Decoherence and the Classical Limit of Quantum Mechanics (original) (raw)
Related papers
A Top-down View of the Classical Limit of Quantum Mechanics
2016
Since its birth in the early twentieth century, quantum mechanics raised a number of questions and problems, many of which are still a source of lively debate. The attempts to address those issues have led to a multiplicity of interpretations and theoretical developments which have enriched the scientific knowledge about the theory. Perhaps the problem most discussed in this context is the socalled quantum measurement problem, based on the theoretical difficulty to explain how measuring devices with classical pointers are able to produce results when acting on quantum systems (von Neumann 1932, Ballentine 1990, Bub 1997). Another question that has been the subject of intensive research is the problem of the classical limit of quantum mechanics (Bohm 1951, Schlosshauer 2007). According the correspondence principle (Bohr 1920; for a recent discussion, see Bokulich 2014), there should be a limiting procedure that accounts for the classical behavior of a system in terms of the laws of quantum mechanics. The problem of classical limit consists in explaining how the classical realm "emerges" from the quantum domain. The two problems just mentioned have something in common: both point to the need for finding a link between the classical and the quantum world. Along the history of quantum mechanics, the classical limit has been approached from many different perspectives, such as those given by the Ehrenfest theorem (Ehrenfest 1927), the Wigner transform (Wigner 1932) and the deformation theory (Bayen et al. 1977, 1978). Traditionally, the problem was conceived as a matter of intertheory relation: classical mechanics should be obtained from quantum mechanics by means of the application of a mathematical limit, in a way analogous to the way in which the classical equations of motion are obtained from special relativity. However, this approach has been weakening over the past decades: at present it is recognized that the classical limit also involves some kind of physical process, which transforms the quantum states in such a way that they finally can be interpreted as classical states. This process is now known as quantum decoherence. One the main features of quantum mechanics is the superposition principle, which leads to the phenomenon of quantum interference, without classical analogue. Decoherence is viewed as a process that cancels interference and selects the candidates to classical states. The cancellation of
The Problem of the Classical Limit of Quantum Mechanics and the Role of Self-Induced Decoherence
Foundations of Physics, 2006
Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity represented by the limith → 0: when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system becomes equivalent to the description of an ensemble of classical trajectories on phase space weighted by their corresponding probabilities.
On the classical limit of quantum mechanics
Arxiv preprint quant-ph/0112009, 2001
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing real objects in an observer-independent way.
The role of self-induced decoherence in the problem of the classical limit of quantum mechanics
2003
Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity: when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system becomes equivalent to the description of an ensemble of classical trajectories on phase space weighted by their corresponding probabilities.
A Continuous Transition Between Quantum and Classical Mechanics. II
Foundations of Physics, 2002
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical mechanics which provides a continuous transition to quantum mechanics via environment-induced decoherence.
2024
The standard notion of a classical limit, represented schematically by → 0, provides a method for approximating a quantum system by a classical one. In this work, we explain why the standard classical limit fails when applied to subsystems, and show how one may resolve this by explicitly modeling the decoherence of a subsystem by its environment. Denoting the decoherence time by τ , we demonstrate that a double scaling limit in which → 0 and τ → 0 such that the ratio E f = /τ remains fixed leads to an irreversible open-system evolution with well-defined classical and quantum subsystems. The main technical result is showing that, for arbitrary Hamiltonians, the generators of partial versions of the Wigner, Husimi, and Glauber-Sudarshan quasiprobability distributions may all be mapped in the above-mentioned double scaling limit to the same completely positive classical-quantum generator. This provides a regime in which one can study effective and consistent classical-quantum dynamics.
Quantum Mechanics As A Limiting Case of Classical Mechanics
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which quantum mechanics emerges as a limiting case of classical mechanics in which the classical system is decoupled from its environment.
A Continuous Transition Between Quantum and Classical Mechanics (I)
2001
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical mechanics which provides a continuous transition to quantum mechanics via environment-induced decoherence.
A Critique of the Classical Limit Problem of Quantum Mechanics
Foundations of Physics Letters, 2006
The complex quantum-classical relationship is reviewed and the inadequacy of quantum mechanical wavefunction description for the centre of mass motion of a macroscopic system is discussed. The emergence of manifest classical reality in this case is analyzed and we interpret the unphysical infinitely rapid oscillations of the wavefunction near the classical regime observed in our earlier studies as the breakdown of wavefunction description for normal macroscopic mass domain above 10 −15 g. It is contended that, production of quantum interference with large macromolecules like viruses (m ∼ 10 −12 g), as proposed by some authors, is impossible. Another testable prediction asserts that particle tracks, whenever observed, will obey classical law and offers an interesting experimental verification.