We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are the physics points of connection between the two descriptions?
Answer
Linear in the quantum mechanics has nothing to do with its complexity. A two-state spin can be described by a simple 2-by-2 matrix; however, 30 interacting spin, in general, must be described by a 1 billion by 1 billion matrix. It grows exponentially as the number of spins increases, for $10^{23}$ spin, you may need a matrix of size $2^{10^{23}}$. It is not easy to understand and not simple in most sense. If you learn some statistical mechanics, you will know that this number is large enough to have new emergent phenomenon.
No comments:
Post a Comment