scholarly journals Conditions for realizing one-point interactions from a multi-layer structure model

2022 ◽  
Author(s):  
A V Zolotaryuk ◽  
Yaroslav Zolotaryuk
Keyword(s):  
System Parameter ◽  
Layer Structure ◽  
Dimensional Space ◽  
One Dimension ◽  
Structure Model ◽  
Point Interactions ◽  
Piecewise Constant ◽  
Quantum Particles ◽  
Constant Potential ◽  
Parameter Values

Abstract A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l1, . . . , lN shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V1, . . . , VN as functions of l1, . . . , lN, respectively. The key point is the derivation of the conditions on the functions V1(l1), . . . , VN(lN) for realizing a family of one-point interactions as l1, . . . , lN tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure, the solution of which determines the system parameter values, under which the non-zero tunneling of quantum particles through a multi-layer structure occurs, is shown to exist and depend on the paths. This tunneling appears as a result of an appropriate cancellation of divergences.

scholarly journals SELF-SIMILAR BEHAVIOR IN SEMICONDUCTOR SUPERLATTICES

Fractals ◽  
2012 ◽  
Vol 20 (01) ◽  
pp. 89-95 ◽  
Author(s):  
JUAN C. CASTRO-PALACIO ◽  
FRANCISCO R. VILLATORO ◽  
OMEL MENDOZA-YERO ◽  
LUISBERIS VELÁZQUEZ-ABAD ◽  
JUAN A. MONSORIU
Keyword(s):  
Particle Energy ◽  
Self Similarity ◽  
Potential Wells ◽  
Piecewise Constant ◽  
Quantum Particles ◽  
Fractal Properties ◽  
Periodic Potentials ◽  
Constant Potential ◽  
Coefficient Versus ◽  
Self Similar

The scattering of particles in fractal superlattices has been analyzed by means of the transfer matrix method. The fractal superlattice consists of alternating layers of semiconductor materials following the rule of a Cantor set. This problem can be represented by a model of quantum particles scattering in piecewise constant potential wells. Fractal properties of the reflection coefficient versus the particle energy curves are examined comparatively to the curves when using the corresponding periodic potentials. The degree of self-similarity of the output variables has been quantified by means of the correlation function.

scholarly journals Calculating the Energy Spectrum of Complex Low-Dimensional Heterostructures in the Electric Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Svetlana N. Khonina ◽  
Sergey G. Volotovsky ◽  
Sergey I. Kharitonov ◽  
Nikolay L. Kazanskiy
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Ground State ◽  
State Energy ◽  
Airy Functions ◽  
Piecewise Constant ◽  
Matrix Rank ◽  
The Matrix ◽  
Constant Potential ◽  
Low Dimensional

An algorithm for solving the steady-state Schrödinger equation for a complex piecewise-constant potential in the presence of theE-field is developed and implemented. The algorithm is based on the consecutive matching of solutions given by the Airy functions at the band boundaries with the matrix rank increasing by no more than two orders, which enables the characteristic solution to be obtained in the convenient form for search of the roots. The algorithm developed allows valid solutions to be obtained for the electric field magnitudes larger than the ground-state energy level, that is, when the perturbation method is not suitable.

THREE SCHEMES TO SYNCHRONIZE CHAOTIC FRACTIONAL-ORDER RUCKLIDGE SYSTEMS

2007 ◽  
Vol 21 (12) ◽  
pp. 2033-2044 ◽  
Author(s):  
YANBIN ZHANG ◽  
TIANSHOU ZHOU
Keyword(s):  
Dynamical Systems ◽  
Fractional Order ◽  
System Parameter ◽  
Chaotic Synchronization ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Synchronization Problem ◽  
Alternate Choice ◽  
Parameter Values ◽  
Fractional Orders

The synchronization problem of chaotic fractional-order Rucklidge systems is studied both theoretically and numerically. Three different synchronization schemes based on the Pecora–Carroll principle, the linear feedback control and the bidirectional coupling are proposed to realize chaotic synchronization. It is shown that such schemes can achieve the same aim for the same set of system parameter values (including fractional orders). This provides an alternate choice for applications of fractional-order dynamical systems in engineering fields.

A simple approach to quasicrystal structure and phason defect formulation

1990 ◽  
Vol 46 (2) ◽  
pp. 142-149 ◽  
Author(s):  
F. H. Li ◽  
Y. F. Cheng
Keyword(s):  
Crystal Structure ◽  
Dimensional Space ◽  
Physical Space ◽  
Simple Approach ◽  
High Dimensional ◽  
Periodic Lattice ◽  
Structure Model ◽  
Continuous Rotation ◽  
Geometrical Relationship ◽  
Quasicrystal Structure

The advantages of the cut or section method in describing quasicrystal structures and phason defects are given. The real and reciprocal quasilattice formulation is derived straightforwardly. It is shown that the linear phason strain which leads to the quasilattice distortion is equivalent to a rotation of physical space relative to the high-dimensional space. A continuous rotation of the physical space will make the quasilattice deviate from its idealized form and turn gradually into a periodic lattice. The derivation of a geometrical relationship between the icosahedral quasilattice and the corresponding b.c.c. lattice becomes simple and clear. This will be beneficial to the construction of a quasicrystal structure model by reference to the corresponding b.c.c. crystal structure.

The Effect of Seal Width on Regenerator Effectiveness

1994 ◽  
Vol 116 (3) ◽  
pp. 574-582 ◽  
Author(s):  
D. S. Beck
Keyword(s):  
System Parameter ◽  
Axial Conduction ◽  
Design Procedures ◽  
The Past ◽  
Parameter Values

The effect of axial conduction on regenerator effectiveness has been studied in the past under the assumption of zero seal width. The effect of axial conduction coupled with finite seal width is presented in this paper. A method for calculating effectiveness assuming axial conduction and finite seal width is presented. Results of sample calculations are presented to give the designer a feel for the dependence of seal-width effects on system-parameter values. It is shown that for typical regenerator designs, reductions in effectiveness due to axial conduction coupled with finite seal width can be twice as great as those due to axial conduction under the assumption of zero seal width. Also, it is shown that the required regenerator size to achieve a given effectiveness can increase dramatically when finite seal width is considered in design procedures. It is concluded that consideration of axial conduction should include finite seal width.

Beyond Description in Interpersonal Construct Validation

Assessment ◽  
2016 ◽  
Vol 24 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Johannes Zimmermann ◽  
Aidan G. C. Wright
Keyword(s):  
Structural Model ◽  
Dimensional Space ◽  
Construct Validation ◽  
Theory Building ◽  
Interpersonal Circumplex ◽  
Real World Data ◽  
Or Groups ◽  
Wide Range ◽  
Parameter Values ◽  
Structural Summary

The interpersonal circumplex is a well-established structural model that organizes interpersonal functioning within the two-dimensional space marked by dominance and affiliation. The structural summary method (SSM) was developed to evaluate the interpersonal nature of other constructs and measures outside the interpersonal circumplex. To date, this method has been primarily descriptive, providing no way to draw inferences when comparing SSM parameters across constructs or groups. We describe a newly developed resampling-based method for deriving confidence intervals, which allows for SSM parameter comparisons. In a series of five studies, we evaluated the accuracy of the approach across a wide range of possible sample sizes and parameter values, and demonstrated its utility for posing theoretical questions on the interpersonal nature of relevant constructs (e.g., personality disorders) using real-world data. As a result, the SSM is strengthened for its intended purpose of construct evaluation and theory building.

scholarly journals NON-RELATIVISTIC FERMIONS, COADJOINT ORBITS OF W∞ AND STRING FIELD THEORY AT c=1

1992 ◽  
Vol 07 (33) ◽  
pp. 3129-3145 ◽  
Author(s):  
AVINASH DHAR ◽  
GAUTAM MANDAL ◽  
SPENTA R. WADIA
Keyword(s):  
Dimensional Space ◽  
Space Distribution ◽  
One Dimension ◽  
Coadjoint Orbits ◽  
Leading Order ◽  
Weak Coupling Regime ◽  
Phase Space Distribution ◽  
Dimensional Space Time ◽  
Area Preserving ◽  
Geometric Formulation

We apply the method of coadjoint orbits of W∞-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum phase space distribution of the Fermi fluid. The action has an infinite series of expansion in the string coupling, which to leading order reduces to the previously discussed geometric action for the classical Fermi fluid based on the group w∞ of area-preserving diffeomorphisms. We briefly discuss the strong coupling limit of the string theory which, unlike the weak coupling regime, does not seem to admit a two-dimensional space-time picture. Our methods are equally applicable to interacting fermions in one dimension.

The Effect of Seal Width on Regenerator Effectiveness

1993 ◽  
Author(s):  
Douglas S. Beck
Keyword(s):  
System Parameter ◽  
Axial Conduction ◽  
Design Procedures ◽  
The Past ◽  
Parameter Values

The effect of axial conduction on regenerator effectiveness has been studied in the past under the assumption of zero seal width. The effect of axial conduction coupled with finite seal width is presented. A method for calculating effectiveness assuming axial conduction and finite seal width is presented. Results of example calculations are presented to give the designer a feel for the dependence of seal-width effects on system-parameter values. It is shown that for typical regenerator designs, reductions in effectiveness due to axial conduction coupled with finite seal width can be twice as great as those due to axial conduction under the assumption of zero seal width. Also, it is shown that the required regenerator size to achieve a given effectiveness can increase dramatically when finite seal width is considered in design procedures. It is concluded that consideration of axial conduction should include finite seal width.

scholarly journals Understanding Saturn’s interior from the Cassini Grand Finale gravity measurements

2020 ◽  
Vol 639 ◽  
pp. A10 ◽  
Author(s):  
Dongdong Ni
Keyword(s):  
Rotation Rate ◽  
Mass Fraction ◽  
Heavy Element ◽  
Equations Of State ◽  
Layer Structure ◽  
Element Abundance ◽  
Structure Model ◽  
Core Mass ◽  
Induced Gravity ◽  
Gravity Measurements

Context. Measurements of Saturn’s gravity field by Cassini Grand Finale have been acquired with high precision. It has been demonstrated that the even gravitational harmonics J6–J10 have larger absolute values than the predictions by typical rigid-body interior models. A four-layer structure model, proposed to interpret Juno’s gravity measurements for Jupiter, has been applied to Saturn, but great attention was paid to the depth of zonal flows in order to interpret the large absolute values of J6–J10. Aims. We aim to understand the internal structure and interior composition of Saturn with a similar model for Jupiter. The additional uncertainties in Saturn’s structure and composition are investigated in detail, such as rotation periods, atmospheric helium mass fractions, and flow-induced gravity corrections. Also, we investigate the effect of equations of state for hydrogen and helium on the predictions of the core mass and heavy element abundance. Methods. In the four-layer structure model, we adjusted the heavy element abundances in the outer two envelopes and the mass of the compact core in order to reproduce Saturn’s equatorial radius as well as the Cassini Grand Finale gravity measurements corrected by the flow-induced gravity signals. Different four-layer interior models are specified in terms of the rotation period, the atmospheric helium mass fraction, and the flow-induced gravity corrections. Two different ab initio equations of state for hydrogen and helium were used in interior structure calculations. Optimized calculations were then performed to explore Saturn’s internal structure and composition. Results. It is found that the absolute values of J6–J10 tend to increase with increasing deep rotation rate and depend on the equations of state adopted in interior calculations. Saturn’s deep rotation rate and atmospheric helium mass fraction are important to determine the distribution of helium and heavy elements in the outer envelopes. We also show that the core mass and heavy element abundance in Saturn are dependent upon the deep rotation rate, the atmospheric helium mass fraction, the flow-induced gravity corrections, and the equations of state for hydrogen and helium.

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