonimply the existence of almost invariant sets over shorter time intervalsif the transport process is slow enough.This fact is used to formulate an algorithm that preselects part of state spaceas a candidate for containing one of the sets of a coherent pair.By this we significantly reduce the related numerical effort.

A transfer operator method is used to calculate the inverse localization length, $\ensuremath{\alpha}$, of the one-dimensional Anderson model as a function of disorder, $\ensuremath{\sigma}$. For small disorder $\ensuremath{\alpha}$ vanishes as $\ensuremath{\alpha}=A{\ensuremath{\sigma}}^{2}+O({\ensuremath{\sigma}}^{4})$, with $A=0.2088$.

The phase behavior of a quasi-one-dimensional fluid of hard spheres is studied in hard cylindrical and rectangular straight channels using the transfer operator method. The radius of the channel (R) is chosen such that only first-neighbor interactions are present, which allows only fluidlike and zigzag solidlike structures to form. It is managed to show that the fluid-solid structural change occurs approximately at ρ=1/〈σ_{∥}〉, where ρ is the one-dimensional density and 〈σ_{||}〉 is the average of the longitudinal contact distance in the case of uniform particle distribution. At this density, the pressure of positionally disordered structure diverges, but the pressure ratio (P/P_{T}), where P is the pressure of the system and P_{T} is the pressure of an effective one-dimensional hard rod fluid, exhibits a peak. At the close packing, while the positional fluctuation (〈Δr^{2}〉) vanishes with P^{β[over ̃]}, where β[over ̃]=-2 for any R and cross section, P/P_{T} (we call it α[over ̃]) goes to 2 in the rectangular and 2.5 in the cylindrical channel. The most striking difference can be observed in the transversal position correlation length (ξ). It exhibits exp(ΔP) dependence in the rectangular channel with Δ being the extra length necessary to create a defect. However, ξ goes with P^{γ[over ̃]} in the cylindrical channel, where γ[over ̃]=1. Interestingly, the cylindrically confined hard spheres obey the sum rules α[over ̃]+β[over ̃]=1/2 and β[over ̃]+γ[over ̃]=-1 for any R.

A transfer operator method is proposed to calculate [Formula: see text], the Hausdorff dimension of the Apollonian gasket. Compared with previous operator-based methods, we make two improvements in this paper. We adopt an infinite set of contractive Möbius transformations (rather than a finite set of parabolic ones) to generate the Apollonian gasket. We also apply an efficient finite matrix approximation of an infinite sum of infinite-dimensional operators. By using this method, a high precision estimate of [Formula: see text] is obtained: [Formula: see text]

We show the full large deviation principle for KMS-states and C*-finitely correlated states on a quantum spin chain. We cover general local observables. Our main tool is Ruelle’s transfer operator method.

MULTIPLE reflexions between close, nearly parallel surfaces of high reflectivity give rise to the well-known sharpened Fizeau fringes of equal thickness1. For two surfaces of equal reflectivity R and equal transmittivity T, neglecting absorption, the successive interfering beams in the transmitted system have intensities T2, R2T2, R4T2. … = T2 (1, R2, R4, …). For the reflected system the intensities are R, RT2, R2T2. . . = R, RT2(1, R2, R4, …). As shown by Tolansky, the Airy summation of the corresponding amplitudes is valid for non-parallel plates provided certain conditions are met, and we thus obtain the intensity distribution of the transmitted and reflected fringe systems. It is found that, except for the term R (and neglecting the factor R, close to unity for high-reflectivities), the reflected series is identical to the transmitted series. The term R represents the beams directly reflected from the upper surface. If these beams can be eliminated from the reflected system we are left with exactly the transmitted fringe system (reduced slightly in intensity by the factor R). That the usual reflexion fringes (minima on a light field) then become ‘transmission-like’ (maxima on a dark field) was shown by Lummer2 for fringes of equal inclination at infinity. Tolansky3 refers to the effect as “a property that can be exploited in special cases”.

Closed form solutions of axisymmetric bending of circular plates having non-linear variable thickness

We study the effect of Marangoni flow on a dynamic contact line formed by a propagating reaction front and a liquid-air interface. The self-sustained iodate-arsenous acid reaction maintains the production of the weakly surface active iodine leading to an unbalanced surface force along the tip of the reaction front. The experiments, performed in microgravity to exclude the contribution of buoyancy, reveal that the fluid flow generated by the surface tension gradient is localized to the contact line. The penetration depth of the surface stress is measured as 1-2 mm; therefore, with greater fluid height the liquid advancement on the upper surface does not lead to enhanced mixing in the bulk. Because the propagation velocity of the reactive interface remains at that of reaction-diffusion, the leading edge consists of two straight lines; a tilted segment connects the contact line on the surface with the vertical segment on bottom. Modeling calculations of the reaction-diffusion-advection system in three dimensions reconstruct the experimental observations and along with the experiments validate a model based on geometric spreading. According to the calculated flow field, the direction of significant fluid flow follows the concentration gradients and hence coincides with the propagation of the reaction front, allowing only negligible transverse flow in the upper fluid layer.

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio , represented by the ratio of amplitude to depth, and the dispersion ratio μ, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(μ2). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

Conducting-State Properties of the KcsA Potassium Channel from Molecular and Brownian Dynamics Simulations

Development and validation of the three-dimensional dynamic code—KIKO3D

The photodissociation dynamics of methyl iodide is investigated on a three-dimensional grid using a time-dependent quantum-mechanical method. Two electronic states which correlate with I and I* fragments are explicitly included in the calculation. The potential-energy functions and the nonadiabatic coupling are adapted from a recent ab initio calculation by Morokuma and co-workers. The dynamically active degrees of freedom include the dissociation coordinate, the umbrella bend of the methyl group which is treated as a stretch between a hypothetic atom X (X=H3) and the carbon atom, and the H3–C–I bend. The discrete variable representation is used to describe the dynamics in the bending coordinate θ while the other two degrees of freedom are treated by a fast Fourier transform (FFT) based approach. The time propagation of the wave packet is carried out using the Chebychev expansion of the time propagator and the grid in the translational coordinate space is shifted during the propagation to avoid reflection at the end of the grid. Absorption spectra calculated from these ab initio surfaces are found to be blue shifted by a few thousand wave numbers and have broader widths when compared with experimental results. These discrepancies can be attributed to the topology of the ab initio potential-energy surfaces in the Franck–Condon region. Vibrational and rotational distributions for both the CH3 and CD3 fragments are calculated at several photon wavelengths. The agreement with experimental results is excellent. The vibration of the methyl fragment has a weak dependence on the photon wavelength and is found to be largely separable from its rotation. The rotational distribution of the methyl fragment is cold in the I* channel, but relatively hot for the lower I channel. The I* yield is strongly influenced by the initial excitation scheme. When both excited states are considered to be optically active, the calculated I* yield gives a better agreement with experimental observations. Our calculations are also compared with several previous theoretical works.

The influence of vacancies diffusion-induced dislocation climb on the creep and plasticity behaviors of nickel-based single crystal superalloy

Semi-analytical solution of cnoidal wave diffraction around a double-layer arc-shaped vertical porous breakwater