Brownian Oscillator Research Articles

Efficient Brownian oscillators and nanoheaters based on gallium-doped ε-Fe2O3.

Wireless actuation at the nanoscale is vital in many contexts, and magnetic fields acting on nanoparticles (NPs) are among the most effective tools when actuation concerns linear forces. However, effective tools to apply torques at the nanoscale are still missing, because NPs where the magnetic moment is strongly coupled to the lattice agglomerate due to their high magnetic moment. Here, we show that gallium-doped ε-iron oxide NPs have small interparticle magnetic interactions and huge lattice-coupling for efficiently applying torques at the nanoscale. In this view, they are expected to be useful tools to efficiently apply mechanical forces to induce cellular apoptosis and to discern between mechanical and thermal contributions to cellular apoptosis currently under debate.

Timescales in the thermal dynamics of magnetic dipolar clusters

The collective behavior of thermally active structures offers clues on the emergent degrees of freedom and the physical mechanisms that determine the low-energy state of a variety of systems. Here, the thermally active dynamics of magnetic dipoles at square plaquettes is modeled in terms of Brownian oscillators in contact with a heat bath. Solution of the Langevin equation for a set of interacting $x\text{\ensuremath{-}}y$ dipoles allows the identification of the timescales and correlation length that reveal how interactions, temperature, damping, and inertia may determine the frequency modes of edge and bulk magnetic mesospins in artificial dipolar systems.

Ultrafast dynamics in rubrene and its spectroscopic manifestation.

A multimode Brownian oscillator model is employed to investigate absorption line shapes of rubrene in solutions and thin films. Excellent agreement has been obtained between simulated and measured absorption spectra. Furthermore, using the parameters obtained from the fitting absorption spectra of rubrene, the dynamics of singlet fission is explored by the Dirac-Frenkel time-dependent variation with multiple Davydov trial states. By comparing the absorption spectra between a conical intersection model and the multimode Brownian oscillator model, the optimal system-bath coupling parameter of η = 0.2 is determined, and ensuing population dynamics of the S1 state is found to concur with a previously proposed coherent singlet fission mechanism. We further simulate the two-dimensional spectra to reveal the wavepacket dynamics on both excited state and ground state potential energy surfaces. It is demonstrated that the wavepacket motion of tuning modes plays a significant role in the evolution of two-dimensional spectra.

Disentangling roots of ergodicity breakdown by spectral analyses

The connection between ergodicity breaking for a forced system and its two-time velocity correlation function is demonstrated using the Khinchin theorem, where the particle dynamics is described by a generalized Langevin equation. Products of observables at a pair of time points are constructed that are correlated with their initial preparations. Three types of nonergodic behaviors are elucidated, specifically the velocity correlation function of the system either approaches a constant, oscillates with time around a non-vanishing constant or oscillates around zero-value at large times. The corresponding noise spectral densities behave as low-hindering and high-passing, band-passing as well as low-passing and high-hindering or simply band-hindering. When a harmonic potential is imposed on the system, the first situation can be transformed into ergodicity whereas the latter two types cannot. Furthermore, the application to the Debye Brownian oscillator as well as the verification of several famous models are discussed.

The role of vibronic modes in formation of red antenna states of cyanobacterial PSI.

Cyanobacterial photosystem I (PSI) constitutes monomeric and trimeric pigment-protein complexes whose optical properties are marked by the presence of long-wavelength absorption bands. In spite of numerous experimental studies, the nature of these bands is still under debate and requires intensive theoretical analysis. Collecting together the data of linear spectroscopy and single-molecule spectroscopy (SMS) of PSI from Arthrospira platensis, we performed quantum modeling of the optical response based on molecular exciton theory (ET) and the multimode Brownian oscillator model (MBOM). Applying MBOM, the spectra of the red antenna state were calculated considering a particular for each red state adjustment of the low-frequency vibronic modes. Within the framework of our PSI exciton model it was shown that the coupling energy between antenna chlorophylls cannot be a factor of the red states formation, thus the long-wavelength bands are calculated without attribution to so-called antenna red chlorophylls. By the fitting of Huang-Rhys factors and frequencies for the lowest vibronic modes, we were able to reproduce the effects of strong and weak electron-phonon coupling experimentally observed in SMS spectra of red antenna states. Based on our theoretical calculations and also analysis of existing crystal structures of cyanobacterial PSI, we assumed that long-wavelength Chls can be localized in the peripheral protein subunits containing one or two pigment molecules.

Optimizing the Multimode Brownian Oscillator Model for the Optical Response of Carotenoids in Solution by Fine Tuning of Differential Evolution

During last twenty years, the Differential evolution algorithm (DE) has proved to be one of the powerful methods to solve minimization problems for multidimensional functions. Being a member of the family of evolutionary optimization algorithms, its main principle is based upon the concepts of natural selection and mutation. In this study, we test the potential of DE to find a proper set of parameters for the multimode Brownian oscillator model, which was then used to simulate absorption lineshapes of carotenoid molecules in solution: spheroidene and spheroidenone. This theory assumes that the correlation function of a particular electronic state of the carotenoid is calculated using the semiclassical spectral density function. Considering our previous studies on photosynthetic pigments, we employed several DE strategies to do fitting of the carotenoid experimental spectra. We found that simulated absorption spectra are very sensitive to several parameters that characterize carotenoid vibronic modes, namely, Huang–Rhys factors. Fine tuning of DE crossover parameter (Cr) and the scaling factor (F) provided acceptable convergence of the algorithm. It appears that to get good convergence of DE, a certain spectral range of carotenoid absorption from 400 to 600 nm must be chosen. This fact can be explained by the limitations of the applied theory, which simply does not predict properly the carotenoid absorption at higher frequencies.

Education

This issue of SIAM Review presents two papers in the Education section. The first paper, “Time Correlation Functions of Equilibrium and Nonequilibrium Langevin Dynamics: Derivations and Numerics Using Random Numbers,” is coauthored by Xiaocheng Shang and Martin Krog̈er. Langevin dynamics is a term describing a mathematical model of the dynamics of molecular systems which uses stochastic differential equations. This model extends the molecular dynamics to allow for describing effects due to friction caused by solvent or air molecules or other phenomena that perturb the system. In this paper, the authors present the model equation for the behavior of a harmonic oscillator in two or three dimensions in the presence of friction, additive noise, and an external field with both rotational and deformational components. They study the time correlation function of the dynamics analytically and numerically. The paper provides a good illustration of the tools of stochastic calculus on a nontrivial application and helps evaluate the numerical solvers for stochastic differential equations (SDEs). The authors argue that the fair assessment of the efficiency and accuracy of numerical solvers for SDEs requires access to analytical reference solutions. However, deriving relevant analytical formulae is possible only for very simple cases. Here a two-dimensional nontrivial benchmark problem is analyzed and an exact solution is derived. The analysis in the paper includes also a discussion on inertial effects. The model equation formulated in section 2 is interesting because it arises in multiple applications. Furthermore, the absence of the restoring force or the external field in the model leads to popular special cases. Among those are the random walk, diffusion models, the motion of atoms in the presence of gravitational or centrifugal potential, nanomagnets subjected to magnetic fields, Brownian oscillators, rotational relaxation of molecules trapped in a three-dimensional crystal, and many others. Relevant literature describing those models is provided. The authors describe a direct approach to the derivation of the time correlation functions for general Langevin dynamics, as well as an approach that uses Fourier transforms and the Wiener--Khinchin theorem, and a complementary approach via the associated Fokker--Planck equation. The last portion of the paper contains the description of two numerical methods and numerical experience. The second paper presents “An Introduction to Quantum Computing, without the Physics,” written by Giacomo Nannicini. This paper introduces discrete mathematicians and computer scientists to quantum computing. While quantum computing uses certain quantum phenomena to perform computation, many scientists may learn about its principles without acquiring deeper knowledge of quantum physics. The author starts with a set of assumptions that are satisfied by a quantum computing device. From those assumptions further properties are derived in a rigorous way. The necessary concepts are formally introduced and all statements are supplied with mathematical proofs. The author adopts a model of computation, which is known as the quantum circuit model. Quoting from the paper, it works as follows: - The quantum computer has a state that is contained in a quantum register and is initialized in a predefined way. - The state evolves by applying operations specified in advance in the form of an algorithm. - At the end of the computation, some information on the state of the quantum register is obtained by means of a special operation, called a measurement. At the beginning of the paper, some properties of the tensor product are reviewed, which are used to express states and operations in a quantum device. For example, qubits are the quantum counterparts of the bits in our computers and the state of a $q$-qubit quantum register is identified with a unit vector in the space $(\mathbb{C}^2)^{\otimes q}$, where $\mathbb{C}^2$ is the complex Euclidean space. The exposition proceeds with the introduction and analysis of the types of states and their properties, the quantum phenomena of superposition and enlargement, measurement gates, and the input-output model for quantum computations. The second portion of the paper discusses several quantum algorithms including a numerical implementation of Grover's algorithm. It may be of interest that, although quantum computing is able to solve some problems much faster than the classical computer, it is still not known to solve NP-complete problems efficiently. The paper concludes with a section containing notes for further reading. According to the author's experience, the paper provides material for a graduate-level module in quantum computing for mathematicians and computer scientists. It is recommended to split the material into five lectures/meetings of 90--120 minutes each. The last meeting would aim at providing a hands-on numerical experience based on section 6 of the paper. The audience should be familiar with linear algebra and with basic concepts in computing such as Turing machines and algorithmic complexity.

Short-time dynamics and decay mechanism of E,E-2,4-hexadienal in the first light-absorbing S2(ππ*) state.

The initial nonadiabatic decay dynamics of E,E-2,4-hexadienal (HAL) in the light absorbing S2(ππ*) state were studied using resonance Raman spectroscopy and complete-active space self-consistent field (CASSCF) calculations. The UV and vibrational spectra were assigned on the basis of the UV absorption, Fourier transform (FT)-Raman and FT-infrared measurements, the density-functional theory computations, and the normal mode analysis. The A-band resonance Raman spectra in cyclohexane and acetonitrile were obtained at 282.4, 273.9, 266.0, 252.7, and 245.9 nm excitation wavelengths, respectively, to probe the corresponding structural dynamics of HAL. The A-band absorption cross section and the corresponding absolute resonance Raman cross sections were simulated using a simple model based on the time-dependent wave-packet theory in a Brownian oscillator model. The geometric structures of the singlet electronic excited states and their curve-crossing points were optimized at the CASSCF level of theory. The obtained short-time structural dynamics in easy-to-visualize internal coordinates were then compared with the CASSCF-predicted structural-parameter changes of S2(ππ*)S1(nπ*)-n (n = 1-4). Our results indicate that the initial population of HAL in the S2 state ramifies in or nearby the Franck-Condon (FC) region, leading to five S2(ππ*) → S1(nπ*) internal conversion pathways due to the flexibility of the molecular chain and the different electronic resonant structures formed nearby FC of the S2 state. Then, the formed S1 transient species, which have different geometric structures and different energy partitions, undergo different photophysical processes, such as S1 → S0 internal conversion, S1 → T1 intersystem crossing, and the S1 → S'1 photoisomerization reaction. The substitution effect on the S2(ππ*) → S1(nπ*) internal conversion dynamics and the trans-cis photoisomerization reaction is proposed in terms of the p-π conjugation interaction or the p-σ superconjugation interaction.

Stochastic thermodynamics of a harmonically trapped colloid in linear mixed flow.

In this paper, motivated by a general interest in the stochastic thermodynamics of small systems, we derive an exact expression-via path integrals-for the conditional probability density of a two-dimensional harmonically confined Brownian particle acted on by linear mixed flow. This expression is a generalization of the expression derived earlier by Foister and Van De Ven [J. Fluid Mech. 96, 105 (1980)10.1017/S0022112080002042] for the case of the corresponding free Brownian particle, and reduces to it in the appropriate unconfined limit. By considering the long-time limit of our calculated probability density function, we show that the flow-driven Brownian oscillator attains a well-defined steady state. We also show that, during the course of a transition from an initial flow-free thermal equilibrium state to the flow-driven steady state, the integral fluctuation theorem, the Jarzynski equality, and the Bochkov-Kuzovlev relation are all rigorously satisfied. Additionally, for the special cases of pure rotational flow we derive an exact expression for the distribution of the heat dissipated by the particle into the medium, and for the special case of pure elongational flow we derive an exact expression for the distribution of the total entropy change. Finally, by examining the system's stochastic thermodynamics along a reverse trajectory, we also demonstrate that in elongational flow the total entropy change satisfies a detailed fluctuation theorem.

Dynamics of hydrodynamically coupled Brownian harmonic oscillators in a Maxwell fluid.

It has been shown recently that the coupled dynamics of micro-particles in a viscous fluid has many interesting aspects including motional resonance which can be used to perform two-point micro-rheology. However, it is expected that this phenomenon in a viscoelastic fluid is much more interesting due to the presence of the additional frequency-dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive characteristics. Initially, the response functions have been calculated and then the fluctuation-dissipation theorem has been used to calculate the correlation functions between the coloured noises present on the concerned particles placed in a Maxwell fluid due to the thermal motions of the fluid molecules. These correlation functions appear to be in a linear relationship with the delta-correlated noises in a viscous fluid. Consequently, this reduces the statistical description of a simple viscoelastic fluid to the statistical representation for an extended dynamical system subjected to delta-correlated random forces. Thereupon, the auto and cross-correlation functions in the time domain and frequency domain and the mean-square displacement functions of the particles have been calculated which are perfectly consistent with their corresponding established forms in a viscous fluid and emerge with exceptional features.

Transient grating spectroscopy of β-carotene pumped with spectrally chirped pulses

Nonlinear optical responses of β-carotene were investigated upon excitation using chirped pulses. We especially focus on spectrally resolved transient grating (TG) signals to discuss the influence of the spectral chirp over a wide spectral range. A significant change in the TG signal was observed when negatively chirped pulses were used. The experimental results were qualitatively reproduced by employing the Brownian oscillator model. The relationship between the wave packet motion in the excited state and spectral chirp is discussed. It is concluded that the third order nonlinear optical response reflects the competition between the spectral chirp and the energy separation of the potential curves.

Anomalous Temperature-Dependent Exciton–Phonon Coupling in Cesium Lead Bromide Perovskite Nanosheets

The role of exciton–phonon coupling in light emission in cesium lead bromide (CsPbBr3) nanosheets is investigated with combined photoluminescence spectroscopy and the multimode Brownian oscillator ...

Transport properties and first-arrival statistics of random motion with stochastic reset times.

Stochastic resets have lately emerged as a mechanism able to generate finite equilibrium mean-square displacement (MSD) when they are applied to diffusive motion. Furthermore, walkers with an infinite mean first-arrival time (MFAT) to a given position x may reach it in a finite time when they reset their position. In this work we study these emerging phenomena from a unified perspective. On one hand, we study the existence of a finite equilibrium MSD when resets are applied to random motion with 〈x^{2}(t)〉_{m}∼t^{p} for 0<p≤2. For exponentially distributed reset times, a compact formula is derived for the equilibrium MSD of the overall process in terms of the mean reset time and the motion MSD. On the other hand, we also test the robustness of the finiteness of the MFAT for different motion dynamics which are subject to stochastic resets. Finally, we study a biased Brownian oscillator with resets with the general formulas derived in this work, finding its equilibrium first moment and MSD and its MFAT to the minimum of the harmonic potential.

Decay dynamics of 6‐azauracil from the light absorbing S2(ππ*) state

AbstractThe initial decay dynamics of 6AU in the S2 state was investigated by using resonance Raman spectroscopy, the time‐dependent wave‐packet theory in a Brownian oscillator model, and complete‐active space self‐consistent field (CASSCF) protocol. The vibrational spectra and the ultraviolet absorption bands were assigned on the basis of the Fourier transform (FT)‐Raman, FT‐infrared measurements, the density‐functional theory computations, and the normal mode analysis. The absorption cross section and the absolute resonance Raman cross sections were simulated simultaneously by using the time‐dependent wave‐packet theory in a Brownian oscillator model. The obtained normal mode displacements of the Franck–Condon active modes were then converted to the short‐time structural dynamics in easy‐to‐visualize internal coordinates. The roles of two pathways via the S2 → S1 internal conversion and the S2 → T3 intersystem crossing were evaluated through the comparison between the short‐time structural dynamics and the CASSCF/CASTP2 calculated structural changes between FC and S2S1 or between FC and S2T3. The results indicate that the structural dynamics in the Franck–Condon region of the S2 state is mostly toward the S2/S1 conical intersection, which supports the conclusion that the S2 → S1 internal conversion dominants the initial decay pathway of 6AU as revealed by the broadband fs TA spectroscopy, whereas the barrierless S2 → T3 intersystem‐crossing process is negligible owing to weak spin‐orbital coupling and unfavorable subsequent T3 → T2 → T1 decay. The reaction coordinates towards the planar S2(ππ*)/S1(nπ*) and severely distorted S2(ππ*)/S0 conical intersection points are proposed respectively, and the solvent effect on the initial decay mechanisms of 6AU, uracil, and thymine is clarified.

Diffusing diffusivity: Fractional Brownian oscillator model for subdiffusion and its solution

Diffusing diffusivity: Fractional Brownian oscillator model for subdiffusion and its solution

Waiting Time for Transient Violations of the Second Law in Brownian Oscillators

In this work, we study the average time a Brownian oscillator coupled to a thermal bath takes to get fluctuations of a given energy. The waiting times are obtained as a function of the system parameters using the Langevin equation and molecular simulations. We found that an oscillators system can exhibit arbitrarily large transient violations of the second law. It is shown that the waiting times give relevant information that is not provided by the solutions of the Fokker–Planck equation.

Fast Bayesian inference of the multivariate Ornstein-Uhlenbeck process.

The multivariate Ornstein-Uhlenbeck process is used in many branches of science and engineering to describe the regression of a system to its stationary mean. Here we present an O(N) Bayesian method to estimate the drift and diffusion matrices of the process from N discrete observations of a sample path. We use exact likelihoods, expressed in terms of four sufficient statistic matrices, to derive explicit maximum a posteriori parameter estimates and their standard errors. We apply the method to the Brownian harmonic oscillator, a bivariate Ornstein-Uhlenbeck process, to jointly estimate its mass, damping, and stiffness and to provide Bayesian estimates of the correlation functions and power spectral densities. We present a Bayesian model comparison procedure, embodying Ockham's razor, to guide a data-driven choice between the Kramers and Smoluchowski limits of the oscillator. These provide novel methods of analyzing the inertial motion of colloidal particles in optical traps.

Application of the differential evolution for simulation of the linear optical response of photosynthetic pigments

For many applications the Differential Evolution (DE) algorithm had proved to be a very efficient tool for getting the best solution especially when the problem has hundreds of free parameters to optimize. This study aims to expend the list of DE successful scientific applications and to use the DE method for photosynthetic pigments optical response modeling. Chlorophyll (Chl) and bacteriochlorophyll (BChl) are the main pigment molecules of the photosynthetic light-harvesting complexes. These complexes are responsible for photon absorption and sequential transport of energy to the photosynthetic reaction center where the charge separation occurs. The DE routines were adopted to perform the fitting of Chl and Bchl Qy band absorption and fluorescence spectra measured in dimethyl ether. To simulate these spectra the stochastic Brownian oscillator model with 49 vibronic modes for Chl and 60 modes for BChl has been applied. By using the artificially calculated spectra, 10 strategies were tested with different settings of the scaling factor (F) and crossover parameter (Cr) before to fit the real experimental data. Once the proper strategy and settings, which give the fastest convergence, were found, the set of parameters representing the electron–phonon coupling (Huang–Rhys factors) and the lowest frequency modes were calculated. These parameters can be used for modeling of the light-harvesting complex nonlinear optical response.

Unified analysis of optical absorption spectra of carotenoids based on a stochastic model

The chemical structures of the carotenoid molecules are very simple and one might think that their electronic features are easily predicted. However, there is still has so much unknown information excepting the correlation between the electronic energy state and the length of effective conjugation chain of carotenoids. To investigate the electronic feature of the carotenoids, the most essential method is measuring the optical absorption spectra, but simulations based on the resonance Raman spectra are also an effective approach. For this reason, we studied the optical absorption spectra as well as resonance Raman spectra of 15 different carotenoid molecules each possessing a cyclic end-group, recorded in tetrahydrofuran (THF) solutions at room temperature. The whole band shapes of the absorption spectra of all these carotenoid molecules were successfully simulated using a stochastic model and Brownian oscillators. The parameters obtained from the simulation make it possible to discuss the intermolecular interaction between carotenoids and solvent THF molecules quantitatively.

Homogeneous and heterogeneous dynamics in native and denatured bovine serum albumin.

A characteristic property of unfolded and disordered proteins is their high molecular flexibility, which enables the exploration of a large conformational space. We present neutron scattering experiments on the dynamics of denatured and native folded bovine serum albumin (BSA) in solution. Global protein diffusion and internal macromolecular dynamics were measured using quasielastic neutron time-of-flight and backscattering spectroscopy on the picosecond to nanosecond time- and Ångstrom length-scale. Internal protein dynamics were analysed in a first approach using stretched exponential functions. In denatured BSA predominantly slow heterogeneous dynamics dominates the observed macromolecular motions. Reduction of disulphide bridges in denatured BSA does not significantly alter the visible motions. In native folded BSA fast homogeneous dynamics and slow heterogeneous dynamics were observed. In an alternative data analysis approach, internal protein dynamics was interpreted using the analytical model of the overdamped Brownian oscillator, which allowed us to extract mean square displacements of protein internal dynamics and the fraction of hydrogen atoms participating in the observed motions. Our results demonstrate that denaturation modifies the physical nature of internal protein dynamics significantly as compared to the native folded structure.