The Energy-Momentum Transport Wave Function

Ronald Newburgh

By assuming wave‐particle duality for those phenomena in which the directions of energy transport and wave propagation are co‐parallel, one can show the co‐variant nature of the deBroglie energy‐frequency and momentum‐wave vector relations. If the energy transport and wave propagation are not parallel, as is the case for light propagation in anisotropic media, it follows necessarily that the deBroglie relations are no longer valid as written. In this paper the relations are generalized for such non‐parallel situations by defining a new wave vector l in the direction of energy transport and distinct from the propagation wave vector. The introduction of l follows the method by which deBroglie associated a wave with an electron. The magnitude of l is ω u/c2 where ω is the angular frequency and u the velocity of energy transport. The physical meaning of l is discussed including its interpretation as the wave vector for the photon wave function.

Christof Wetterich

Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function. Its unitary evolution obeys a Schrödinger equation. Statistical observables measure properties of the classical probability distribution. In the quantum formalism they are represented by operators which do not commute with the ones associated to classical observables. Momentum, quantum energy and angular momentum or charges yield conserved quantities which constrain the evolution of the classical probability distribution. The characteristic features of quantum mechanics, as the superposition of wave functions, interference, the importance of phases, non-commuting operators or a unitary time evolution, are realized by probabilistic classical transport equations. Stochastic transport equations are described by a quantum system with a stochastic Hamiltonian.

Peter J. Riggs

Daxing Xiong, Felix Thiel, Eli Barkai

We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular quantum walks. Through this strategy, we obtain the quantum wave function from the classical evolution. Specially, this goal is achieved with the classical momenta of the particles on the chain and their Hilbert transform, from which we construct the many-body momentum and Hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function, respectively. With such a wave function, we show that the classical chain's energy and heat spreading densities can be related to the wave function's modulus square. This relation provides a new perspective to understand ballistic heat transport. The results here may give a definite answer to Feynman's idea of using a classical device to simulate quantum physics.

Antti‐Pekka Jauho