- #1
Luqman Saleem
- 18
- 3
Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian:
$$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$
where ##c^\dagger (c)## are creation (annihilation) operators, ##n## is number operator, ##t## is hopping parameter, ##V## is nearest-neighbor interaction, ##L## is the total number of sites and ##\mu## is chemical potential.
What I understand by chemical potential is, if we set μ=some constant, then no matter how many sites (L) we add to the system, the number of particles will always be conserved. (Please correct me if I am wrong)
QUESTION:
What is the relation between chemical potential and the number of particles? i.e. if I set μ = 10 then how many particles are allowed in the system?
$$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$
where ##c^\dagger (c)## are creation (annihilation) operators, ##n## is number operator, ##t## is hopping parameter, ##V## is nearest-neighbor interaction, ##L## is the total number of sites and ##\mu## is chemical potential.
What I understand by chemical potential is, if we set μ=some constant, then no matter how many sites (L) we add to the system, the number of particles will always be conserved. (Please correct me if I am wrong)
QUESTION:
What is the relation between chemical potential and the number of particles? i.e. if I set μ = 10 then how many particles are allowed in the system?