For the standard Quantum Brownian Motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard, one Brownian particle, we show there is at least another one system undergoing the dynamics described by the QBM effect. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. A generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in any interpretational context.
For the standard Quantum Brownian Motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard, one Brownian particle, we show there is at least another one system undergoing the dynamics described by the QBM effect. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. A generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in any interpretational context.
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their relations, are considered. Emphasis is placed on mutually global and irreducible structures. Is there a privileged structure of the closed system? Is there a preferred (bipartite) structure of an open system? Are there any practical advantages of certain alternative structures of the system? Is there a simple dynamical relation for a pair of structures? The [necessarily partial] answers are rather intriguing. Relativity of quantum correlations (that include entanglement as well as the "one-way" and "two-way" discord) is carefully presented. Emphasis is placed on the "parallel occurrence of decoherence" in the quantum Brownian motion. The environment-selected preferred structure of an open composite system is presented for a pair of harmonic oscillators (or the field modes). A limitation of the Nakajima-Zwanzig projection method appears as a consequence of quantum correlations relativity. Hence, describing dynamics of an alternate open-system is a delicate task. Certain interpretational issues, which include "quantum reference frames" issue, are discussed. Some recent experiments are also discussed. To this end, the option that "there are no particles" on the most fundamental physical level naturally follows. Certain open questions and prospects for further research are highlighted.
We investigate the conditions which can lead to the occurrence of "decoherence" (i.e., of "environment-induced superselection"), in a quantum system interacting with another, infinite quantum system (an apparatus, environment, etc.), in the context of the nonrelativistic quantum mechanics. We are particularly concerned with: a kind of interaction, its relative strength, initial state of the apparatus (environment), and compatibility of the self-Hamiltonian and the interaction Hamiltonian of the composite system, "system plus apparatus", including time dependent interactions. As necessary conditions concerning occurrence of decoherence appear the two requirements: (i) That the interaction Hamiltonian is of the separable kind , and (ii) That the complete Hamiltonian, Ĥ u satisfies commutator relation [Ĥ u ( t ), Ĥ u ( t ')] = 0 ( t and t ' arbitrary instants). Since non-separable interaction cannot produce the same, we conclude that occurrence of decoherence is neither a rule (as it is sometimes assumed in the context of the "environment theory"), nor an exceptional consequence of the dynamics of a system interacting with its environment (as it is sometimes claimed in the criticism of the environment theory). Exhaustiveness and generality of our analysis extend applicability of related results (which are independent on a particular model of (infinite) environment), at least as a qualitative test and/or quantitative estimation of the results of the calculations obtained by the use of the different methods (semiclassical methods, path-integration technique, etc.) in quantum many-particle physics.
Quantum decoherence is widely regarded as the principal dynamical mechanism through which classical behaviour emerges from quantum dynamics. This review presents a technical account of decoherence as an open-system phenomenon, emphasizing its mathematical framework, microscopic models, experimental evidence, and foundational implications. Starting from system-environment interactions and reduced density operators, we introduce completely positive trace-preserving maps and Lindblad master equations. We then discuss pure dephasing, pointer-state selection, quantum Brownian motion, spin-boson dynamics, and collisional decoherence. Experimental evidence from atom and molecular interferometry, superconducting qubits, and mesoscopic platforms is examined. Finally, the review assesses the role of decoherence in the quantum measurement problem. Decoherence explains preferred-basis selection and practical suppression of interference, but it does not independently account for the occurrence of a unique measurement outcome.
Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although these models can yield very general classical phenomenology, they are incapable of reproducing relevant characteristics expected of a local environment on a quantum system, such as the characteristic dependence of decoherence on environment spatial correlations. I discuss the characteristics of Quantum Brownian Motion in a local environment by examining aspects of first principle calculations and by the construction of phenomenological models. Effective quantum Langevin equations and master equations are presented in a variety of representations. Comparisons are made with standard results such as the Caldeira-Leggett master equation.
In quantum computation, it is of paramount importance to locate the parameter space where maximal coherence can be preserved in the qubit system. In recent years environment-induced decoherence based the quantum Brownian motion (QBM) models have been applied to two level systems (2LS) interacting with an electromagnetic field, leading to the general belief that 2LS are easily decohered. In a recent paper C. Anastopoulos and B. L. Hu [Phys. Rev. A62, (2000) 033821] derived a new exact non-Markovian master equation at zero temperature, from which they showed that this belief is actually misplaced. For a two-level atom (2LA)- electromagnetic field (EMF) system the decoherence time is rather long, comparable to the relaxation time. Theoretically this is because the dominant interaction is the hatsigmapm type of coupling between the two levels (what constitutes the qubit) and the field, not the hatsigmaz type, which shows the QBM behavior. Depending on the coupling the field can act as a resonator (in an atom cavity) or as a bath (in QBM) and produce very different decoherent behavior in the system. This is not new to Cavity QED experimentalists: the 2LA-EMF system maintaining its coherence in sufficiently long duration is the reason why they can manipulate them so well to show interesting quantum coherence effects.
Quantum decoherence is a proposed mechanism for the emergence of classical physics from the quantum mechanics. It has been developed extensively in recent years, but is sufficiently technically complicated to discourage widespread understanding. In this paper we provide a gentle introduction to quantum decoherence. We introduce state operators and their density matrix representations to describe composite systems, such as an experiment and its environment. We illustrate how the loss of information about a subsystem can cause a quantum system to appear classical. We first analyze a discrete example of phase randomization, then a Bell state, and finally a continuous system. In the final case we provide an accessible derivation of a major early result of decoherence theory, the master equation of quantum Brownian motion. We conclude by applying the master equation to the decoherence of a simple harmonic oscillator, with results reminiscent of our earlier discrete examples.