Equivalence between finite state stochastic machine, non-dissipative and dissipative tight-binding and Schrödinger model

Abstract

The mathematical equivalence between finite state stochastic machine and non-dissipative and dissipative quantum tight-binding and Schrödinger model is derived. Stochastic Finite state machine is also expressed by classical epidemic model and can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results show that quantum mechanical phenomena might be simulated by classical statistical model as represented by finite state stochastic machine. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore, the existence of Aharonov–Bohm effect in quantum systems (Becker et al., 2019) can also be reproduced by the classical epidemic model or in broader sense by finite state stochastic machine. Every quantum system made from quantum dots and described by simplistic tight-binding model by use of position-based qubits can be effectively described by classical statistical model encoded in finite stochastic state machine with very specific structure of S matrix that has twice bigger size as it is the case of quantum matrix Hamiltonian. Furthermore, the description of linear and non-linear stochastic finite state machine is mapped to tight-binding and Schrödinger model. The concept of N dimensional complex time is incorporated into tight-binding model, so the description of dissipation in most general case is possible. Obtained results help in approximation of non-dissipative or dissipative quantum mechanical phenomena by classical statistical physics expressed by finite state stochastic machine. Furthermore, the equivalence of Wannier tight-binding dissipative or non-dissipative formalism to dissipative or non-dissipative Schrödinger formalism and to finite state stochastic machine was shown.