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Quantum techniques for stochastic mechanics (book) (Rev #2, changes)

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A Course on Quantum Techniques for Stochastic Mechanics is a course book written on a series of blog posts on network theory. The book course is available freely online here

Please tell us about errata and your other thoughts on the book here

Book abstract

Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of chemical reaction networks, which describes the interactions of molecules in a stochastic rather than quantum way. Computer science and population biology use the same ideas under a different name: stochastic Petri nets. But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas—but in a context where probabilities replace amplitudes. In this course we will explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics. We will study the overlap of quantum mechanics and stochastic mechanics, which involves Hamiltonians that can generate either unitary or stochastic time evolution. These Hamiltonians are called Dirichlet forms, and they arise naturally from electrical circuits made only of resistors. The area is ripe to be further connected with modern topics in quantum computation and quantum information theory.

errata

  • Typo on p. 150: “or in a superposition of at least two eigensvectors”

  • p. 151: “good both for stochastic mechanics and stochastic mechanics.”

  • p. 152: “The probability of finding a state in the iith configuration is defined to be |ψ(x)| 2|\psi(x)|^2.”

  • state -> system

  • ψ(x) \psi(x) replace with ψ i \psi_i

  • p. 26: “In Section 2 we’ll get to the really interesting part, where ideas from quantum theory enter the game!”

  • Section 2 -> Section 3

  • p. 28: “—that is, random— about a stochastic Petri net.”

  • random— about -> random—about

  • p. 47: “It’s like if someone says a party is `formal’, so need to wear a white tie:”

  • so need -> so you need

  • p. 54: “This sort of balance is necessary for HH to be a sensible Hamiltonian in this sort of stochastic theory `infinitesimal stochastic operator’, to be precise).”

  • p. 145: “it would be gives us”

  • theory infinitesimal -> theory (an infinitesimal

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