Quantum Dynamics for Classical Systems

The role of information in a two-traders market

“…In [5] several useful rules have been proposed to fix the expression of H. We need now to incorporate in H the effect described by the pilot wave function, extending, for instance, what is discussed in [17]. See also [6].…”

“…in fixing the initial status of the various traders after they have been reached by the information but before they start to trade. For this reason, if we call H f ull = H + H ex the Hamiltonian describing the traders and the information, and if with H ex we mean that part of H f ull describing the exchanges between τ 1 and τ 2 , see [5], we will only be interested here in H. It is like if we are considering two different time intervals: in the first one, [0, t 1 ], the two traders, which are indistinguishable at t = 0, receive a different amount of information. This allows them to react in different ways, so that, at time t 1 , they are expected to become different.…”

“…All the other commutators are zero. The meaning of these operators is widely discussed in [5]: s j destroys a share in the portfolio of τ j , see below, while s † j creates a share. The operators c j and c † j respectively lower and rise the amount of cash of τ j .…”

“…After these original applications, the same tools were also used for rather different macroscopic systems. A recent monograph on these topics is [5]. In the cited papers and in [5] the role of information was, in a certain sense, only incorporated by properly choosing some of the constants defining the Hamiltonian of the system we were considering.…”

“…In essence, the use of quantum mechanical techniques into social science revolve really around formalizing information. See [5].…”