Time-dependent Correlation Functions Research Articles

Simulations of Stochastic Fluid Dynamics near a Critical Point in the Phase Diagram.

We present simulations of stochastic fluid dynamics in the vicinity of a critical endpoint belonging to the universality class of the Ising model. This study is motivated by the challenge of modeling the dynamics of critical fluctuations near a conjectured critical endpoint in the phase diagram of quantum chromodynamics (QCD). We focus on the interaction of shear modes with a conserved scalar density, which is known as model H. We show that the observed dynamical scaling behavior depends on the correlation length and the shear viscosity of the fluid. As the correlation length is increased or the viscosity is decreased we observe a crossover from the dynamical exponent of critical diffusion, z≃4, to the expected scaling exponent of model H, z≃3. We use our method to investigate the time-dependent correlation function of non-Gaussian moments M^{n}(t) of the order parameter. We find that the relaxation time depends in a nontrivial manner on the power n.

Dissipative Dynamics in Open Fermionic Chains

By merging the Feynman-Vernon’s approach with the out-of-equilibrium Keldysh-Schwinger formalism, we construct the reduced generating functional through which all the time-dependent correlation functions of an open fermionic system can be directly derived by applying the appropriate functional derivatives. As a concrete example, we investigate the transverse Ising model, we derive the covariance matrix at the steady state of the system and we investigate its critical behaviour.

Kardar-Parisi-Zhang universality in two-component driven diffusive models: Symmetry and renormalization group perspectives.

We elucidate the universal spatiotemporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion processes. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We connect these universal scaling exponents with the symmetries of the model equations. We thus establish that these models belong to the 1D KPZ universality class.

Dynamic Light Scattering for the Measurement of Transport Properties of Fluids

The present article summarizes experimental and theoretical considerations required for a proper use of dynamic light scattering (DLS) for the measurement of transport properties of fluids. It addresses not only recent advancements of the method, but also aims to provide recommendations to researchers who intend to apply the technique in the future. As outlined in this study, DLS is based on the analysis of scattered light governed by microscopic statistical or periodic fluctuations that originate from the thermal movement of molecules and/or particles at macroscopic thermodynamic equilibrium. The dynamics of these hydrodynamic fluctuations in the bulk of fluids or at their phase boundaries are related to the underlying diffusive processes and, thus, to the associated transport properties, and are reflected by the time-dependent correlation function of the scattered light intensity. The fundamentals of this type of detection, known as photon correlation spectroscopy (PCS), will be discussed in the present contribution in some more detail. It is emphasized that the experiments need to be designed carefully in accordance with theory in order to assign the measurement signals to the corresponding hydrodynamic fluctuations. If the necessary conditions are fulfilled, DLS allows the accurate determination of several transport properties including kinematic and dynamic viscosity, thermal diffusivity, mutual diffusivity, and sound attenuation, which may be accessed together with other thermophysical properties such as speed of sound and surface or interfacial tension. In some instances, also the simultaneous determination of several transport properties is possible. With the exception of the sound attenuation, expanded uncertainties for the mentioned transport properties down to 1 % can be achieved for various types of fluid systems over a wide range of thermodynamic states up to elevated temperatures and pressures as well as in the vicinity of critical points. This performance and versatility of the DLS technique is documented in the present study by highlighting measurement examples from recent thermophysical property research on different classes of working fluids relevant for process and energy technology.

A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation

In this paper, we give a microscopic derivation of Gibbs measures for the focusing cubic nonlinear Schrödinger equation on the one-dimensional torus from many-body quantum Gibbs states. Since we are not making any positivity assumptions on the interaction, it is necessary to introduce a truncation of the mass in the classical setting and of the rescaled particle number in the quantum setting. Our methods are based on a perturbative expansion of the interaction, similarly as in [1]. Due to the presence of the truncation, the obtained series have infinite radius of convergence. We treat the case of bounded, L 1 and delta function interaction potentials, without any sign assumptions. Within this framework, we also study time-dependent correlation functions. This is the first such known result in the focusing regime.

Spectral Relaxation Imaging Microscopy II: Complex Dynamics.

The dynamics of condensed matter can be measured by the time-dependent Stokes shift of a suitable fluorescent probe. The time-dependent spectral correlation function is typically described by one or more spectral relaxation correlation times, which, in liquid solvents, characterize the timescales of the dipolar relaxation processes around the excited-state probe. The phasor plot provides a powerful approach to represent and analyze time and frequency-domain data acquired as images, thus providing a spatial map of spectral dynamics in a complex structure such as a living cell. Measurements of the phase and modulation at two emission wavelength channels were shown to be sufficient to extract a single excited-state lifetime and a single spectral relaxation correlation time, supplying estimates of the mean rate of excited-state depopulation and the mean rate of spectral shift. In the present contribution, two more issues were addressed. First, the provision of analytic formulae allowing extraction of the initial generalized polarization and the relaxed generalized polarization, which characterize the fluorescence spectrum of the unrelaxed state and the fully relaxed state. Second, improved methods of model discrimination and model parameter extraction for more complex spectral relaxation phenomena. The analysis workflow was illustrated with examples from the literature.

Low-energy excitations and transport functions of the one-dimensional Kondo insulator

Using variational matrix product states, we analyze the finite temperature behavior of a half-filled periodic Anderson model in one dimension, a prototypical model of a Kondo insulator. We present an extensive analysis of single-particle Green’s functions, two-particle Green’s functions, and transport functions creating a broad picture of the low-temperature properties. We confirm the existence of energetically low-lying spin excitations in this model and study their energy-momentum dispersion and temperature dependence. We demonstrate that charge-charge correlations at the Fermi energy exhibit a different temperature dependence than spin-spin correlations. While energetically low-lying spin excitations emerge approximately at the Kondo temperature, which exponentially depends on the interaction strength, charge correlations vanish already at high temperatures. Furthermore, we analyze the charge and thermal conductivity at finite temperatures by calculating the time-dependent current-current correlation functions. While both charge and thermal conductivity can be fitted for all interaction strengths by gapped systems with a renormalized band gap, the gap in the system describing the thermal conductivity is generally smaller than the system describing the charge conductivity. Thus, two-particle correlations affect the charge and heat conductivities in a different way resulting in a temperature region where the charge conductivity of this one-dimensional Kondo insulator is already decreasing while the heat conductivity is still increasing.

Stochastic theory of ferroelectric domain structure formation dominated by quenched disorder

A self-consistent stochastic model of domain structure formation in a uniaxial ferroelectric, quenched from a high-temperature paraelectric phase to a low-temperature ferroelectric phase, is developed with an account of the applied electric field and the feedback effect via local depolarization fields. Both polarization and field components are considered as Gauss random variables. A system of integro-differential equations for correlation functions of all involved variables is derived and solved analytically and numerically. Phase diagram in terms of the average value and dispersion of polarization reveals different possible equilibrium states and available final single-domain and multi-domain states. The time-dependent evolution of the average polarization and dispersion discloses a bifurcation behavior and the temperature-dependent value of the electric field, deciding between the single-domain and multi-domain final states, which can be interpreted as the coercive field. Analytical and numerical results for the time-dependent correlation length and correlation functions exhibit plausible agreement with available experimental data.

Photon bound state dynamics from a single artificial atom

The interaction between photons and a single two-level atom constitutes a fundamental paradigm in quantum physics. The nonlinearity provided by the atom leads to a strong dependence of the light–matter interface on the number of photons interacting with the two-level system within its emission lifetime. This nonlinearity unveils strongly correlated quasiparticles known as photon bound states, giving rise to key physical processes such as stimulated emission and soliton propagation. Although signatures consistent with the existence of photon bound states have been measured in strongly interacting Rydberg gases, their hallmark excitation-number-dependent dispersion and propagation velocity have not yet been observed. Here we report the direct observation of a photon-number-dependent time delay in the scattering off a single artificial atom—a semiconductor quantum dot coupled to an optical cavity. By scattering a weak coherent pulse off the cavity–quantum electrodynamics system and measuring the time-dependent output power and correlation functions, we show that single photons and two- and three-photon bound states incur different time delays, becoming shorter for higher photon numbers. This reduced time delay is a fingerprint of stimulated emission, where the arrival of two photons within the lifetime of an emitter causes one photon to stimulate the emission of another.

Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system

We investigate the time-dependent R\'{e}nyi entanglement entropy after a quantum quench starting from the Mott-insulating and charge-density-wave states in a one-dimensional free boson system. The second R\'{e}nyi entanglement entropy is found to be the negative of the logarithm of the permanent of a matrix consisting of time-dependent single-particle correlation functions. From this relation and a permanent inequality, we obtain rigorous conditions for satisfying the volume-law entanglement growth. We also succeed in calculating the time evolution of the R\'{e}nyi entanglement entropy in unprecedentedly large systems by brute-force computations of the permanent. We discuss possible applications of our findings to the real-time dynamics of noninteracting bosonic systems.

The Hydrophobic Effect Studied by Using Interacting Colloidal Suspensions.

Interactions between nanoparticles (NPs) determine their self-organization and dynamic processes. In these systems, a quantitative description of the interparticle forces is complicated by the presence of the hydrophobic effect (HE), treatable only qualitatively, and due to the competition between the hydrophobic and hydrophilic forces. Recently, instead, a sort of crossover of HE from hydrophilic to hydrophobic has been experimentally observed on a local scale, by increasing the temperature, in pure confined water and studying the occurrence of this crossover in different water-methanol solutions. Starting from these results, we then considered the idea of studying this process in different nanoparticle solutions. By using photon correlation spectroscopy (PCS) experiments on dendrimer with OH terminal groups (dissolved in water and methanol, respectively), we show the existence of this hydrophobic-hydrophilic crossover with a well defined temperature and nanoparticle volume fraction dependence. In this frame, we have used the mode coupling theory extended model to evaluate the measured time-dependent density correlation functions (ISFs). In this context we will, therefore, show how the measured spectra are strongly dependent on the specificity of the interactions between the particles in solution. The observed transition demonstrates that just the HE, depending sensitively on the system thermodynamics, determines the hydrophobic and hydrophilic interaction properties of the studied nanostructures surface.

TBPLaS: A tight-binding package for large-scale simulation

TBPLaS is an open-source software package for the accurate simulation of physical systems with arbitrary geometry and dimensionality utilizing the tight-binding (TB) theory. It has an intuitive object-oriented Python application interface (API) and Cython/Fortran extensions for the performance-critical parts, ensuring both flexibility and efficiency. Under the hood, numerical calculations are mainly performed by both exact diagonalization and the tight-binding propagation method (TBPM) without diagonalization. Especially, the TBPM is based on the numerical solution of the time-dependent Schrödinger equation, achieving linear scaling with system size in both memory and CPU costs. Consequently, TBPLaS provides a numerically cheap approach to calculate the electronic, optical, plasmon and transport properties of large tight-binding models with billions of atomic orbitals. Current capabilities of TBPLaS include the calculations of band structure, density of states, local density of states, quasi-eigenstates, optical conductivity, electrical conductivity, Hall conductivity, polarization function, dielectric function, plasmon dispersion, carrier mobility and velocity, localization length and free path, Z2 topological invariant, wave-packet propagation, etc. All the properties can be obtained with only a few lines of code. Other algorithms involving tight-binding Hamiltonians can be implemented easily due to the extensible and modular nature of the code. In this paper, we discuss the theoretical framework, implementation details and common workflow of TBPLaS, and give a few demonstrations of its applications. Program summaryProgram Title:TBPLaSCPC Library link to program files:https://doi.org/10.17632/5cjmzj9jwm.1Code Ocean capsule:https://codeocean.com/capsule/8296734Licensing provisions: BSD 3-clauseProgramming language: Python, Cython, FortranNature of problem: The TB method is a powerful tool for investigating the electronic structures and many other properties in condensed matter physics. However, the costs of memory and CPU time using standard diagonalization-based TB techniques scale as O(N2) and O(N3) with the model size N, severely limiting their applications in large complex systems. The development of numerical methods to solve TB problems without any diagonalization, as well as the implementation of these techniques in software packages, are urgently needed to promote the capability of TB methods to large systems with billions of atoms.Solution method: We proposed the TBPM and implemented it in the TBPLaS package. In TBPM, the electronic properties of a TB model are calculated numerically by solving the time-dependent Schrödinger equation without any diagonalization, which ensures a linear scaling of both memory and CPU costs with the system size. Models with billions of atoms (orbitals) can be easily handled, with many properties available from the evolution of time-dependent correlation functions. The TBPLaS package features an intuitive object-oriented Python API and Cython/Fortran extensions for performance-critical parts, ensuring both flexibility and efficiency. Moreover, TBPLaS implements hybrid MPI+OpenMP parallelism, which can exploit the modern hardware of high-performance computers.

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finite-temperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperatures. For the polaron in the weak and intermediate electron-phonon coupling regimes, we analyze the influence of phonon dispersion relations on the spectra. For strong electron-phonon coupling, the known result of an asymmetric Gaussian is reproduced for a flat phonon band. For a finite phonon bandwidth, the center of the Gaussian is either shifted to larger or smaller frequencies, depending on the sign of the phonon hopping. We illustrate that this can be well understood by considering the Born-Oppenheimer surfaces. A similar behavior is seen for the bipolaron for strong coupling. For the bipolaron with weak and intermediate coupling strengths and a flat phonon band, we obtain two very different spectra. The latter also has a temperature-dependent resonance at a frequency below the phonon frequency.

Dynamics of non-Gaussian fluctuations in model A

Motivated by the experimental search for the QCD critical point we perform simulations of a stochastic field theory with purely relaxational dynamics (model A). We verify the expected dynamic scaling of correlation functions. Using a finite size scaling analysis we obtain the dynamic critical exponent $z=2.026(56)$. We investigate time dependent correlation functions of higher moments $M^n(t)$ of the order parameter $M(t)$ for $n=1,2,3,4$. We obtain dynamic scaling with the same critical exponent $z$ for all $n$, but the relaxation constant depends on $n$. We also study the relaxation of $M^n(t)$ after a quench, where the simulation is initialized in the high temperature phase, and the dynamics is studied at the critical temperature $T_c$. We find that the evolution does not follow simple scaling with the dynamic exponent $z$, and that it involves an early time rise followed by late stage relaxation.

Dynamic scaling in rotating turbulence: A shell model study.

We investigate the scaling form of appropriate timescales extracted from time-dependent correlation functions in rotating turbulent flows. In particular, we obtain precise estimates of the dynamic exponents z_{p}, associated with the timescales, and their relation with the more commonly measured equal-time exponents ζ_{p}. These theoretical predictions, obtained by using the multifractal formalism, are validated through extensive numerical simulations of a shell model for such rotating flows.

Power functional theory for many-body dynamics

The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is often an essential step. Power functional theory provides a unique and microscopically sharp formulation of this concept. The approach is based on an exact one-body variational principle to describe the dynamics of both overdamped and inertial classical and quantum many-body systems. In equilibrium, density functional theory is recovered, and hence spatially inhomogeneous systems are described correctly. The dynamical theory operates on the level of time-dependent one-body correlation functions. Two- and higher-body correlation functions are accessible via the dynamical test particle limit and the nonequilibrium Ornstein-Zernike route. We describe the structure of this functional approach to many-body dynamics, including much background as well as applications to a broad range of dynamical situations, such as the van Hove function in liquids, flow in nonequilibrium steady states, motility-induced phase separation of active Brownian particles, lane formation in binary colloidal mixtures, and both steady and transient shear phenomena.

Vibronic Coupling Effect on the Vibrationally Resolved Electronic Spectra and Intersystem Crossing Rates of a TADF Emitter: 7-PhQAD.

Assessing and improving the performance of organic light-emitting diode (OLED) materials require quantitative prediction of rate coefficients for the intersystem crossing (ISC) and reverse ISC (RISC) processes, which are determined not only by the energy gap and the direct spin-orbit coupling (SOC) between the first singlet and triplet excited-states at a thermal equilibrium position of the initial electronic state but also by the non-Condon effects such as the Herzberg-Teller-like vibronic coupling (HTVC) and the spin-vibronic coupling (SVC). Here we apply the time-dependent correlation function approaches to quantitatively calculate the vibrationally resolved absorption and fluorescence spectra and ISC/RISC rates of a newly synthesized multiple-resonance-type (MR-type) thermally activated delayed fluorescence (TADF) emitter, 7-phenylquinolino[3,2,1-de]acridine-5,9-dione (7-PhQAD), with the inclusion of the Franck-Condon (FC), HTVC, and Duschinsky rotation (DR) effects. The SVC effect on the rates has also been approximately evaluated. We find that the experimentally measured ISC rates of 7-PhQAD originate predominantly from the vibronic coupling, consistent with the previous reports on other MR-type TADF emitters. The SVC effect on ISC rates is about 10 times larger than the HTVC effect, and the latter increases the ISC rates by more than 1 order of magnitude while it slightly affects the vibrationally resolved absorption and fluorescence spectra. The discrepancy between the theoretical and experimental results is attributed to inaccurately describing excited-states calculated by the time-dependent density functional theory as well as to not fully accounting for the complex experimental conditions. This work provides a demonstration of what proportion of ISC and RISC rate coefficients of a MR-type TADF emitter can be covered by the HTVC effect, and it opens design routes that go beyond the FC approximation for the future development of high-performance OLED devices.

Nontrivial damping of quantum many-body dynamics

Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schrödinger picture. We show that a nontrivial damping in the Schrödinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.

Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.

From operator statistics to wormholes

For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper we analyse the time dependence of correlation functions of operators. We study them in the ergodic limit as well as their approach to the ergodic limit which is controlled by non-universal massive modes. An effective field theory (EFT) corresponding to the causal symmetry and its breaking describes the ergodic phase. We demonstrate that the resulting Goldstone-mode theory has a topological expansion, analogous to the one described in arXiv:2008.02271 with added operator sources, whose leading non-trivial topologies give rise to the universal ramp seen in correlation functions. The ergodic behaviour of operators in our EFT is seen to result from a combination of RMT-like spectral statistics and Haar averaging over wave-functions. Furthermore we analytically capture the plateau behaviour by taking into account the contribution of a second saddle point. Our main interest are quantum many-body systems with holographic duals and we explicitly establish the validity of the EFT description in the SYK-class of models, starting from their microscopic description. By studying the tower of massive modes above the Goldstone sector we get a detailed understanding of how the ergodic EFT phase is approached and derive the relevant Thouless time scales. We point out that the topological expansion can be reinterpreted in terms of contributions of bulk wormholes and baby-universes.