Help about the Nonequilibrium Green's Function

In summary, the Nonequilibrium Green's Function (NEGF) method is a theoretical framework used to study quantum mechanical systems that are not in thermodynamic equilibrium. It takes into account both the quantum and statistical mechanical aspects of a system, making it a powerful tool for studying nonequilibrium systems. Its main applications include electronic transport in materials, chemical reactions, and heat transport in nanoscale systems. However, the method also has challenges, such as requiring numerical solutions and accurate descriptions of the system's Hamiltonian, and limitations, such as not being applicable at absolute zero temperature and not accounting for quantum coherence effects.
  • #1
snooper007
33
1
help about the Nonequilibrium Green's Function
in H. Haug and A.-P. Jauho Book
Quantum kinetics in transport and Optics of Semiconductors
Eq.(4.31)

[tex]C^r(t,t')=A^<(t,t')B^r(t,t')+A^r(t,t')B^<(t,t')+A^r(t,t')B^r(t,t')[/tex]

I can not derive this equation, my result has a extra term [tex]\theta(t-t')[/tex]
i.e.
[tex]C^r(t,t')=\theta(t-t')[A^<(t,t')B^r(t,t')+A^r(t,t')B^<(t,t')+A^r(t,t')B^r(t,t')][/tex]
 
Physics news on Phys.org
  • #2
I have understood this problem
 
  • #3


The Nonequilibrium Green's Function (NEGF) is a powerful theoretical tool used to study the dynamics of open quantum systems. It is particularly useful in the field of quantum transport, where it allows for the calculation of transport properties in systems that are not in thermal equilibrium.

In the equation provided, C^r(t,t') represents the retarded correlation function, which describes the time evolution of a system from an initial time t' to a final time t. A^< and B^< represent the lesser Green's functions, which describe the behavior of the system when it is not in equilibrium. A^r and B^r are the retarded Green's functions, which describe the system's behavior when it is in equilibrium.

The extra term \theta(t-t') in your result is known as the Heaviside step function and it ensures that the correlation function is only non-zero for positive time differences, as expected for a physical system. This term is often included in the NEGF formalism to ensure causality and maintain the correct time ordering of events.

To fully understand and derive the NEGF equation, it is necessary to have a strong background in quantum mechanics and statistical mechanics. I recommend consulting the book "Quantum Kinetics in Transport and Optics of Semiconductors" by H. Haug and A.-P. Jauho, as it provides a comprehensive and detailed explanation of the NEGF formalism and its applications. Additionally, seeking guidance from a mentor or colleague with expertise in this area can also be helpful in understanding and applying the NEGF equation.
 

1. What is the Nonequilibrium Green's Function (NEGF) method?

The NEGF method is a theoretical framework used to study quantum mechanical systems that are not in thermodynamic equilibrium. It allows for the calculation of the time evolution of a system under applied electric or thermal bias. It is often used in the field of condensed matter physics to study electronic transport in materials.

2. How does the NEGF method differ from other theoretical approaches?

The NEGF method takes into account both the quantum and statistical mechanical aspects of a system, making it a powerful tool for studying nonequilibrium systems. It also allows for the treatment of open systems, where particles can enter and leave the system, making it particularly useful for studying electronic transport in materials.

3. What are the main applications of the NEGF method?

The NEGF method has a wide range of applications in the study of electronic transport in materials, such as transistors, semiconductors, and quantum dots. It is also used in the study of chemical reactions, molecular electronics, and heat transport in nanoscale systems.

4. What are the main challenges of using the NEGF method?

The NEGF method requires the numerical solution of complex equations, which can be computationally intensive. It also relies on the accurate description of the system's Hamiltonian, which can be challenging for large systems or those with strong interactions. Additionally, the NEGF method is limited to systems that can be described by a small number of degrees of freedom.

5. Are there any limitations to the NEGF method?

While the NEGF method is a powerful tool for studying nonequilibrium systems, it is not applicable to systems at absolute zero temperature and cannot capture effects due to thermal fluctuations. It also does not account for the effects of quantum coherence, making it less suitable for studying systems at very low temperatures or in highly coherent states.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
663
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
135
  • Differential Equations
Replies
1
Views
716
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
1
Views
2K
  • Differential Equations
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
440
Replies
4
Views
305
  • Introductory Physics Homework Help
Replies
6
Views
1K
Back
Top