Energy eigenvalues from an analytical transfer matrix method

A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.

The analytical transfer matrix method for quantum reflection

In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics （Non-relativistic Theory） （New York： Pergamon）], which proves that ATMM is a simple and effective method for quantum reflection.

Photon tunneling and transmittance resonance through a multi-layer structure with a left-handed material

This paper investigates the photon tunneling and transmittance resonance through a multi-layer structure including a left-handed material（LHM）. An analytical expression for the transmittance in a five-layer structure is given by the analytical transfer matrix method. The transmittance is studied as a function of the refractive index and the width of the LHM layer. The perfect photon tunneling results from the multi-layer structure, especially from the relation between the magnitude of the refractive index and the width of the LHM layer and those of the adjoining layers. Photons may tunnel through a much greater distance in this structure. Transmittance resonance happens, the peaks and valleys appear periodically at the resonance thickness. For an LHM with inherent losses, the perfect transmittance is suppressed.

Quantization rules for low dimensional quantum dots

This paper applies the analytical transfer matrix method （ATMM） to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of this system. It presents three cases in which the applied method works very well. In the first quantum dot, the energy eigenvalues and eigenfunction are obtained, and compared with those acquired from the exact numerical analysis and the WKB （Wentzel, Kramers and Brillouin） method; in the second or the third case, we get the energy eigenvalues by the ATMM, and compare them with the EBK （Einstein, Brillouin and Keller） results or the wavefunction outcomes. From the comparisons, we find that the semiclassical method （WKB, EBK or wavefunction） is inexact in such systems.

Quantum reflection as the reflection of subwaves

This paper studies quantum reflection with recent research on reflection coefficient. Based on the analytical transfer matrix method, a novel explanation for this phenomenon is proposed that quantum reflection is the reflection of subwaves, which originate inherently from the inhomogeneity of the fields and is always neglected in the semiclassical regime. Comparison with exact formula and the numerical calculations for different potentials has confirmed the reliability and the validity of the proposed theory.

On the tunneling time of arbitrary continuous potentials and the Hartman effect

This paper obtains a generalized tunneling time of one-dimensional potentials via time reversal invariance. It also proposes a simple explanation for the Hartman effect using the useful concept of the scattered subwaves.

ANALYSIS OF A CONTINUOUS TIME SM[K]/PH[K]/1/FCFS QUEUE:AGE PROCESS,SOJOURN TIMES,AND QUEUE LENGTHS

This paper studies a continuous time queueing system with multiple types of customers and a first-come-first-served service discipline. Customers arrive according to a semi-Markov arrival process and the service times of individual types of customers have PH-distributios. A GI/M/1 type Markov process for a generalized age process of batches of customers is constructed. The stationary distribution of the GI/M/1 type Markov process is found explicitly and, consequently, the distributions of the age of the batch in service, the total workload in the system, waiting times, and sojourn times of different batches and different types of customers are obtained. The paper gives the matrix representations of the PH-distributions of waiting times and sojourn times. Some results are obtained for the distributions of queue lengths at departure epochs and at an arbitrary time. These results can be used to analyze not only the queue length, but also the composition of the queue. Computational methods are developed for calculating steady state distributions related to the queue lengths, sojourn times, and waiting times.

Analysis of a multi-component system with double threshold control policy

This paper investigates a multi-component repairable system with double threshold control policy.The system is composed of n identical and independent components which operate simultaneously at the beginning,and it is down when the number of operating components decreases to k−1(k≤n).When the number of failed components is less than the value L,the repairman repairs them with a low repair rate.The high repair rate is activated as soon as L failed components present,and continues until the number of failed components drops to the value N−1.Applying the matrix analytical method,the Laplace transform technique and the properties of the phase type distribution,various performance measures including the availability,the rate of occurrence of failures,and the reliability are derived in transient and stationary regimes.Further,numerical examples are reported to show the behaviour of the system.