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Resonant Tunning Through Quantum Dot Array
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RECOMMENDATION
1. Transport through a single quantum dot weakly coupled to two contacts has been the subject of many experimental and theoretical works, and a fairly clear picture has emerge
2. Relatively little work has been done on arrays of quantum dots though it now seems feasible to fabricate such structure.
3. It seems reasonable then to model an array of quantum dots using the Hubbard Hamiltonian characterized mainly by two parameters.
4. It might thus be possible to study various aspects of the Hubbard model using such artificial quantum dot arrays.
5. This treatment of the contact should be accurate as long as the temperature is higher than the Kondo temperature.
6. However, it is expected that in semiconductor quantum-dot arrays such interdot coherent will play an important role in determining the transport properties.
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ABSRACT - [ Total Page(s): 1 ]Abstract coming soon ... Continue reading---
CHAPTER ONE - [ Total Page(s): 4 ]CHAPTER ONERESONANT TUNNELING THROUGH QUANTUM DOT ARRAYS1.1 IntroductionResonant tunneling through Quantum dot arrays is the quantum-mechanical effect of transition through a classically-forbidden energy state.Consider rolling a ball up a hill. If the ball is not given enough velocity, then it will not roll over the hill. This makes sense classically. But in quantum mechanics, objects exhibit wavelike behavior. For a quantum particle moving against a potential hill, the wave function descr ... Continue reading---
CHAPTER TWO - [ Total Page(s): 2 ]CHAPTER TWORESONANT TUNNELING THROUGH QUANTUM DOT ARRAY PROCESSE is incident on a potential barrier of height V0 . Classically the electron is reflected when E< V0, but quantum mechanically there is a certain probability that the electron is transmitted through the barrier.Tunneling is a purely quantum mechanical phenomena which enables electrons to penetrate potential barriers even though it is classically forbidden. The scheme is illustrated in Figure above. Classically the electron would be r ... Continue reading---
CHAPTER THREE - [ Total Page(s): 9 ]The Hamiltonian equation above is a representation of Quantum dot array i.e 1- Darray of N coupled dots index from left to right as 1- N. looking at the energy of a quantum dot confined dots (20 energy states been treated as a single quantum systemFrom the equationεka is the energy levels in leadsεia is the ith dot of the energy Ui is theith inter- dot repulsion and the inter-dot coupling between theith dot and its rightneighbor (the (i+1)th dot)V L and V R are the tunnels matrix element c ... Continue reading---
CHAPTER FOUR - [ Total Page(s): 2 ]CHAPTER FOURDISCUSSION OF RESULTSFrom the matrices gotten in the previous chapter, it is seen that the diagonal four-by-four matrices are proportional to the partition function Z.In Eq. (2), En, is the energy of many-body state (n, i), the ith of the n-particle states, RL ,®ij are the transition rates between state (n,i) and (n-I,j) by losing or getting one electron through the left (right) lead, and peqn,I is the occupation probability of state (n,i) at equilibriumEquation (2) is basically t ... Continue reading---
REFRENCES - [ Total Page(s): 1 ]REFERENCESFriedlander, Michael W. 2000 A Thin Cosmic Rain: Particles from Outer Space (Cambridge:Harvard University Press).Watson, Alan 2001 “Ultra High Energy Cosmic Rays: What we Know Now and What the FutureHolds,†in Relativistic Astrophysics: 20th Texas Symposium (AIP Conference Procedings, volume 586, J. C. Wheeler and H. Martel (eds.) American Institure of Physics, pp. 817–826. (The original abstract was different from the published abstract)Anderson, Carl D ... Continue reading---
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ABSRACT - [ Total Page(s): 1 ]Abstract coming soon ... Continue reading---