Master Equation Research Articles

Extrinsic fluctuations in the p53 cycle

Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robustness. These fluctuations can be categorized as intrinsic, stemming from the system’s inherent structure and dynamics, and extrinsic, arising from external factors, such as temperature variations. Understanding the interplay between these fluctuations is crucial for obtaining a comprehensive understanding of biological phenomena. However, studying these effects poses significant computational challenges. In this study, we used an underexplored methodology to analyze the effect of extrinsic fluctuations in stochastic systems using ordinary differential equations instead of solving the master equation with stochastic parameters. By incorporating temperature fluctuations into reaction rates, we explored the impact of extrinsic factors on system dynamics. We constructed a master equation and calculated the equations for the dynamics of the first two moments, offering computational efficiency compared with directly solving the chemical master equation. We applied this approach to analyze a biological oscillator, focusing on the p53 model and its response to temperature-induced extrinsic fluctuations. Our findings underscore the impact of extrinsic fluctuations on the nature of oscillations in biological systems, with alterations in oscillatory behavior depending on the characteristics of extrinsic fluctuations. We observed an increased oscillation amplitude and frequency of the p53 concentration cycle. This study provides valuable insights into the effects of extrinsic fluctuations on biological oscillations and highlights the importance of considering them in more complex systems to prevent unwanted scenarios related to health issues.

Fast and robust production of quantum superposition states by the fractional shortcut to adiabaticity

The fractional shortcut to adiabaticity (f-STA) for the production of quantum superposition states is proposed firstly via a three-level system with a Λ-type linkage pattern and a four-level system with a tripod structure. The fast and robust production of the coherent superposition states is studied by comparing the populations for the f-STA and the fractional stimulated Raman adiabatic passage (f-STIRAP). The states with equal proportions can be produced by fixing the controllable parameters of the driving pulses at the final moment of the whole process. The effects of the pulse intensity and the time delay of the pulses on the production process are discussed by monitoring the populations on all of the quantum states. In particular, the spontaneous emission arising from the intermediate state is investigated by the quantum master equation. The result reveals that the f-STA exhibits superior advantages over the f-STIRAP in producing the superposition states.

Well-Posedness for a Class of Mean-Field-Type Forward-Backward Stochastic Differential Equations and Classical Solutions of Related Master Equations

Well-Posedness for a Class of Mean-Field-Type Forward-Backward Stochastic Differential Equations and Classical Solutions of Related Master Equations

Continuous-variable electromechanical quantum thermal transistors

Abstract We present a scheme to realize quantum thermal transistor effects in a continuous-variable electromechanical system including two microwave cavities and one mechanical oscillator. The thermal noise fluxes between the quantum system and its baths are evaluated by quantum master equation. It is shown that the thermal noise flux at one microwave cavity as an emitter can be dissipated into the other as a collector by combining the heating Stokes and cooling anti-Stokes processes. The indirect energy transfers between the two microwave modes can be significantly amplified by small energy changes at the mechanical oscillator as the base. The extremely high amplification depends sensitively on the detunings of the two microwave modes, which provides a new tool for precision measurements. This study opens the door for constructing quantum thermal transistors using various continuous-variable systems and is well accessible based on current experimental techniques.

Exact finite-time correlation functions for multiterminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics

Transport in open quantum systems can be explored through various theoretical frameworks, including the quantum master equation, scattering matrix, and Heisenberg equation of motion. The choice of framework depends on factors such as the presence of interactions, the coupling strength between the system and environment, and whether the focus is on steady-state or transient regimes. Existing literature mainly treats these frameworks independently. Our work establishes connections between them by clarifying the role and status of these approaches using two paradigmatic models for single and multipartite quantum systems in a two-terminal setup under voltage and temperature biases. We derive analytical solutions in both steady-state and transient regimes for the populations, currents, and current correlation functions. Exact results from the Heisenberg equation are shown to align with scattering matrix and master equation approaches within their respective validity regimes. Crucially, we establish a protocol for the weak-coupling limit, bridging the applicability of master equations at weak-coupling with Heisenberg or scattering matrix approaches at arbitrary coupling strength. Published by the American Physical Society 2024

Investigating tidal heating in neutron stars via gravitational Raman scattering

We present a scattering amplitude formalism to study the tidal heating effects of nonspinning neutron stars incorporating both worldline effective field theory and relativistic stellar perturbation theory. In neutron stars, tidal heating arises from fluid viscosity due to various scattering processes in the interior. It also serves as a channel for the exchange of energy and angular momentum between the neutron star and its environment. In the interior of the neutron star, we first derive two master perturbation equations that capture fluid perturbations accurate to linear order in frequency. Remarkably, these equations receive no contribution from bulk viscosity due to a peculiar adiabatic incompressibility which arises in stellar fluid for nonbarotropic perturbations. In the exterior, the metric perturbations reduce to the Regge-Wheeler equation which we solve using the analytical Mano-Suzuki-Takasugi method. We compute the amplitude for gravitational waves scattering off a neutron star, also known as gravitational Raman scattering. From the amplitude, we obtain expressions for the electric quadrupolar static Love number and the leading dissipation number to all orders in compactness. We then compute the leading dissipation number for various realistic equations of state and estimate the change in the number of gravitational-wave cycles due to tidal heating during inspiral in the LIGO-Virgo-KAGRA band. Published by the American Physical Society 2024

Quantum entanglement and non-Hermiticity in free-fermion systems

Abstract This topical review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the Lindblad master equation, alongside a review of typical non-Hermitian free-fermion systems that exhibit unique features. A pedagogical discussion is provided on the relationship between entanglement quantities and the correlation matrix in Hermitian systems. Building on this foundation, we focus on how entanglement concepts are extended to non-Hermitian systems from their Hermitian free-fermion counterparts, with a review of the general properties that emerge. Finally, we highlight various concrete studies, demonstrating that entanglement entropy remains a powerful diagnostic tool for characterizing non-Hermitian physics. The entanglement spectrum also reflects the topological characteristics of non-Hermitian topological systems, while unique non-Hermitian entanglement behaviors are also discussed. The review is concluded with several future directions. Through this review, we hope to provide a useful guide for researchers who are interested in entanglement in non-Hermitian quantum systems.

Three perspectives on entropy dynamics in a non-Hermitian two-state system

Abstract A comparative study of entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. To begin with, we illustrate the phase portrait of this non-Hermitian model on the Bloch sphere, elucidating the changes in behavior as one moves across the phase transition boundary, as well as the emergent feature of unidirectional state evolution in the spontaneously broken PT-symmetry regime. This is followed by an examination of the purity and entropy dynamics. Here we distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping. In this it is demonstrated that their differences are rooted in the treatment of the environmental coupling mode. For unbroken PT symmetry of the system, a notable characteristic feature of the perspective taken is the presence or absence of purity oscillations, with an associated entropy revival. The description of the system is then continued from its PT-symmetric pseudo-Hermitian phase into the regime of spontaneously broken symmetry, in the latter two approaches through a non-analytic operator-based continuation, yielding a Lindblad master equation based on the PT charge operator C. This phase transition indicates a general connection between the pseudo-Hermitian closed-system and the Lindbladian open-system formalism through a spontaneous breakdown of the underlying physical reflection symmetry.

Analogous Hawking Radiation in Dispersive Media

In the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improvements to the analysis. As our main result, we provide a complete set of connection formulas for both the subluminal and superluminal cases without resorting to suitable boundary conditions, first introduced by Corley, but simply on the grounds of a rigorous mathematical setting. Moreover, we provide an extension to the four-dimensional case, showing explicitly that, apart from obvious changes, adding transverse dimensions does not substantially modify the Hawking temperature in the dispersive case. Furthermore, an important class of exact solutions of the so-called reduced equation that governs the behavior of non-dispersive modes is also provided.

Entropies, level-density parameters and fission probabilities along the triaxially- and axially-symmetric fission paths in 296Lv

We investigate the variation of statistical properties of the fissile nucleus, especially entropy, and nuclear level density, along different fission paths. The calculations were focused on comparing axial and triaxial trajectories leading to fission of 296Lv. We observe that change of shell effects and their suppression rates with deformation can substantially influence fission dynamics. Furthermore, the fission process exhibits iso-entropic behavior at high excitation energies, while pronounced entropy variations are observed at lower energies. We derive a deformation-dependent level density parameter that plays a critical role in estimating the survival probability of a superheavy nucleus. The competition between different fission paths was further studied by employing a master equation approach, thereby demonstrating the critical role of entropy and thermodynamic properties in shaping fission dynamics within multidimensional deformation spaces.

StaR-LIF: State-resolved laser-induced fluorescence modeling for diatomic molecules

This study introduced a new model for quantitative analysis of the state-resolved laser-induced fluorescence signal of diatomic molecules, namely StaR-LIF. This model is built upon a master equation of the collisional-radiative transfer processes, which incorporated the latest data on the collisional energy transfer rates between individual spin- and parity-resolved rovibronic quantum levels, together with the most recent updates on the energy levels, line strengths and broadening/shift parameters of the relevant absorption and fluorescence transitions. To facilitate the use of this model, a web-based graphic user interface has been developed and made available at https://starlif.pku.edu.cn. Example applications of the current model have been demonstrated for NO, OH and CH, including parametric studies on the effects of variable pulse width and saturating excitation, as well as the temporal evolution of fluorescence spectrum during collisional transfer. The StaR-LIF model can provide quantitative modeling and analysis capabilities over a wide range of gasdynamic and excitation conditions, and promises to be useful in future LIF studies of complex reacting flows.

Dynamics of the nonequilibrium spin-boson model: A benchmark of master equations and their validity

Dynamics of the nonequilibrium spin-boson model: A benchmark of master equations and their validity

Dynamics of high-dimensional quantum systems coupled to a harmonic bath. General theory and implementation via multiconfigurational wave packets and truncated hierarchical equations for the mean-fields.

Modeling the dynamics of a quantum system coupled to a dissipative environment becomes particularly challenging when the system's dimensionality is too high to permit the computation of its eigenstates. This problem is addressed by introducing an eigenstate-free formalism, where the open quantum system is represented as a mixture of high-dimensional, time-dependent wave packets governed by coupled Schrödinger equations, while the environment is described by a multi-component quantum master equation. An efficient computational implementation of this formalism is presented, employing a variational mixed Gaussian/multiconfigurational time-dependent Hartree (G-MCTDH) ansatz for the wave packets and propagating the environment dynamics via hierarchical equations, truncated at the first or second level of the hierarchy. The effectiveness of the proposed methodology is demonstrated on a 61-dimensional model of phonon-driven vibrational relaxation of an adsorbate. G-MCTDH calculations on 4- and 10-dimensional reduced models, combined with truncated hierarchical equations for the mean fields, nearly quantitatively replicate the full-dimensional quantum dynamical results on vibrational relaxation while significantly reducing the computational time. This approach thus offers a promising quantum dynamical method for modeling complex system-bath interactions, where a large number of degrees of freedom must be explicitly considered.

Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle.

We have developed a computer code for the thermodynamic hierarchical equations of motion derived from a spin subsystem coupled to multiple Drude baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code can simulate the reduced dynamics of the subsystem under isothermal, isentropic, thermostatic, and entropic conditions. The extensive and intensive thermodynamic variables are calculated as physical observables, and Gibbs and Helmholtz energies are evaluated as intensive and extensive work. The energy contribution of the system-bath interaction is evaluated separately from the subsystem using the hierarchical elements of the hierarchical equations of motion. The accuracy of the calculated results for the equilibrium distribution and the two-body correlation functions is assessed by contrasting the results with those obtained from the time-convolution-less Redfield equation. It is shown that the Lindblad master equation is inappropriate for the thermodynamic description of a spin-boson system. Non-Markovian effects in thermostatic processes are investigated by sequentially turning on and off the baths at different temperatures with different switching times and system-bath coupling. In addition, the Carnot cycle is simulated under quasi-static conditions. To analyze the work performed for the subsystem in the cycle, thermodynamic work diagrams are plotted as functions of intensive and extensive variables. The C++ source codes are provided as supplementary material.

Unconventional magnon blockade in a dissipative photon–magnon coupling system

We investigate unconventional magnon blockade (UMB) in a dissipative photon–magnon coupling cavity, where the coherent and dissipative coupling between photon and magnon can be adjusted by the position of the yttrium iron garnet sphere in the cavity. An approximate analytical solution for the statistical property of magnon is provided, which is in good agreement with the results obtained by numerically solving the Lindblad master equation. Our results indicate that UMB can be achieved in the case of dissipative photon–magnon coupling, but not in the case of coherent photon–magnon coupling. Secondly, by adjusting the amplitude of the external laser field, dynamic control of UMB can be achieved. Finally, by solving the Lindblad master equation containing the occupation number of thermal magnon and photon, the statistical properties of magnons will transition from nonclassical to classical. It is shown that the above phenomena originate from the interference between different quantum paths. Our research may provide theoretical possibilities for quantum manipulation schemes at the single-magnon level and open up a new avenue for designing single-magnon sources in a dissipative photon–magnon coupling system.

Two-mode subharmonic generating system with coherent and thermal light

The statistical and squeezing characteristics of the light generated by a two-mode subharmonic generating system in a cavity pumped by two-mode coherent light and coupled to a two-mode thermal reservoir through a single-port mirror have been studied in this study. We construct the c-number Langevin equations linked to the normal ordering using the master equation for the system under discussion, and we establish the correlation characteristics of the noise forces. The mean and variance of the photon number of the cavity light are then determined using the solutions of the resulting differential equations. We have discovered that the cavity light mode’s photon statistics are super-Poissonian because the variance of the photon number is more significant than the mean of the photon number. Additionally, using the same solutions, we were able to extract the antinormally ordered characteristic function, which is used to calculate the Q function. In addition, the photon number distribution for the cavity mode is computed using the Q function. The variance of the plus and minus quadrature of the two-mode cavity light generated by the two-mode subharmonic generating system is also obtained. It is discovered that the cavity mode’s squeezing characteristics are unaffected by the two-mode driving coherent light, however, the thermal light has the effect of decreasing the squeezing of the cavity light and the squeezing takes place in the plus quadrature. Finally, we discovered that when the cavity is coupled to a vacuum reservoir, there is a 50%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} maximum squeezing of the two-mode cavity at a steady state and at the threshold. The nondegenerate subharmonic generator generates a two-mode cavity light that is 50%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} entangled.

Investigation of non-equilibrium phenomena in nitrogen RF inductively coupled plasma discharges: a state-to-state approach

Abstract This work presents a vibrational and electronic (vibronic) state-to-state (StS) model for nitrogen plasmas implemented within a multi-physics modular computational framework to study non-equilibrium effects in inductively coupled plasma (ICP) discharges. The vibronic master equations are solved in a tightly coupled fashion with the flow governing equations eliminating the need for invoking any simplifying assumptions when computing the state of the plasma, leading to a high-fidelity physical modeling. The model’s computational complexity is reduced via a maximum entropy coarse-graining approach, verified through zero-dimensional isochoric calculations. The coarse-grained StS model is employed to study the plasma discharge in the ICP facility at the von Karman Institute for Fluid Dynamics, Belgium. Results reveal pronounced discrepancies between StS predictions and those obtained based on local thermodynamic equilibrium (LTE) models, which are conventionally used in the simulation of such facilities. The analysis demonstrates a substantial departure of the internal state populations of atoms and molecules from the Boltzmann distribution. This has significant implications for energy coupling dynamics, affecting the discharge morphology. Further analysis reveals a quasi-steady-state population distribution in the plasma core, allowing for the construction of an efficient and ‘self-consistent’ macroscopic two-temperature (2T) formulation. Non-LTE simulations indicate significant disparities between the StS model and the commonly used Park 2T model, whereas the newly proposed 2T model aligns closely with StS simulations, capturing key features of non-equilibrium plasma formation. In particular, the current study highlights the importance of the vibrational-translational energy transfer term in shaping the plasma core morphology, suggesting a notable sensitivity to heavy-impact vibrational excitations and dissociative processes.

Impact of Loss Mechanisms on Linear Spectra of Excitonic and Polaritonic Aggregates.

The presence of loss mechanisms governed by empirical timescales can profoundly affect the dynamics in molecular systems, leading to changes in their spectra. However, incorporation of these effects along with the system's interaction with the thermal dissipative environments proves to be challenging. In this work, we demonstrate the possibility of utilizing the recently developed path integral Lindblad dynamics (PILD) method to study the linear spectra of molecular aggregates. PILD presents a uniquely powerful simulation technique for retaining the effects of the vibrations in a numerically exact manner through the Feynman-Vernon influence functional while incorporating the effects of losses in an empirical manner using the Lindbald master equation. As illustrations of this technique, we provide examples taken from chiral excitonic and polaritonic aggregates for which we simulate both the absorption spectra and circular dichroism (CD) spectra. We demonstrate that the effect of loss on particular states can differ not just on the basis of the symmetries of the state but also on the basis of complicated "interactions" of the structured dissipative environments with the system and its loss mechanisms. Due to the different selection rules between the absorption and CD spectra and the relative intensities and broadening of the peaks, the two linear spectra together give an interesting insight into the contributions of the various eigenstates to the correlation functions. While the focus here is on linear spectroscopy, it should be possible in the future to use PILD to study multidimensional spectra under loss mechanisms as well.

Ultrafast superconducting qubit readout with the quarton coupler.

Fast, high-fidelity, and quantum nondemolition (QND) qubit readout is an essential element of quantum information processing. For superconducting qubits, state-of-the-art readout is based on a dispersive cross-Kerr coupling between a qubit and its readout resonator. The resulting readout can be high fidelity and QND, but readout times are currently limited to the order of 50 nanoseconds due to the dispersive cross-Kerr of magnitude 10 megahertz. Here, we present a readout scheme that uses the quarton coupler to facilitate a large (greater than 200 megahertz) cross-Kerr between a transmon qubit and its readout resonator. Full master equation simulations of the coupled system show a 5-nanosecond readout time with greater than 99% readout fidelity and greater than 99.9% QND fidelity. The quartonic readout circuit is experimentally feasible and preserves the coherence properties of the qubit. Our work reveals a path for order of magnitude improvements of superconducting qubit readout by engineering nonlinear light-matter couplings in parameter regimes unreachable by existing designs.

Understanding Li6.24La3Zr2Al0.24O11.98 effect on poly(ionic liquid)-based electrolytes for high voltage solid-state lithium batteries working at room temperature

Hybrid electrolytes composed of poly(ionic liquid), ionic liquids (ILs), and fillers are very promising candidates for solid-state lithium metal batteries (SSLMBs). However, a significant knowledge gap in the field of hybrid electrolytes lies in the understanding of filler effect on properties and performance. Herein, we have investigated hybrid electrolytes based on poly(diallyldimethylammonium) bis(fluorosulfonyl)imide (PDDA-FSI), N-propyl-N-methylpyrrolidinium bis(fluorosulfonyl)imide (PYR13FSI), lithium bis(fluorosulfonyl)imide (LiFSI) and different loadings (from 0 to 19.2 vol%) of Li6.24La3Zr2Al0.24O11.98 (Al-LLZO) particles. All the electrolytes present a homogeneous morphology and excellent thermal stability. Moreover, our results demonstrate that Al-LLZO particles do not contribute to the ionic conductivity of the hybrid electrolytes. A 2.6 vol% of Al-LLZO led to the excellent performance in full cells at room temperature. Surprisingly, the battery performance was not correlated with the transport properties. Instead, this study found out a mechanical-performance relationship, which follows a master equation: t = A (−12.48 (1-e(1.53x10-4σy))) / P that enables to correlate the effect Al-LLZO particles on the cell performance, and predicts, for the first time, the lifetime of the battery through the mechanical properties.