Single electron transistor at high-temperature

In summary, the conversation discusses the proof of the equation Ck=[e^(-Scl)*{gamma(1+a-k)*gamma(1+b-k)}]/{gamma(1+u)} to show that it is equal to Ck=[{gamma(1+a)*gamma(1+b)}/{gamma^2(1+k)*gamma(1+u)}]*e^(Scl). The conversation also mentions the use of the definition of the gamma function, gamma(N+1+a)=(N+a)(N+a-1)...(1+a)a!, and the value of u=[g*Beta*Ec]/[2*(pi)^2]. It is also noted that the correction of order 1/N can be
  • #1
zendosqueeze
1
0
From Ck=[{e^(-Scl)*gamma(N+1)*gamma(N+1+u)}/{gamma(1+u)}]/[{gamma(N+1+a-k)*gamma(N+1+b-k)}/{gamma(1+a-k)*gamma(1+b-k)}]

How to prove Ck=[e^(-Scl)*{gamma(1+a-k)*gamma(1+b-k)}]/{gamma(1+u)}

to get Ck=[{gamma(1+a)*gamma(1+b)}/{gamma^2(1+k)*gamma(1+u)}]*e^(Scl)?

by u=[g*Beta*Ec]/[2*(pi)^2]

where the correction of order 1/N may be ignored. Employing the definition of the gamma function ; gamma(N+1+a)=(N+a)(N+a-1)...(1+a)a!
 
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  • #2
zendosqueeze said:
From Ck=[{e^(-Scl)*gamma(N+1)*gamma(N+1+u)}/{gamma(1+u)}]/[{gamma(N+1+a-k)*gamma(N+1+b-k)}/{gamma(1+a-k)*gamma(1+b-k)}]

How to prove Ck=[e^(-Scl)*{gamma(1+a-k)*gamma(1+b-k)}]/{gamma(1+u)}

to get Ck=[{gamma(1+a)*gamma(1+b)}/{gamma^2(1+k)*gamma(1+u)}]*e^(Scl)?

by u=[g*Beta*Ec]/[2*(pi)^2]

where the correction of order 1/N may be ignored. Employing the definition of the gamma function ; gamma(N+1+a)=(N+a)(N+a-1)...(1+a)a!

Your post looks like nonsense or trolling to me. What does the body of your post have to do with the title of your thread? You need to provide a lot more explanatory details to make this thread make sense, IMO.
 

1. What is a single electron transistor at high-temperature?

A single electron transistor is a device that controls the flow of single electrons through a circuit, allowing for extremely precise and sensitive measurements. At high-temperatures, these devices can operate in environments with elevated temperatures, making them useful for a variety of applications.

2. How does a single electron transistor at high-temperature work?

A single electron transistor at high-temperature typically consists of a source and drain electrode connected by a central island, with a gate electrode controlling the flow of electrons between them. At high-temperatures, the electrons have more energy and can overcome potential barriers, allowing for current to flow through the device.

3. What are some potential applications of a single electron transistor at high-temperature?

Single electron transistors at high-temperature have potential applications in fields such as nanotechnology, quantum computing, and high-precision sensing. They can also be used in harsh environments where traditional transistors may not function properly.

4. What are the benefits of using a single electron transistor at high-temperature?

One of the main benefits of using a single electron transistor at high-temperature is its high precision and sensitivity, allowing for accurate measurements and control of electron flow. Additionally, these devices can operate in extreme environments, making them useful for a variety of applications.

5. What are the challenges associated with single electron transistors at high-temperature?

One of the main challenges with single electron transistors at high-temperature is maintaining stability and avoiding unwanted electron tunneling. High-temperature environments can also introduce noise and interference, which can affect the performance of the device. Additionally, manufacturing these devices can be complex and require specialized techniques.

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