scholarly journals Scattering in Quantum Dots via Noncommutative Rational Functions

2021 ◽  
Author(s):  
László Erdős ◽  
Torben Krüger ◽  
Yuriy Nemish
Keyword(s):  
Quantum Dots ◽  
Degrees Of Freedom ◽  
Joint Probability ◽  
Rational Functions ◽  
Borderline Case ◽  
Random Matrix Model ◽  
The Matrix ◽  
Matrix Ensemble ◽  
Rational Expressions ◽  
Global And Local

AbstractIn the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via $$N\ll M$$ N ≪ M channels, the density $$\rho $$ ρ of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio $$\phi := N/M\le 1$$ ϕ : = N / M ≤ 1 ; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit $$\phi \rightarrow 0$$ ϕ → 0 , we recover the formula for the density $$\rho $$ ρ that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any $$\phi <1$$ ϕ < 1 but in the borderline case $$\phi =1$$ ϕ = 1 an anomalous $$\lambda ^{-2/3}$$ λ - 2 / 3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries.

Distribution of Wrench-Twist Duality in Over-Constrained Mechanisms

2003 ◽  
Vol 125 (1) ◽  
pp. 81-91 ◽  
Author(s):  
M. Fayet
Keyword(s):  
Degrees Of Freedom ◽  
Contact Forces ◽  
Simple Test ◽  
The Matrix

First, a procedure is presented in order to build the space of statically admissible wrenches. The matrix which generates them is obtained in an intrinsic way. It uses intersection of spaces for the edges (of the associated graph) and the new operation of “triangular projection” for the vertices. From this matrix, the choice of any set of indeterminable contact forces is achieved via a very simple test. This matrix allows to determine also all the possible degrees of freedom to add to the over-constrained mechanism in order to transform it into a non over-constrained one. Wrench-twist duality arises clearly in this last procedure.

An Iterative Approach to Dynamic Elastic-Plastic Analysis

1998 ◽  
Vol 65 (4) ◽  
pp. 811-819 ◽  
Author(s):  
F. Giambanco ◽  
L. Palizzolo ◽  
L. Cirone
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Degrees Of Freedom ◽  
Linear Complementarity ◽  
Iterative Approach ◽  
Loading History ◽  
Constraint Matrix ◽  
Elastic Plastic ◽  
Recursive Solution ◽  
The Matrix

The step-by-step analysis of structures constituted by elastic-plastic finite elements, subjected to an assigned loading history, is here considered. The structure may possess dynamic and/or not dynamic degrees-of-freedom. As it is well-known, at each step of analysis the solution of a linear complementarity problem is required. An iterative method devoted to solving the relevant linear complementarity problem is presented. It is based on the recursive solution of a linear complementarity, problem in which the constraint matrix is block-diagonal and deduced from the matrix of the original linear complementarity problem. The convergence of the procedure is also proved. Some particular cases are examined. Several numerical applications conclude the paper.

Fabrication of Low Cost 1D CdSe Nanowires using Near-field Electrospinning

2011 ◽  
Vol 1302 ◽  
Author(s):  
Leroy Magwood ◽  
Binil Starly
Keyword(s):  
Quantum Dots ◽  
Fluorescence Microscopy ◽  
Fiber Diameter ◽  
Low Cost ◽  
Near Field ◽  
Light Attenuation ◽  
Dimethyl Formamide ◽  
Cdse Quantum Dot ◽  
The Matrix ◽  
Cdse Nanowires

ABSTRACTWell-aligned, 1D CdSe quantum dot (QD) fibers (0.3μm to 2.5μm) containing up to 20wt% fluorescent quantum dots (QDs) were prepared by near-field electrospinning (NFES) process. Electrospun solutions were prepared using PVAc as the matrix polymer, dimethyl formamide (DMF) solvent and colloidal QDs in chloroform (CHCl3). The diameter of the fibers decreased as the ratio of DMF/CHCl3 is varied. QDs showed good dispersion and a linear relationship between QD loading and fiber diameter, as determined by the morphology measurements taken using TEM and SEM, respectively. Fluorescence microscopy shows that there is light attenuation throughout the fibers. Results also show that the NFES process may be used as a method to create aligned, 1D fibers of QDs and potentially other nanofibers.

Initial Stages of InAs Quantum Dots Evolution in GaAs/AlAs Matrixes

2002 ◽  
Vol 749 ◽  
Author(s):  
Michael Yakimov ◽  
Vadim Tokranov ◽  
Alex Katnelson ◽  
Serge Oktyabrsky
Keyword(s):  
Quantum Dots ◽  
Direct Evidence ◽  
Matrix Material ◽  
Single Layer ◽  
High Energy ◽  
Inas Quantum Dots ◽  
Auger Signal ◽  
The Matrix ◽  
Growth Evolution

ABSTRACTWe have studied the first phases of post-growth evolution of InAs quantum dots (QDs) using in-situ Auger electron spectroscopy in conjunction with Reflection High Energy Electron Diffraction (RHEED). Direct evidence for InAs intermixing with about 6ML (monolayers) of the matrix material is found from Auger signal behavior during MBE overgrowth of InAs nanostructures. Re-establishment of 2D growth mode by overgrowth with GaAs or AlAs was monitored in single-layer and multi-layer QD structures using RHEED. Decay process of InAs QDs on the surface is found to have activation energy of about 1.1 eV that corresponds to In intermixing with the matrix rather than evaporation from the surface.

An Improved Method for Calculating Free Vibrations in Systems of Several Degrees of Freedom

1938 ◽  
Vol 5 (2) ◽  
pp. A61-A66
Author(s):  
Winston M. Dudley
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Matrix Theory ◽  
Free Vibrations ◽  
Initial Disturbance ◽  
Improved Method ◽  
Matrix Methods ◽  
Computing Machine ◽  
The Matrix ◽  
Time Required

Abstract In 1934 two English investigators (1) published a method for calculating the various modes and frequencies of vibration of a system having several degrees of freedom. Their method, which is based on matrices, greatly shortens the time spent in obtaining numerical solutions in many important problems, notably those with immovable foundations. In this paper is presented a new theorem which (a) makes possible a further reduction of nearly one half in the time required, so that solutions up to 20 deg or more of freedom are now practical and (b) makes it then possible to determine the motion of the system after any initial disturbance in a few minutes, instead of several hours as required by older methods. It is useful in the latter respect whether the modes have been determined by matrix methods, or not. Although the paper gives simpler proofs than any previously published, knowledge of the matrix theory is not required in using the method. Problems are analyzed by a tabular process, in which an ordinary computing machine helps greatly. Comments based on computing experience are given. A simple numerical example has been given elsewhere (1).

Global and local scaling limits for the β = 2 Stieltjes–Wigert random matrix ensemble

2021 ◽  
pp. 2250020
Author(s):  
Peter J. Forrester
Keyword(s):  
Statistical Physics ◽  
Scaling Limit ◽  
Pair Potential ◽  
Exact Expression ◽  
Correlation Kernel ◽  
Local Scaling ◽  
Gaussian Unitary Ensemble ◽  
Matrix Ensemble ◽  
Many Body Systems ◽  
Global And Local

The eigenvalue probability density function (PDF) for the Gaussian unitary ensemble has a well-known analogy with the Boltzmann factor for a classical log-gas with pair potential [Formula: see text], confined by a one-body harmonic potential. A generalization is to replace the pair potential by [Formula: see text]. The resulting PDF first appeared in the statistical physics literature in relation to non-intersecting Brownian walkers, equally spaced at time [Formula: see text], and subsequently in the study of quantum many-body systems of the Calogero–Sutherland type, and also in Chern–Simons field theory. It is an example of a determinantal point process with correlation kernel based on the Stieltjes–Wigert polynomials. We take up the problem of determining the moments of this ensemble, and find an exact expression in terms of a particular little [Formula: see text]-Jacobi polynomial. From their large [Formula: see text] form, the global density can be computed. Previous work has evaluated the edge scaling limit of the correlation kernel in terms of the Ramanujan ([Formula: see text]-Airy) function. We show how in a particular [Formula: see text] scaling limit, this reduces to the Airy kernel.

The mechanics of locating earthquakes

1976 ◽  
Vol 66 (1) ◽  
pp. 173-187
Author(s):  
Ray Buland
Keyword(s):  
Degrees Of Freedom ◽  
A Priori Estimates ◽  
A Priori ◽  
Joint Probability ◽  
Step Length ◽  
Earth Model ◽  
Random Errors ◽  
Qr Algorithm ◽  
Location Parameters ◽  
Chi Squared

abstract A complete reexamination of Geiger's method in the light of modern numerical analysis indicates that numerical stability can be insured by use of the QR algorithm and the convergence domain considerably enlarged by the introduction of step-length damping. In order to make the maximum use of all data, the method is developed assuming a priori estimates of the statistics of the random errors at each station. Numerical experiments indicate that the bulk of the joint probability density of the location parameters is in the linear region allowing simple estimates of the standard errors of the parameters. The location parameters are found to be distributed as one minus chi squared with m degrees of freedom, where m is the number of parameters, allowing the simple construction of confidence levels. The use of the chi-squared test with n-m degrees of freedom, where n is the number of data, is introduced as a means of qualitatively evaluating the correctness of the earth model.

scholarly journals THE HAGEDORN TRANSITION AND THE MATRIX MODEL FOR STRINGS

1998 ◽  
Vol 13 (26) ◽  
pp. 2085-2094 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Matrix Model ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Low Energy ◽  
Matrix Formalism ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
The Continuum ◽  
String Worldsheet

We use the matrix formalism to investigate what happens to strings above the Hagedorn temperature. We show that is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of N D-0-branes arranged to form a string having N units of light-cone momentum. We find that at high temperatures the favored phase is one where the string worldsheet has disappeared and the low-energy degrees of freedom consists of N2 massless particles ("gluons"). The nature of the transition is very similar to the deconfinement transition in large-N Yang–Mills theories.

QUANTUM PHASE GATING WITH SEMICONDUCTOR QUANTUM DOTS IN A MICROCAVITY

2004 ◽  
Vol 18 (23) ◽  
pp. 1195-1203
Author(s):  
MANG FENG
Keyword(s):  
Quantum Dots ◽  
Degrees Of Freedom ◽  
Cavity Mode ◽  
Nearest Neighbor ◽  
Single Mode ◽  
Laser Pulses ◽  
Semiconductor Quantum Dots ◽  
Quantum Phase ◽  
Conduction Band Electron ◽  
Excitonic States

We propose a scheme to carry out quantum phase gate in one step by bichromatic radiation method with semiconductor quantum dots (QDs) embedded in a single mode microcavity. The spin degrees of freedom of the only excess conduction band electron are employed as qubits and excitonic states are used as auxiliary states. The nearest-neighbor coupling is not required because the cavity mode plays the role of data bus. We show how to perform quantum computing with properly tailored laser pulses and Pauli-blocking effect, without exciting the cavity mode.

SPECTRAL PROPERTIES OF ADMITTANCE MATRICES OF RESISTIVE TREE NETWORKS

1994 ◽  
Vol 04 (01) ◽  
pp. 53-70
Author(s):  
I. CEDERBAUM
Keyword(s):  
Characteristic Frequency ◽  
Spectral Properties ◽  
Rational Functions ◽  
Resistive Network ◽  
Admittance Matrix ◽  
Sturm Sequences ◽  
Classical Work ◽  
Mechanical Analogue ◽  
The Matrix ◽  
General Tree

In this paper spectral properties of the admittance matrix of a resistive network whose underlying graph forms a general tree are studied. The algebraic presentation of the network is provided by its real node admittance matrix with respect to one of its terminal vertices, considered to be the root of the tree. The spectral properties of this matrix are studied by application of the theory of two-element-kind (R, C) networks. A mechanical analogue of a particular case of a similar problem, corresponding to a linear tree has been studied in the classical work of Gantmacher and Krein.7 Generalization of the study to networks based on trees of arbitrary structure calls for a modification of the mathematical approach. Instead of polynomial Sturm sequences applied in Ref. 7 the paper applies sequences of rational functions obeying the two basic Sturm conditions. In the special case of a linear tree these rational functions turn out to be polynomials, and the results are equivalent to those in Ref. 7. For a general tree the paper takes into consideration any root—leaf path of the tree. It is shown that the conditions on such a path are similar to those taking place on a linear tree. Some difference occurs in the number of sign reversals in the sequence of coordinates of characteristic vectors. In the case of a linear tree this number depends only on the position of the corresponding characteristic frequency in the spectrum of the matrix. In the case of a root-leaf path of a general tree, this number has to be normally decreased. The correction (which might be zero) is equal to the number of poles of the determinant of the reduced admittance matrix corresponding to the path considered, which does not exceed the characteristic frequency.

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