Tunneling and Percolation Behavior in Granular Metals

1990 ◽  
Vol 195 ◽  
Author(s):  
I. Balberg ◽  
N. Wagner ◽  
Y. Goldstein ◽  
S.Z. Weisz
Keyword(s):  
Computer Simulation ◽  
Critical Behavior ◽  
Quantum Mechanical ◽  
Electrical Noise ◽  
Quantum Mechanical Tunneling ◽  
Percolation Process ◽  
Percolation Behavior ◽  
Metallic Grains ◽  
First Time ◽  
Special Case

ABSTRACTThe nature of the percolation process in granular metals is examined for the first time by a computer simulation of a system of metallic grains embedded in an insulating matrix. Assuming that the intergrain conduction is due to quantum mechanical tunneling it is found that a percolation-like critical behavior of the conductivity is obtained, but that a percolation universal behavior will be found only in a very special case. In contrast, the behavior of the electrical noise does not deviate substantially from the universal one. Comparison of these results with recent experimental observations suggests that in the metallic range, both transport properties are controlled by the continuous metallic network rather than by intergrain tunnelin.. We propose that the metallic network resembles the previously studied system of ‘inverted random voids’.

Spin-forbidden heavy-atom tunneling in the ring-closure of triplet cyclopentane-1,3-diyl

2021 ◽  
Author(s):  
Luís P. Viegas ◽  
Cláudio Manaia Nunes ◽  
Rui Fausto
Keyword(s):  
Heavy Atom ◽  
Ring Closure ◽  
Quantum Mechanical ◽  
Quantum Mechanical Tunneling

In 1975, Buchwalter and Closs reported one of the first examples of heavy-atom quantum mechanical tunneling (QMT) by studying the ring closure of triplet cyclopentane-1,3-diyl to singlet bicyclo[2.1.0]pentane in cryogenic...

scholarly journals Convergence properties of the Broyden-like method for mixed linear–nonlinear systems of equations

2021 ◽  
Author(s):  
Florian Mannel
Keyword(s):  
Linear Independence ◽  
Affine Subspace ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Convergence Properties ◽  
Initial Matrix ◽  
First Time ◽  
Special Case ◽  
Dimensional Mapping ◽  
Finite Number Of Iterations

AbstractWe consider the Broyden-like method for a nonlinear mapping $F:\mathbb {R}^{n}\rightarrow \mathbb {R}^{n}$ F : ℝ n → ℝ n that has some affine component functions, using an initial matrix B0 that agrees with the Jacobian of F in the rows that correspond to affine components of F. We show that in this setting, the iterates belong to an affine subspace and can be viewed as outcome of the Broyden-like method applied to a lower-dimensional mapping $G:\mathbb {R}^{d}\rightarrow \mathbb {R}^{d}$ G : ℝ d → ℝ d , where d is the dimension of the affine subspace. We use this subspace property to make some small contributions to the decades-old question of whether the Broyden-like matrices converge: First, we observe that the only available result concerning this question cannot be applied if the iterates belong to a subspace because the required uniform linear independence does not hold. By generalizing the notion of uniform linear independence to subspaces, we can extend the available result to this setting. Second, we infer from the extended result that if at most one component of F is nonlinear while the others are affine and the associated n − 1 rows of the Jacobian of F agree with those of B0, then the Broyden-like matrices converge if the iterates converge; this holds whether the Jacobian at the root is invertible or not. In particular, this is the first time that convergence of the Broyden-like matrices is proven for n > 1, albeit for a special case only. Third, under the additional assumption that the Broyden-like method turns into Broyden’s method after a finite number of iterations, we prove that the convergence order of iterates and matrix updates is bounded from below by $\frac {\sqrt {5}+1}{2}$ 5 + 1 2 if the Jacobian at the root is invertible. If the nonlinear component of F is actually affine, we show finite convergence. We provide high-precision numerical experiments to confirm the results.

scholarly journals Contact Electrification by Quantum-Mechanical Tunneling

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Morten Willatzen ◽  
Zhong Lin Wang
Keyword(s):  
Potential Versus ◽  
Coulomb Repulsion ◽  
Quantum Mechanical ◽  
Quantum Mechanical Tunneling ◽  
One Dimensional ◽  
Contact Electrification ◽  
Order Of Magnitude ◽  
Left And Right ◽  
Tunneling Dynamics ◽  
Vacuum Gap

A simple model of charge transfer by loss-less quantum-mechanical tunneling between two solids is proposed. The model is applicable to electron transport and contact electrification between e.g. a metal and a dielectric solid. Based on a one-dimensional effective-mass Hamiltonian, the tunneling transmission coefficient of electrons through a barrier from one solid to another solid is calculated analytically. The transport rate (current) of electrons is found using the Tsu-Esaki equation and accounting for different Fermi functions of the two solids. We show that the tunneling dynamics is very sensitive to the vacuum potential versus the two solids conduction-band edges and the thickness of the vacuum gap. The relevant time constants for tunneling and contact electrification, relevant for triboelectricity, can vary over several orders of magnitude when the vacuum gap changes by one order of magnitude, say, 1 Å to 10 Å. Coulomb repulsion between electrons on the left and right material surfaces is accounted for in the tunneling dynamics.

Computer Simulations

2019 ◽  
pp. 9-20
Author(s):  
Paul Humphreys
Keyword(s):  
Computer Simulation ◽  
Numerical Methods ◽  
Computer Simulations ◽  
Scientific Progress ◽  
Computational Science ◽  
Working Definition ◽  
Mathematical Techniques ◽  
Definition Of ◽  
Special Case ◽  
Numerical Treatments

The need to solve analytically intractable models has led to the rise of a new kind of science, computational science, of which computer simulations are a special case. It is noted that the development of novel mathematical techniques often drives scientific progress and that even relatively simple models require numerical treatments. A working definition of a computer simulation is given and the relation of simulations to numerical methods is explored. Examples where computational methods are unavoidable are provided. Some epistemological consequences for philosophy of science are suggested and the need to take into account what is possible in practice is emphasized.

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