Bath Of Oscillators Research Articles

Application of the frozen-modes approximation to classical harmonic oscillator systems

The problems of open classical systems usually correspond to a motion of a test particle that interacts with a large number of bath oscillators. Often, the test particle itself can be considered a harmonic oscillator. For such composite systems, exact numerical solutions are available, but they can become increasingly costly for a large number of bath oscillators. Here we take inspiration from the recent work on open quantum systems and investigate the applicability of the frozen-modes approximation to such classical systems. This approach assumes that some part of the low-frequency bath modes are frozen, thus only their initial values need to be considered. We show that by applying the frozen-modes approximation one can significantly increase the accuracy of the perturbative multiple-scales solution, especially for slow baths. This approach provides a good accuracy even for strong system–bath couplings, a regime that is not accessible to straightforward applications of the perturbation theory. We also suggest a rule for the splitting of spectral density to the fast and slow bath modes. We find that our approach gives excellent results for the ohmic spectral density, but it could be applied for other similar spectral densities as well.

Influence of initial correlations on evolution over time of an open quantum system

A novel approach to accounting for the influence of initial system–bath correlations on the dynamics of an open quantum system, based on the conventional projection operator technique, is suggested. To avoid the difficulties of treating the initial correlations, the conventional Nakajima–Zwanzig inhomogeneous generalized master equations (GMEs) for a system’s reduced statistical operator and correlation function are exactly converted into the homogeneous GMEs (HGMEs), which take into account the initial correlations in the kernel governing the evolution of these HGMEs. In the second order (Born) approximation in the system–bath interaction, the obtained HGMEs are local in time and valid at all timescales. They are further specialized for a realistic equilibrium Gibbs initial (at t=t0) system+bath state (for a system reduced statistical operator an external force at t>t0 is applied) and then for a bath of oscillators (Boson field). As an example, the evolution of a selected quantum oscillator (a localized mode) interacting with a Boson field (Fano-like model) is considered at different timescales. It is shown explicitly how the initial correlations influence the oscillator evolution process. In particular, it is shown that the equilibrium system’s correlation function acquires at the large timescale the additional constant phase factor conditioned by survived initial system–bath correlations.

Experimental study on dynamic adsorption properties of methylene blue onto coal-based activated carbon using a hydrocyclone

To address the issues of low adsorption efficiency of activated carbon in dyeing wastewater treatment, a dynamic adsorption process using activated carbon for wastewater treatment was proposed. A hydrocyclone was used as the carrier, and the adsorbent separation process was integrated into the same single device. Methylene blue (MB) was used to simulate printing and dyeing wastewater. The effects of initial concentration of MB solution, ratio of activated carbon quality to wastewater flow, and adsorption temperature on the adsorption efficiency were investigated. The results showed that the optimal adsorption efficiency of MB by activated carbon was 95.2 % when the initial concentration of MB solution was 12 mg/L, the ratio of activated carbon quality to wastewater flow was 0.5 mg/mL, and the adsorption temperature of MB solution was 44.5 °C. In addition, compared with the water bath oscillation method, the removal efficiency of MB was increased by 731 % under the same adsorption conditions. The research shows that it is feasible to treat printing and dyeing wastewater by using a hydrocyclone to enhance activated carbon adsorption. The research aims to provide a practical basis for future optimization of the structure and operation parameters of hydrocyclone and to reveal their wide application prospects.

Mimicking classical noise in ion channels by quantum decoherence

The mechanism of selectivity in ion channels is still an open question in biology. Recent studies suggest that the selectivity filter may exhibit quantum coherence, which could help explain how ions are selected and conducted. However, environmental noise causes decoherence and loss of quantum effects. It is hoped that the effect of classical noise on ion channels can be modeled using the framework provided by quantum decoherence theory. In this paper, the behavior of the ion channel system was simulated using two models: the Spin–Boson model and the stochastic Hamiltonian model under classical noise. Additionally, using a different approach, the system’s evolution was modeled as a two-level Spin–Boson model with tunneling, interacting with a bath of harmonic oscillators, based on decoherence theory. We investigated under what conditions the decoherence model approaches and deviates from the noise model. Specifically, we examined Gaussian noise and Ornstein-Uhlenbeck noise in our model. Gaussian noise shows a very good agreement with the decoherence model. By examining the results, it was found that the Spin–Boson model at a high hopping rate of potassium ions can simulate the behavior of the system in the classical noise approach for Gaussian noise.

Vibration assisted electron tunnelling in COVID-19 infection using quantum state diffusion.

The spread of the COVID-19 virus has become a global health crisis, and finding effective treatments and preventions is a top priority. The field of quantum biology primarily focuses on energy or charge transfer, with a particular emphasis on photosynthesis. However, there is evidence to suggest that cellular receptors such as olfactory or neural receptors may also use vibration-assisted electron tunnelling to enhance their functions. Quantum tunnelling has also been observed in enzyme activity, which is relevant to the invasion of host cells by the SARS-CoV-2 virus. Additionally, COVID-19 appears to disrupt receptors such as olfactory receptors. These findings suggest that quantum effects could provide new insights into the mechanisms of biological systems and disease, including potential treatments for COVID-19. We have applied the open quantum system approach using Quantum State Diffusion to solve the non-linear stochastic Schrödinger equation (SSE) for COVID-19 virus infection. Our model includes the mechanism when the spike protein of the virus binds with an ACE2 receptor is considered as dimer. These two entities form a system and then coupled with the cell membrane, which is modelled as a set of harmonic oscillators (bath). By simulating the SSE, we find that there is vibration-assisted electron tunnelling happening in certain biological parameters and coupling regimes. Furthermore, our model contributes to the ongoing research to understand the fundamental nature of virus dynamics. It proposes that vibration-assisted electron tunneling could be a molecular phenomenon that augments the lock-and-key process for olfaction. This insight may enhance our understanding of the underlying mechanisms governing virus-receptor interactions and could potentially lead to the development of novel therapeutic strategies.

Time‐Resolved Optical Response of the Dicke's Model via the Nonequilibrium Green's Function Approach

Due to their conceptual appeal and computational convenience, two‐level systems (TLSs) and generalizations are used to investigate nonlinear behavior in quantum optics and assess the applicability of theoretical methods. Herein, the focus is on second‐harmonic generation (SHG) and, as system of interest, on the Dicke model, which consists of several TLSs inside an optical cavity. The main aspect addressed is the scope of nonequilibrium Green's function (NEGF) to describe the effect of inhomogeneities and electron–electron (e–e) interactions on the SHG signal. For benchmarking purposes, exact diagonalization (ED) results are also presented and discussed. SHG spectra obtained with NEGF and ED are found to be in very good mutual agreement in most situations. Furthermore, inhomogeneity in the TLS and e–e interactions reduce the SHG signal, and the reduction is stronger with inhomogeneity than with interactions. This trend is consistently noted across different (small to large) system sizes. Finally, a modified NEGF approach is proposed to account for cavity leakage, where the quantum photon fields are coupled to a bath of classical oscillators. As expected, within this mixed quantum‐classical scheme, a decrease in the intensity of the fluorescent spectra takes place depending on the entity of leakage.

Dynamic embedding of effective harmonic normal mode vibrations in all-atomistic energy gap fluctuations: Case study of light harvesting 2 complex.

Environmental effects in excitation energy transfer have mostly been modeled by baths of harmonic oscillators, but to what extent such modeling provides a reliable description of actual interactions between molecular systems and environments remains an open issue. We address this issue by investigating fluctuations in the excitation energies of the light harvesting 2 complex using a realistic all-atomistic simulation of the potential energy surface. Our analyses reveal that molecular motions exhibit significant anharmonic features, even for underdamped intramolecular vibrations. In particular, we find that the anharmonicity contributes to the broadening of spectral densities and substantial overlaps between neighboring peaks, which complicates the meaning of mode frequencies constituting a bath model. Thus, we develop a strategy to construct a minimally underdamped harmonic bath that has a clear connection to all-atomistic dynamics by utilizing actual normal modes of molecules but optimizing their frequencies such that the resulting bath model can best reproduce the all-atomistic simulation results. By subtracting the underdamped contribution from the entire fluctuations, we also show that identifying a residual spectral density representing all other contributions with overdamped behavior is possible. We find that this can be fitted well with a well-established analytic form of a spectral density function or, alternatively, modeled as explicit time dependent fluctuations with muti-exponential or power law type correlation functions. We provide an assessment and the implications of these possibilities. The approach presented here can also serve as a general strategy to construct a simplified bath model that can effectively represent the underlying all-atomistic bath dynamics.

Quantum information scrambling and chemical reactions

The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.

Identifying an Environment-Induced Localization Transition from Entropy and Conductance.

Environment-induced localization transitions (LT) occur when a small quantum system interacts with a bath of harmonic oscillators. At equilibrium, LTs are accompanied by an entropy change, signaling the loss of coherence. Despite extensive efforts, equilibrium LTs have yet to be observed. Here, we demonstrate that ongoing experiments on double quantum dots that measure entropy using a nearby quantum point contact realize the celebrated spin-boson model and allow to measure the entropy change of its LT. We find a Kosterlitz-Thouless flow diagram, leading to a universal jump in the spin-bath interaction, reflected in a discontinuity in the zero temperature QPC conductance.

Development of electronic nose for detection of micro-mechanical damages in strawberries.

A self-developed portable electronic nose and its classification model were designed to detect and differentiate minor mechanical damage to strawberries. The electronic nose utilises four metal oxide sensors and four electrochemical sensors specifically calibrated for strawberry detection. The selected strawberries were subjected to simulated damage using an H2Q-C air bath oscillator at varying speeds and then stored at 4°C to mimic real-life mechanical damage scenarios. Multiple feature extraction methods have been proposed and combined with Principal Component Analysis (PCA) dimensionality reduction for comparative modelling. Following validation with various models such as SVM, KNN, LDA, naive Bayes, and subspace ensemble, the Grid Search-optimised SVM (GS-SVM) method achieved the highest classification accuracy of 0.84 for assessing the degree of strawberry damage. Additionally, the Feature Extraction ensemble classifier achieved the highest classification accuracy (0.89 in determining the time interval of strawberry damage). This experiment demonstrated the feasibility of the self-developed electronic nose for detecting minor mechanical damage in strawberries.

Generalized dynamics and fluctuation-dissipation theorem for a parabolic potential.

This article revisits the fluctuation-dissipation relationship of a generalized Brownian particle constrained in a harmonic potential and immersed in a thermal bath whose degrees of freedom also interact with the external field. The generalized Langevin equationput forth herein keeps its original form. The different terms now depend on a compound strength related to those of the field and bath oscillators. The resulting theorem keeps Kubo's original form with the memory kernel depending on the frequency of the field. It has the consequence that friction is not a constant but is a function of the field frequency as predicted by molecular dynamics simulations. The position particle distribution and the Fokker-Planck equationassociated with the generalized Langevin equationare also derived.

Bath-induced phase transition in a Luttinger liquid

We study an XXZ spin chain, where each spin is coupled to an independent ohmic bath of harmonic oscillators at zero temperature. Using bosonization and numerical techniques, we show the existence of two phases separated by an Kosterlitz-Thouless (KT) transition. At low coupling with the bath, the chain remains in a Luttinger liquid phase with a reduced but finite spin stiffness, while above a critical coupling the system is in a dissipative phase characterized by a vanishing spin stiffness. We argue that the transport properties are also inhibited: the Luttinger liquid is a perfect conductor while the dissipative phase displays finite resistivity. Our results show that the effect of the bath can be interpreted as annealed disorder inducing signatures of localization.

Truncated Wigner approximation for the bosonic model of large spin baths

The central spin model has a wide applicability. It is ideally suited to describe a small quantum system, for instance a quantum bit, in contact to a bath of spins, e.g., nuclear spins or other small quantum systems in general. According to previous work [R. R\"ohrig et al., Phys. Rev. B 97, 165431 (2018)], a large bath of quantum spins can be described as a bath of quantum harmonic oscillators. But the resulting quantum model is still far from being straightforwardly solvable. Hence we consider a chain representation for the bosonic degrees of freedom to study how well a semi-classical truncated Wigner approximation of the effective model of harmonic oscillators (bTWA) works in comparison with other approximate and exact methods. We find that the bTWA works well for short times, but deviates from the results of other methods for long times. The general message is that the applicability of semi-classical approaches strongly depends on the variables in terms of which the model is formulated. Numerically, we examine the effect of the number of bath spins and of the truncation level, i.e., the chain length.

The simultaneous removal of cadmium (II) and lead (II) from wastewater with the application of green synthesized magnesium silicate hydrate

To the purpose of solving the problems of coal-gangue accumulation in the mine and pollution of cadmium (II) and lead (II) in wastewater, magnesium silicate hydrate (M-S-H) was synthesized from coal-gangue by thermochemical. M-S-H had removed Cd(II) and Pb(II) by adsorption. The characterization of M-S-H and adsorption effects factors, including initial solution pH, initial metal concentration, adsorbent dose, temperature, reaction time, and coexisting ions were explored for adsorption performance. The solution pH was precisely controlled by a pH meter. The adsorption temperature was controlled by a thermostatic gas bath oscillator with an error of ±0.3. These results from this study revealed that M-S-H surface area increased from 8.12 to 26.15 m2/g with a pore volume of 0.12 cm3/g. The maximum adsorptions of Cd(II) and Pb(II) by M-S-H were 59.52 and 83.33 mg g−1, respectively. The adsorption performance for Cd(II) and Pb(II) reached saturation at pH 5, temperature 25°C, M-S-H 6 g/L, reaction time 90 min, and metal concentration 300 mg/L. Cd(II) and Pb(II) adsorption were spontaneous and endothermic and well fitted with the pseudo-second-order kinetic and Langmuir isotherm adsorption models. The adsorption mechanisms were electrostatic interaction, ion exchange, and surface complexation. This research indicated that the synthesized M-S-H from coal gangue was efficiently eliminated metal ions from water, opening up new possibilities for coal gangue reuse.

Reconciling nonlinear dissipation with the bilinear model of two Brownian particles.

The Brownian motion of a single particle is a paradigmatic model of the nonequilibrium dynamics of dissipative systems. In the system-plus-reservoir approach, one can derive the particle's equationsof motion from the reversible dynamics of the system coupled to a bath of oscillators representing its thermal environment. However, extending the system-plus-reservoir approach to multiple particles in a collective environment is not straightforward, and conflicting models have been proposed to that end. Here, we set out to reconcile some aspects of the nonlinear and the bilinear models of two Brownian particles. We show how the nonlinear dissipation originally derived from exponential system-reservoir couplings can alternatively be obtained from the bilinear Lagrangian, with a modified spectral function that explicitly depends on the distance between the particles. We discuss applications to the contexts of anomalous diffusion and of hydrodynamic interactions. Our results thus broaden the applicability of the bilinear model.

Anharmonic lattice dynamics from vibrational dynamical mean-field theory

We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative systematically improvable through its cluster extensions, usable with classical or quantum impurity solvers (depending on the importance of nuclear quantum effects) and can be combined with existing low-level diagrammatic theories of anharmonicity. When tested on models of anharmonic optical and acoustic phonons; we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures. We test the description of nonlocal anharmonicity via cellular VDMFT and the combination with self-consistent phonon (SCPH) theory, yielding the powerful SCPH $+$ VDMFT approach.

Partially polaron-transformed quantum master equation for exciton and charge transport dynamics.

Polaron-transformed quantum master equation (PQME) offers a unified framework to describe the dynamics of quantum systems in both limits of weak and strong couplings to environmental degrees of freedom. Thus, the PQME serves as an efficient method to describe charge and exciton transfer/transport dynamics for a broad range of parameters in condensed or complex environments. However, in some cases, the polaron transformation (PT) being employed in the formulation invokes an over-relaxation of slow modes and results in premature suppression of important coherence terms. A formal framework to address this issue is developed in the present work by employing a partial PT that has smaller weights for low frequency bath modes. It is shown here that a closed form expression of a second order time-local PQME including all the inhomogeneous terms can be derived for a general form of partial PT, although more complicated than that for the full PT. All the expressions needed for numerical calculation are derived in detail. Applications to a model of a two-level system coupled to a bath of harmonic oscillators, with test calculations focused on those due to homogeneous relaxation terms, demonstrate the feasibility and the utility of the present approach.

Entanglement dynamics of non-linearly coupled spin-boson model using hierarchical equation of motion approach

One of the most intensively studied problems in the field of open quantum systems is the spin-boson model. In this paper, we consider an extension of the spin-boson model with non-linear coupling. We solve the entanglement dynamics of two independent spins quadratically coupled to a bath of harmonic oscillators, using numerically ”exact” approach of hierarchical equations of motion (HEOM). Without Markovian approximation, generalized influence functional formulation by Hu et.al is used to describe the environmental effect of noisy quadratic bath in high-temperature regime. Wotters concurrence is then applied to numerically solved reduced density matrix to visualize the entanglement dynamics. By adjusting the environmental parameters, we vary the degree of non-markovianity and found the elongated time of entanglement.

Partition of free energy for a Brownian quantum oscillator: Effect of dissipation and magnetic field

Recently, the quantum counterpart of energy equipartition theorem has drawn considerable attention. Motivated by this, we formulate and investigate an analogous statement for the free energy of a quantum oscillator linearly coupled to a passive heat bath consisting of an infinite number of independent harmonic oscillators. We explicitly demonstrate that the free energy of the Brownian oscillator can be expressed in the form F(T)=〈f(ω,T)〉 where f(ω,T) is the free energy of an individual bath oscillator. The overall averaging process involves two distinct averages: the first one is over the canonical ensemble for the bath oscillators, whereas the second one signifies averaging over the entire bath spectrum of frequencies from zero to infinity. The latter is performed over a relevant probability distribution function P(ω) which can be derived from the knowledge of the generalized susceptibility encountered in linear response theory. The effect of different dissipation mechanisms is exhibited. We find two remarkable consequences of our results. First, the quantum counterpart of energy equipartition theorem follows naturally from our analysis. The second corollary we obtain is a natural derivation of the third law of thermodynamics for open quantum systems. Finally, we generalize the formalism to three spatial dimensions in the presence of an external magnetic field.

Improving the efficiency of open-quantum-system simulations using matrix product states in the interaction picture

Modeling open quantum systems---quantum systems coupled to a bath---is of value in condensed-matter theory, cavity quantum electrodynamics, nanosciences, and biophysics. The real-time simulation of open quantum systems was advanced significantly by the recent development of chain mapping techniques and the use of matrix product states that exploit the intrinsic entanglement structure in open quantum systems. The computational cost of simulating open quantum systems, however, remains high when the bath is excited to high-lying quantum states. We develop an approach to reduce the computational costs in such cases. The interaction representation for the open quantum system is used to distribute excitations among the bath degrees of freedom so that the occupation of each bath oscillator is ensured to be low. The interaction picture also causes the matrix dimensions to be much smaller in a matrix product state of a chain-mapped open quantum system than in the Schr\"odinger picture. Using the interaction representation accelerates the calculations by one to two orders of magnitude over the existing matrix-product-state method. In the regime of strong system-bath coupling and high temperatures, the speedup can be as large as three orders of magnitude. The approach developed here is especially promising to simulate the dynamics of open quantum systems in high-temperature and strong-coupling regimes.