Abstract
We discuss the conditions for the classicality of quantum states with a very large number of identical particles. By defining the center of mass from a large set of Bohmian particles, we show that it follows a classical trajectory when the distribution of the Bohmian particle positions in a single experiment is always equal to the marginal distribution of the quantum state in physical space. This result can also be interpreted as a single experiment generalization of the well-known Ehrenfest theorem. We also demonstrate that the classical trajectory of the center of mass is fully compatible with a quantum (conditional) wave function solution of a classical non-linear Schrödinger equation. Our work shows clear evidence for a quantum–classical inter-theory unification, and opens new possibilities for practical quantum computations with decoherence.
Highlights
Since the beginning of quantum theory a century ago, the study of the frontier between classical and quantum mechanics has been a constant topic of debate [1, 2, 3, 4, 5, 6, 7, 8]
Throughout the article, we will consider a quantum system composed of N particles of mass m governed by the wave function Ψ(r1, . . . , rN, t) solution of the many-particle non-relativistic Schrodinger equation
Since we have shown that (21) is a quantum state full of identical particles at t = 0, we conclude that any quantum state with the wave function Ψ(r1, . . . , rN, t) solution of the many-particle Schrodinger equation in (1), with or without external Vext or inter-particle Vint potentials, and with the initial state defined by Eqs. (21) and (22) is a quantum state full of identical particles when N → ∞
Summary
Since the beginning of quantum theory a century ago, the study of the frontier between classical and quantum mechanics has been a constant topic of debate [1, 2, 3, 4, 5, 6, 7, 8]. In the instantaneous collapse theories [12] (like the GRW interpretation [13]), a new stochastic equation is used that breaks the superposition principle at a macroscopic level, while still keeping it at a microscopic one [12] Another possibility is substituting the linear Schrodinger equation by a non-linear collapse law only when a measurement is performed [1, 14]. This is the well-known orthodox (or Copenhagen) solution, and most of the attempts to reach a quantum-to-classical transition have been developed under this last approach [4, 5, 6, 7, 8, 15, 16, 17]. We summarize the main results, contextualize them within previous approaches and comment on further extensions of this work
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