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arXiv:1605.00834 · Physical Review A

Time scale of stationary decoherence

János Polonyi

Published Jul 5, 2017• 1 citation
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Abstract

The decoherence of a test particle interacting with an ideal gas is studied by the help of the effective Lagrangian, derived in the leading order of the perturbation expansion and in order $O({\ensuremath{\partial}}_{t}^{2})$. The stationary decoherence time is found to be comparable to or longer than the diffusion time. The decoherence time reaches its minimal value for classical, completely decohered environment, suggesting that physical decoherence is slowed down as compared with diffusion by the quantum coherence of the environment.

DOI
10.1103/physreva.96.012104

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The decoherence of a test particle interacting with an ideal gas is studied by the help of the effective Lagrangian, derived in the leading order of the perturbation expansion and in order O(\ensuremath∂t2)O({\ensuremath{\partial}}_{t}^{2})O(\ensuremath∂t2​). The stationary decoherence time is found to be comparable to or longer than the diffusion time. The decoherence time reaches its minimal value for classical, completely decohered environment, suggesting that physical decoherence is slowed down as compared with diffusion by the quantum coherence of the environment.
To study the phenomenon of decoherence the effective Lagrangian of a test particle interacting with an ideal gas is derived in the leading order of the perturbation expansion and in order $\ord{\partial^2_t}$. Two concepts of decoherence are distinguished and investigated in details: The general dynamical decoherence and the stationary decoherence, an approximation of the dynamical phenomenon corresponding to the assumption of a static test particle trajectory. Comparison of the stationary decoherence described by the present effective theory with the traditional description of decoherence based on collision theory reveals a qualitative similarity within their domain of applicability. However, the effective theory predicts comparable time scales for decoherence and dissipation in contrast to the deviation of this scales by many orders of magnitudes, estimated by referring to the collision approach. In particular the extremely fast decoherence predicted by the collisional approach can only be reproduced by the effective theory for parameter values which violate the applicability of both approaches. On the other hand, in harmonic systems, the true dynamical decoherence is indeed an extremely fast process involving a double exponential time dependence. It is argued that, in realistic systems, the dissipative effective dynamics is non-perturbative in nature and its asymptotic, relaxed state incorporates strong quantum fluctuations.
We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.
Starting from the thermodynamic limit of information recording, this paper derives a complete, universal decoherence formula consisting of three linked equations: 1. A **non-zero lower bound on the decoherence time** of a quantum system: `τ_min = (ℏ / k_B T) · (1 / ln N_eff)`, where `N_eff` is the number of effective environmental degrees of freedom participating in the irreversible recording of the system's information. 2. A **quantitative criterion for the macroscopic–microscopic boundary**: `N_eff^(c) = exp( ℏ / (k_B T · T_sys) )`, where `T_sys` is the characteristic evolution time of the system. When `N_eff > N_eff^(c)`, decoherence completes before a single coherent evolution, and classical behavior emerges. 3. A **thermodynamic lower bound on interference fringe visibility**: `V ≥ exp( − ln N_eff / ln N_eff^(c) )`, derived from the first two equations without additional assumptions. The first equation predicts a *saturation effect*: the decoherence time no longer shortens indefinitely as environmental coupling increases. The second shows that for nearly all laboratory-accessible systems, `N_eff^(c) ≈ 1`, meaning any non-zero environmental coupling suffices to trigger the transition—explaining why macroscopic objects are inevitably classical. The third provides a directly measurable observable for the continuous quantum–classical phase transition. The framework is universal, applies to any quantum system in contact with an environment at temperature `T`, and its three core predictions are independently falsifiable. Based on the boundary criterion, wave–particle duality in double-slit experiments is reinterpreted as a special case of this phase transition occurring under the limiting condition `N_eff^(c) ≈ 1`. Three experimental schemes—a decoherence-saturation ratio test, a temperature-dependence test of the boundary criterion, and a direct observation of the continuous wave–particle transition via ultrafast electron diffraction or circuit QED—are proposed, all feasible on existing quantum information platforms without requiring new equipment.