Master Equation Research Articles

Master equation modeling of water dissociation in small ionic water clusters: Ag+(H2O) n , n = 4-6.

We model temperature-dependent blackbody infrared radiative dissociation (BIRD) rate coefficients of Ag+(H2O) n , n = 4-6, a system with loosely bound water molecules. We employ a master equation modeling (MEM) approach with consideration of absorption and emission of blackbody radiation, comparing single and multiple-well descriptions. The unimolecular dissociation rate coefficients are obtained using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, employing two approaches to model the sum of states in the transition state, the rigid activated complex (RAC) and the phase space limit (PSL) approach. A genetic algorithm is used to find structures of low-lying isomers for the kinetic modeling. We show that the multiple-well MEM approach with PSL RRKM in the All Wells and Transition States Are Relevant (AWATAR) variant provides a reliable description of Ag+(H2O) n BIRD, in agreement with previously published experimental data. Higher-lying isomers contribute significantly to the overall dissociation rate coefficient, underlying the importance of the multiple-well ansatz in which all isomers are treated on the same footing.

Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity

Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity

Geometric BV for twisted Courant sigma models and the BRST power finesse

We study twisted Courant sigma models, a class of topological field theories arising from the coupling of 3D 0-/2-form BF theory and Chern-Simons theory and containing a 4-form Wess-Zumino term. They are examples of theories featuring a nonlinearly open gauge algebra, where products of field equations appear in the commutator of gauge transformations, and they are reducible gauge systems. We determine the solution to the master equation using a technique, the BRST power finesse, that combines aspects of the AKSZ construction (which applies to the untwisted model) and the general BV-BRST formalism. This allows for a geometric interpretation of the BV coefficients in the interaction terms of the master action in terms of an induced generalised connection on a 4-form twisted (pre-)Courant algebroid, its Gualtieri torsion and the basic curvature tensor. It also produces a frame independent formulation of the model. We show, moreover, that the gauge fixed action is the sum of the classical one and a BRST commutator, as expected from a Schwarz type topological field theory.

Ladder symmetries and Love numbers of Reissner-Nordström black holes

It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner-Nordström black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.

Relativistic coupled-cluster simulation of the kinetics of the hydrolysis of uranium hexafluoride

Uranium hexafluoride ( UF 6 ) is used ubiquitously in the nuclear fuel cycle. Its spontaneous hydrolysis in the presence of atmospheric moisture is well known but the associated reaction mechanism is poorly understood. Here a computational study was undertaken with the aim of characterizing the rate-limiting step of the hydrolysis of UF 6 under dry conditions. Toward this end, we began by examining the convergence of various energy contributions to the atomization enthalpy ( Δ H at ) of UF 6 and its hydrolysis product, UO 2 F 2 . This enabled a refinement of our previous composite method, resulting in a composite method with improved accuracy that also scales well by leveraging existing massively-parallel codes. We find that extremely high levels of theory are required to obtain Δ H at within experimental error bars, in agreement with the literature. Having calibrated our composite scheme, we proceed to investigate approximations appropriate for computing accurate binding energies and barrier heights on the potential energy surface governing the hydrolysis of UF 6 . In combination with high-accuracy relative energies, a master equation approach is used to generate rate constants, and comparisons are made with recent measurements [Richards et al., RSC Adv., 2020, 10, 34729]. Based on kinetic and equilibrium arguments, we conclude that the hydrolysis of U F 6 , when proceeding under very dry conditions, is unlikely to be initiated via U F 6 + H 2 O → UF 5 OH + HF type reactions. Finally, computed equilibrium constants and rate coefficients are tabulated for the temperature range 300–1800 K.

High-Temperature Pyrolysis Study of 2-Methyl-2-butanol behind Reflected Shock Wave: Shock Tube and Computational Study.

Pyrolysis of a branched alcohol, 2-methyl-2-butanol (2M2BOH), was carried out behind the reflected shock wave in the temperature range of 1011-1303 K and under pressures varying from 9.3 to 14.6 atm. Qualitative and quantitative analysis of the postshock mixture was performed using gas chromatography-mass spectrometry and gas chromatography with a flame ionization detector, respectively. The rate coefficients for the C-C and C-O bond cleavage reaction pathways were calculated using the variational transition-state theory. The Rice-Ramsperger-Kessel-Marcus/Master equation was employed to calculate the rate coefficients for the H2O-elimination reactions, unimolecular dissociation, and isomerization reaction pathways. The overall decomposition rate coefficient for the 2-methyl 2-butanol (2M2BOH) was estimated to be , where activation energy is given in kcal mol-1. The reaction path analysis was performed, which gives information regarding the contribution of individual intermediate species toward the decomposition of 2M2BOH. A set of reactions was proposed and used to simulate the combustion chemistry of 2M2BOH, which consists of 48 reactions and 39 species. The experimentally measured and simulated mole fractions for the reactant and products showed reasonably good agreement. This work additionally investigates the effect of branching on the decomposition kinetics of long-chain alcohols.

Quantum speedup and non-Markovianity of an atom in structured reservoirs: pseudomodes as a good description of environmental memory

Following the recent paper (Teittinen et al 2019 New J. Phys. 21 123041), one can see that in general there is no simple relation between non-Markovianity and quantum speed limit. Here, we investigate the connection between quantum speed limit time and non-Markovianity of an atom in structured environments (reservoirs) whose dynamics is governed by an exact pseudomode master equation (Garraway 1997 Phys. Rev. A 55 2290). In particular, we find an inverse relation between them, which means that the non-Markovian feature of the quantum process leads to speedup of evolution. Thus, there is a link between quantum speedup and memory effects for specific cases of dynamical evolution. Our results might shed light on the relationship between the speedup of quantum evolution and the backflow of information from the environment to the system.

Gibbons' conjecture for entire solutions of master equations

Gibbons' conjecture for entire solutions of master equations

Velocity selective multiple two-photon dark and bright resonances in Potassium vapor

We report the observation of two additional sub-natural line width quantum interferences in the D 2 manifold of 39 K vapor, in addition to the usual single Electromagnetically Induced Transparency (EIT) peak. In a typical three level Λ-type system, only one EIT peak is observed. However, here we report observation of two additional line shapes riding on top of the absorption profile. The fact that the hyperfine splitting is smaller than the Doppler width in 39 K allows the probe and control beams to swap their transition pathways in different velocity groups of atoms even when their frequencies are kept constant. Our observations are in striking contrast to standard EIT measurements. These findings are in quantitative agreement with density matrix formalism taking into account velocity-selective two-photon resonances. Owing to the favorably low ground hyperfine splitting (Δ hf ) in 39 K, which allows a significantly large number of atoms with a Doppler shift greater than or equal to the Δ hf , the strength of these additional resonances is strong compared to that of other alkali atoms such as 87 Rb, 133 Cs where these resonances can not be observed. The control photon detuning to atomic transition captures the nature of the coherence; therefore an unusual phenomenon of conversion from perfect transparency to enhanced absorption of the probe photon is observed and explained by utilizing the adiabatic elimination of the excited state in the Master equation. Controlling such dark and bright resonances leads to new applications in quantum technologies such as frequency-offset laser stabilization and long-lived quantum memory.

Classifying topology in photonic crystal slabs with radiative environments

In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. However, the out-of-plane radiative losses in those photonic Chern slabs has been previously neglected, yielding limited accuracy for predictions of these systems’ topological protection. Here, we develop a general framework for measuring the topological protection in photonic systems, such as in photonic crystal slabs, while accounting for in-plane and out-of-plane radiative losses. Our approach relies on the spectral localizer that combines the position and Hamiltonian matrices of the system to draw a real-picture of the system’s topology. This operator-based approach to topology allows us to use an effective Hamiltonian directly derived from the full-wave Maxwell equations after discretization via finite-elements method (FEM), resulting in the full account of all the system’s physical processes. As the spectral FEM-localizer is constructed solely from FEM discretization of the system’s master equation, the proposed framework is applicable to any physical system and is compatible with commonly used FEM software. Moving forward, we anticipate the generality of the method to aid in the topological classification of a broad range of complex physical systems.

Motorized chain models of the ideal chromosome

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.

Entropy variances of pure coherent states in the diffusion channel

Abstract Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, we solve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation of its analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in the diffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions in the diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes of the initial coherent states.

Diagnosing Thermalization Dynamics of Non-Hermitian Quantum Systems via GKSL Master Equations

Abstract The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we derive two versions of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we identify a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we exemplify the precise dynamics of thermalization and thermodynamic properties with test models.

Exact solutions of the simplified March model for organizational learning.

March's celebrated agent-based simulation model for organizational learning [J.G. March, Org. Sci. 2, 71 (1991)] has been extensively studied in recent decades. Yet the model has not been fully understood due to the lack of analytical solutions of the model. We simplify the March model to take an analytical approach using master equations. We then derive exact solutions for some of the simplest yet nontrivial cases, and perform numerical estimation of master equationsfor more complicated cases. Both analytical and numerical results are in good agreement with agent-based simulations. These results are also compared to those of the original March model. Our approach enables us to rigorously understand the results of the simplified model as well as the original model, to a large extent.

Spin-polarization and Coulomb interaction dependent thermal rectification in a quantum dot system

Based on the master equation approach, we investigate the thermal transport through a diode composed of a quantum dot under Coulomb interaction and tunnel-coupled to two ferromagnetic leads with antiparallel spin polarizations. We analyze the effects of spin polarizations, Coulomb interaction, mean temperature and Zeeman splitting on the thermal rectification. Firstly, we find that the thermal rectification effect is enhanced with the increase of spin polarization, because the mirror-symmetry of the system is broken by the anti-parallel spin polarization. Especially, when both leads are fully spin polarized, the asymmetry of the heat transferred by Coulomb interaction under the opposite temperature bias leads to the appearance of perfect thermal rectification and negative differential thermal conductance. Secondly, we find whether the system is in a Coulomb blockade state greatly affects the thermal rectification coefficient. As the average temperature increases or the intradot Coulomb interaction decreases, the system gradually escapes from the Coulomb blockade state, resulting in a reversal of the thermal rectification direction and ultimately leading to an increase in the rectification coefficient. Thirdly, we also find that the Zeeman splitting can be utilized to modulate the behavior of thermal rectification. Thermal rectification occurs only when Zeeman splitting and spin polarization coexist, and under different spin polarizations, the rectification coefficient exhibits different trends with the change of Zeeman splitting. These observations indicate that this structure holds potential application at a thermal rectifier as well as a thermal detector of magnetic fields.

Utilizing quantum coherence in Cs Rydberg atoms for high-sensitivity room-temperature terahertz detection: a theoretical exploration

In recent years, terahertz (THz) technology has made significant progress in numerous applications; however, the highly sensitive, room-temperature THz detectors are still rare, which is one of the bottlenecks in THz research. In this paper, we proposed a room-temperature electrometry method for THz detection by laser spectroscopy of cesium (Cs133) Rydberg atoms, and conducted a comprehensive investigation of the five-level system involving electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA), and Autler–Townes (AT) splitting in Cs133 cascades. By solving the Lindblad master equation, we found that the influence of the THz electric field, probe laser, dressing laser, and Rydberg laser on the ground state atomic population as well as the coherence between the ground state and the Rydberg state, plays a crucial role in the transformation and amplitude of the EIT and EIA signals. Temperature and the atomic vapor cell’s dimensions affect the number of Cs133 atoms involved in the detection, and ultimately determine the sensitivity. We predicted the proposed quantum coherence THz detection method has a remarkable sensitivity of as low as 10−9 V m−1 Hz−1/2. This research offers a valuable theoretical basis for implementing and optimizing quantum coherence effects based on Rydberg atoms for THz wave detection with high sensitivity and room-temperature operation.

Quasinormal modes and greybody factor of a Lorentz-violating black hole

Recently, a static spherically symmetric black hole solution was found in gravity nonminimally coupled a background Kalb-Ramond field. The Lorentz symmetry is spontaneously broken when the Kalb-Ramond field has a nonvanishing vacuum expectation value. In this work, we focus on the quasinormal modes and greybody factor of this black hole. The master equations for the perturbed scalar field, electromagnetic field, and gravitational field can be written into a Schrödinger equation. We use three methods to solve the quasinormal frequencies in the frequency domain. The results agree well with each other. The time evolution of a Gaussian wave packet is studied. The quasinormal frequencies fitted from the time evolution data agree well with that of frequency domain. The greybody factor is calculated by Wentzel-Kramers-Brillouin (WKB) method. The effect of the Lorentz-violating parameter on the quasinormal modes and greybody factor are also studied.

Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions

Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system’s complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.

Doppler-enhanced quantum magnetometry with thermal Rydberg atoms

We report experimental measurements showing how one can combine quantum interference and thermal Doppler shifts at room temperature to detect weak magnetic fields. We pump 87 Rb atoms to a highly-excited, Rydberg level using a probe and a coupling laser, leading to narrow transmission peaks of the probe due to destructive interference of transition amplitudes, known as Electromagnetically Induced Transparency. While it is customary in such setups to use counterpropagating lasers to minimize the effect of Doppler shifts, here we show, on the contrary, that one can harness Doppler shifts in a copropagating arrangement to produce an enhanced response to a magnetic field. In particular, we demonstrate an order-of-magnitude bigger splitting in the transmission spectrum as compared to the counterpropagating case. We explain and generalize our findings with theoretical modeling and simulations based on a Lindblad master equation. Our results pave the way to using quantum effects for magnetometry in readily deployable room-temperature platforms.

Attraction by pairwise coherence explains the emergence of ideological sorting.

Political polarization has become a growing concern in democratic societies, as it drives tribal alignments and erodes civic deliberation among citizens. Given its prevalence across different countries, previous research has sought to understand under which conditions people tend to endorse extreme opinions. However, in polarized contexts, citizens not only adopt more extreme views but also become correlated across issues that are, a priori, seemingly unrelated. This phenomenon, known as "ideological sorting", has been receiving greater attention in recent years but the micro-level mechanisms underlying its emergence remain poorly understood. Here, we study the conditions under which a social dynamic system is expected to become ideologically sorted as a function of the mechanisms of interaction between its individuals. To this end, we developed and analyzed a multidimensional agent-based model that incorporates two mechanisms: homophily (where people tend to interact with those holding similar opinions) and pairwise-coherence favoritism (where people tend to interact with ingroups holding politically coherent opinions). We numerically integrated the model's master equations that perfectly describe the system's dynamics and found that ideological sorting only emerges in models that include pairwise-coherence favoritism. We then compared the model's outcomes with empirical data from 24,035 opinions across 67 topics and found that pairwise-coherence favoritism is significantly present in datasets that measure political attitudes but absent across topics not considered related to politics. Overall, this work combines theoretical approaches from system dynamics with model-based analyses of empirical data to uncover a potential mechanism underlying the pervasiveness of ideological sorting.