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arXiv:1810.10588 · Physical Review Research

Prominent interference peaks in the dephasing Anderson model

Yannic Rath, Florian Mintert

Published May 12, 2020• 9 citations
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Abstract

This paper discusses the dynamics of interference structures in the Anderson model with decoherence. Due to an intricate interplay of interference, disorder, and decoherence there is a rise and decay of interference peaks on transient time scales, that is the transition from a quantum mechanical interference pattern to a classical probability distribution is of non-monotonic character. An analytic solution in the limit of weak dephasing supplemented with a numerical analysis beyond this limiting case provides an intuitive understanding for the observed phenomena.

DOI
10.1103/physrevresearch.2.023161

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This paper discusses the dynamics of interference structures in the Anderson model with decoherence. Due to an intricate interplay of interference, disorder, and decoherence there is a rise and decay of interference peaks on transient time scales, that is the transition from a quantum mechanical interference pattern to a classical probability distribution is of non-monotonic character. An analytic solution in the limit of weak dephasing supplemented with a numerical analysis beyond this limiting case provides an intuitive understanding for the observed phenomena.
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This gives rise to full revivals of initial wavepackets, fractional revivals (multiple wavepackets appearing at fractions of the revival time) and the striking quantum carpets. A variety of analytic techniques are used to consider the interference that gives rise to these phenomena while skirting calculations involving cross-terms. Novel results include a new theorem on the weighting coefficients ama_mam​ that govern fractional revivals, a demonstration that ΨclΨ_{cl}Ψcl​, the function that governs the distribution and features of these fractional revivals, really does behave classically, a treatment of the wavepacket dephasing in the infinite square well by means of the Poisson summation formula, and a correct analysis of the spatial distribution of intermode traces. Also, this work presents a coherent treatment of these phenomena, which before now did not exist.
This work presents a numerical exploration of a phase-structured time model for quantum dynamics, implemented using QuTiP. In this framework, the quantum state phase is governed by a time-dependent scalar field τ(t), with energy defined through E = ℏ dτ/dt. The study investigates how different τ models — including deterministic, stochastic, and correlated stochastic processes — influence observable quantum behavior. Three key phenomena are analyzed: 1. Spectral structure: Structured τ-fields generate richer frequency spectra compared to linear phase evolution, quantified using spectral entropy and bandwidth measures. 2. Interference: The relation between phase differences (Δτ) and quantum overlap is examined. For deterministic and correlated τ models, interference patterns remain highly consistent with cos(Δτ), suggesting robustness of phase-based descriptions. 3. Decoherence: Ensemble-averaged stochastic τ-fields produce decoherence-like behavior. The resulting dynamics are compared against standard Lindblad dephasing models. Significant deviations are observed, including non-exponential decay and non-monotonic behavior, indicating non-Markovian structure. A key result is that a single parameter — the correlation time of τ fluctuations — induces systematic and predictable changes across spectral properties, interference agreement, and decoherence mismatch. This suggests that certain forms of quantum noise may exhibit temporal structure rather than being purely random, and that such structure can be modeled within a unified phase-based framework. This study is exploratory and numerical in nature and does not claim a new physical theory. Instead, it proposes a modeling approach that may be relevant for understanding structured noise, non-Markovian dynamics, and potential improvements in quantum control or error mitigation. Code is available at:https://github.com/bahman2017/tdf_qutip
We study the intrinsic, disorder-induced decoherence of an isolated quantum system under its own dynamics. Specifically, we investigate the characteristic time scale (i.e., the decoherence time) associated with an interacting many-body system losing the memory of its initial state. To characterize the erasure of the initial state memory, we define a time scale, the intrinsic decoherence time, by thresholding the gradual decay of the disorder-averaged return probability. We demonstrate the system-size independence of the intrinsic decoherence time in different models, and we study its dependence on the disorder strength. We find that the intrinsic decoherence time increases monotonically as the disorder strength increases in accordance with the relaxation of locally measurable quantities. We investigate several interacting spin (e.g., Ising and Heisenberg) and fermion (e.g., Anderson and Aubry-Andr\'e) models to obtain the intrinsic decoherence time as a function of disorder and interaction strength.
We investigate the fidelity susceptibility, which quantifies the sensitivity of single-particle eigenstates to perturbations, in the three-dimensional Anderson model. As a function of disorder strength WWW, it exhibits two distinct peaks. The first peak signals a crossover at weak disorder strength from plane-wave states to single-particle quantum chaos, and its position shifts toward W→0W\to 0W→0 in the thermodynamic limit. The second peak emerges, to high numerical accuracy, at the critical disorder strength associated with the Anderson localization transition. We further show that the divergence of the first peak is maximal, scaling as the square of the inverse frequency cutoff, whereas the divergence of the second peak is submaximal. We relate the latter suppression to the fractal structure of single-particle eigenstates at criticality. We discuss two distinct scenarios that give rise to the peaks in the fidelity susceptibilities. Moreover, studying the scaling of typical fidelity susceptibilities above the Anderson transition, we find evidence of two distinct regimes of nonergodic behavior.
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is contrasted with the decoherence effect of dynamic disorder having strength WWW, where a quantum to classical crossover at time ${t}_{c}\ensuremath{\propto}{W}^{\ensuremath{-}2}$ transforms the quantum walk into an ordinary random walk with diffusive spreading. We demonstrate these localization and decoherence phenomena in quantum carpets of the observed time evolution, we relate our results to previously studied models of decoherence for quantum walks, and examine in detail a dimer lattice which corresponds to a single qubit subject to randomness.