Multifractal mesoscopic fluctuations in the quantum dynamics of a spatially modulated chain

Abstract. Multifractal fluctuations in the time dynamics of geoelectrical data, recorded in a seismic area of southern Italy, have been revealed using the Multifractal Detrended Fluctuation Analysis (MF-DFA), which allows to detect multifractality in nonstationary signals. Our findings show that the geoelectrical time series, recorded in the seismic area of southern Apennine Chain (Italy), is multifractal. The time evolution of the multifractality suggests that the multifractal degree increases prior the occurrence of earthquakes. This study aims to propose another approach to investigate the complex dynamics of earthquake-related geoelectrical signals.

The electron mobilities of two n-type pentacenequinone derivative organic semiconductors, 5,7,12,14-tetraaza-6,13-pentacenequinone (TAPQ5) and 1,4,8,11-tetraaza-6,13-pentacenequinone (TAPQ7), are investigated with use of the methods of electronic structure and quantum dynamics. The electronic structure calculations reveal that the two key parameters for the control of electron transfer, reorganization energy and electronic coupling, are similar for these two isomerization systems, and the charge carriers essentially display one-dimensional transport properties. The mobilities are then calculated by using the time-dependent wavepacket diffusion approach in which the dynamic fluctuations of the electronic couplings are incorporated via their correlation functions obtained from molecular dynamics simulations. The predicted mobility of TAPQ7 crystal is about six times larger than that of TAPQ5 crystal. Most interestingly, Fermi's golden rule predicts the mobilities very close to those from the time-dependent wavepacket diffusion method, even though the electronic couplings are explicitly large enough to make the perturbation theory invalid. The possible reason is analyzed from the dynamic fluctuations.

The study of optomechanical systems has attracted much attention, most of which are concentrated in the physics in the small-amplitude regime. While in this article, we focus on optomechanics in the extremely-large-amplitude regime and consider both classical and quantum dynamics. Firstly, we study classical dynamics in a membrane-in-the-middle optomechanical system in which a partially reflecting and flexible membrane is suspended inside an optical cavity. We show that the membrane can present self-sustained oscillations with limit cycles in the shape of sawtooth-edged ellipses and exhibit dynamical multistability. Then, we study the dynamics of the quantum fluctuations around the classical orbits. By using the logarithmic negativity, we calculate the evolution of the quantum entanglement between the optical cavity mode and the membrane during the mechanical oscillation. We show that there is some synchronism between the classical dynamical process and the evolution of the quantum entanglement.

This chapter reviews recent work where dynamic pump depletion and quantum fluctuations are examined in the buildup of three-level superfluorescence (SF) with the use of a unidirectional semi classical model in conjunction with either an average Langevin force or quantum fluctuations as an initiation process. Using the computational methods previously developed for pulse propagation studies, the dynamic evolution of SF from an optically pumped system has been studied. The code used has been extensively applied to self-induced transparency (SIT) and two-level SF and is well documented in the literature. Results generated by it have been validated by quantitative agreement with experiments by several groups on Na, Ne, I, HF, Cs, and 87Rb.

The many-body localization transition is a dynamical quantum phase transition between a localized and an extended phase. We study this transition in the XXZ model with disordered magnetic field and focus on the time evolution following a global quantum quench. While the dynamics of the bipartite entanglement and spin fluctuations are already known to provide insights into the nature of the many-body localized phases, we discuss the relevance of these quantities in the context of the localization transition. In particular, we observe that near the transition the long time limits of both quantities show behavior similar to divergent thermodynamic fluctuations.

Quantum phase transitions have long been studied in their relation to quantum fluctuations. These fluctuations can be quantified as the degree of spin squeezing in spin models, where one of the two noncommutative observables breaks the standard quantum limit of measurement by minimizing its uncertainty. However, the understanding of their role in dynamical quantum phase transitions (DQPTs) is still incomplete. In this work, we combine the Loschmidt amplitude, which detects DQPTs, and the spin-squeezing parameter (SSP), the quantification of spin squeezing, to study the spin dynamics in a quenched interacting spin model around DQPT. We show that the extremum, mostly maximum, of SSP occurs near DQPTs when the system is quenched between different phases. These phenomena further unveil the spin correlations during DQPTs, for which the highest contribution aligns with the preferred direction of spin interactions in the postquenched phase. We also demonstrate that the time evolution of SSP differs for various quench scenarios. These findings provide us with physical insights into the dynamics of quantum fluctuations around DQPTs and their relation to the equilibrium phase diagrams.

Lattice softness has a significant impact on charge carrier dynamics in condensed matter systems, contributing to the emergence of various properties and functions. Examples include the remarkable carrier lifetimes and defect tolerances of hybrid organic-inorganic perovskites. Recent studies suggest the contribution of quartic anharmonicity of the lattice vibrations. The quartic anharmonicity can be discussed with a double-well potential, and the transition between the two minima can be coarse grained as a two-state jump stochastic process. Such a stochastic approach is typically employed to describe dynamic fluctuations introduced into a system by two-state transitions in the surroundings. To investigate charge transport in materials, however, it is crucial to describe not only the fluctuations but also the dynamic lattice distortions associated with charge transport. Therefore, there is a need for a theory to describe the charge carrier dynamics proceeding alongside the lattice distortion dynamics. In this study, we present a theory that describes quantum dynamics under the influence of an environment with two stable states, termed a bistable environment. The theory describes the effects of fluctuations and dissipation induced from the bistable environment in a reasonable manner, and the effects exhibit a different temperature dependence than the widely employed Gaussian environment. The physical implication of this temperature dependence is provided in terms of the environmental dynamics. The results of this study are expected to provide a step forward in describing charge carrier dynamics in materials with lattice softness and pronounced lattice anharmonicity, e.g., hybrid organic-inorganic perovskites. Moreover, these findings represent an advancement in our understanding of and capacity to predict and control the physical properties and functions of these materials. Published by the American Physical Society 2025

A new method called “Fluctuation Expansion” has been recently proposed for solving quantum dynamical problems . This method is succesfully applied to the dynamics of expectation values such that not the wave function itself but the expectation values of the position and momentum operator are taken into consideration and then the expectation value of certain entities depending on position and momentum operators are expressed via fluctuation expansion. This brings an infinite number of new unknown, fundamental and associate fluctuation terms. The derivatives of expectation values of the position and momentum operators and fluctuation operators are expressed in terms of these terms again. The resulting infinite set of differential equations and accompanying initial conditions are truncated at certain fluctuation order and then tried to be solved. Here we take a one dimensional time independent Hamiltonian and consider the zeroth and first order truncations. Equations obtained in this way are investigated in the sense of phase space which is defined by the expextation values of the position and momentum operator and the fluctuations entering the truncated equations. We find certain subspaces of the phase space such that there, certain expressions remain constant . This helps us to reduce the dimension of the problem.