Thermodynamics of the gray atmosphere. II - Unattainability of detailed balancing.
Unattainability of detailed balancing in thermodynamic equilibrium of gray atmosphere
GRAY GAS↗
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Detailed balance as a check on impact parameter calculations.
It is demonstrated numerically that detailed balance indeed is well satisfied in the multi-state impact parameter formulation of proton-hydrogen atom collisions. It is also demonstrated numerically that detailed balance is a much more sensitive test of computational accuracy than is the charge conservation test usually employed in such impact parameter calculations. It is suggested that detailed balance be used as a check on all impact parameter calculations. That even agreement with detailed balance may not be a sufficient test for accuracy of the results is pointed out.
Tai, H.↗
Enforcing detailed balance in the Borgnakke–Larsen redistribution method with temperature dependent relaxation models
For decades, it has been observed that the commonly used Borgnakke–Larsen method for energy redistribution in Direct Simulation Monte Carlo codes fails to satisfy the principle of detailed balance when coupled to a wide variety of temperature dependent relaxation models, while seemingly satisfying detailed balance when coupled to others. Many attempts have been made to remedy the issue, yet much ambiguity remains, and no consensus appears in the literature regarding the root cause of the intermittent compatibility of the Borgnakke–Larsen method with temperature dependent relaxation models. This paper alleviates that ambiguity by presenting a rigorous theoretical derivation of the Borgnakke–Larsen method's requirement for satisfying detailed balance. Specifically, it is shown that the Borgnakke–Larsen method maintains detailed balance if and only if the probability of internal-energy exchange during a collision depends only on collision invariants (e.g., total energy). Here, the consequences of this result are explored in the context of several published definitions of relaxation temperature, including translational, total, and cell-averaged temperatures. Of particular note, it is shown that cell-averaged temperatures, which have been widely discussed in the literature as a way to ensure equilibrium is reached, also fail in a similar, although less dramatic, fashion when the aforementioned relationship is not enforced. The developed theory can be used when implementing existing or new relaxation models and will ensure that detailed balance is satisfied.
74 ATOMIC AND MOLECULAR PHYSICS↗
Forbidden lines of np/q/ ions. I - Detailed balance and line intensity ratios
The detailed balance equations are solved in the ground state terms of 37 ions of C, N, O, Ne, Mg, Si, S and Fe; atomic data for 235 transitions of these ions are tabulated, and 14 line ratios of q = 2,4 ions and eight line ratios of q = 3 ions are graphed. Forbidden emission lines of these ions are in the far and near UV, visible, and near and far IR regions of the spectrum. In addition, detailed calculations of the relative populations of the levels of the ground state are presented as a function of temperature and density.
Kafatos, M.↗
A far-wing line shape theory which satisfies the detailed balance principle
A far-wing theory in which the validity of the detailed balance principle is maintained in each step of the derivation is presented. The role of the total density matrix including the initial correlations is analyzed rigorously. By factoring out the rapidly varying terms in the complex-time development operator in the interaction representation, better approximate expressions can be obtained. As a result, the spectral density can be expressed in terms of the line-coupling functions in which two coupled lines are arranged symmetrically and whose frequency detunings are omega - 1/2(omega(sub ji) + omega (sub j'i'). Using the approximate values omega - omega(sub ji) results in expressions that do not satisfy the detailed balance principle. However, this principle remains satisfied for the symmetrized spectral density in which not only the coupled lines are arranged symmetrically, but also the initial and final states belonging to the same lines are arranged symmetrically as well.
Ma, Q.↗
Violation of detailed balance in non-equilibrium magnons observed by inelastic neutron scattering
Traditional inelastic neutron scattering (INS) characterizes excitations—such as phonons and magnons—in condensed matter systems at thermodynamic equilibrium. However, the most intriguing and puzzling many-body effects in open quantum systems often emerge from dissipative dynamics that are inherently out of equilibrium. Here, we use a combination of laser pumping and INS to experimentally observe long-lived nonequilibrium magnons in a two-dimensional (2D) square-lattice Heisenberg antiferromagnet. These nonequilibrium magnons manifest themselves as a violation of detailed balance in the dynamic structure factor and reach steady states under periodic driving, analogous to nonequilibrium steady states in driven dissipative systems. Furthermore, we show that the violation of detailed balance reflects the quantum-mechanical nature of the underlying dynamical system, where out-of-time-ordered correlations of creation and annihilation operators do not satisfy commutation relations. The in operando INS technique developed here provides a new approach to studying nonequilibrium magnons in prototypical 2D quantum magnets and can be extended to other systems, including one-dimensional spin chains and topological many-body spin systems, where nonequilibrium effects are widespread and rich in discovery potential.
Hua, Chengyun [Oak Ridge National Laboratory (ORNL↗
Efficient Quantum Gibbs Samplers with Kubo–Martin–Schwinger Detailed Balance Condition
Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial thermostat in classical Monte Carlo or molecular dynamics methods, rather than being treated as an approximation to weakly coupled system-bath unitary dynamics. Recently, Chen, Kastoryano, and Gilyén (arXiv:2311.09207) introduced the first efficiently implementable Lindbladian satisfying the Kubo–Martin–Schwinger (KMS) detailed balance condition, which ensures that the Gibbs state is a fixed point of the dynamics and is applicable to non-commuting Hamiltonians. This Gibbs sampler uses a continuously parameterized set of jump operators, and the energy resolution required for implementing each jump operator depends only logarithmically on the precision and the mixing time. In this work, we build upon the structural characterization of KMS detailed balanced Lindbladians by Fagnola and Umanità, and develop a family of efficient quantum Gibbs samplers using a finite set of jump operators (the number can be as few as one), akin to the classical Markov chain-based sampling algorithm. Compared to the existing works, our quantum Gibbs samplers have a comparable quantum simulation cost but with greater design flexibility and a much simpler implementation and error analysis. Moreover, it encompasses the construction of Chen, Kastoryano, and Gilyén as a special instance.
97 MATHEMATICS AND COMPUTING↗
Best of both worlds: Enforcing detailed balance in machine learning models of transition rates
The slow microstructural evolution of materials often plays a key role in determining material properties. When the unit steps of the evolution process are slow, direct simulation approaches such as molecular dynamics become prohibitive and Kinetic Monte-Carlo (kMC) algorithms, where the state-to-state evolution of the system is represented in terms of a continuous-time Markov chain, are instead frequently relied upon to efficiently predict long-time evolution. The accuracy of kMC simulations however relies on the complete and accurate knowledge of reaction pathways and corresponding kinetics. This requirement becomes extremely stringent in complex systems such as concentrated alloys where the astronomical number of local atomic configurations makes the a priori tabulation of all possible transitions impractical. Machine learning models of transition kinetics have been used to mitigate this problem by enabling the efficient on-the-fly prediction of kinetic parameters. While conventional KMC methods based on transition state theory naturally yield reversible dynamics that exactly obey the detailed balance criterion, providing strong guarantees on the properties of the stationary distribution, many recently-proposed ML-based approaches to barrier predictions provide no such guarantees. In this study, we derive conditions under which physics-informed ML architectures exactly enforce the detailed balance condition by construction, even when relying on non-extensive descriptions of states in terms of local environments around mobile defects. In conclusion, using the diffusion of a vacancy in a concentrated alloy as an example, we show that such ML architectures also exhibit superior performance in terms of prediction accuracy, demonstrating that the imposition of physical constraints can facilitate the accurate learning of barriers at no increase in computational cost.
36 MATERIALS SCIENCE↗
Mixed quantum–classical approach to model non-adiabatic electron–nuclear dynamics: Detailed balance and improved surface hopping method
We develop a density matrix formalism to describe coupled electron–nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional “virtual” nuclear wave packets whose interference with the “real” (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phase shifts lead to the detailed balance condition in the strong decoherence limit.
74 ATOMIC AND MOLECULAR PHYSICS↗
Detailed-balance limits for sunlight-to-protonic energy conversion from aqueous photoacids and photobases based on reversible mass-action kinetics
(Photo)chemical and photophysical detailed balance analyses are used to predict optimal properties and efficiency limits for sunlight-to-protonic energy conversion from aqueous photoacids or photobases.
Chemistry↗
The detailed balance requirement and general empirical formalisms for continuum absorption
Two general empirical formalisms are presented for the spectral density which take into account the deviations from the Lorentz line shape in the wing regions of resonance lines. These formalisms satisfy the detailed balance requirement. Empirical line shape functions, which are essential to provide the continuum absorption at different temperatures in various frequency regions for atmospheric transmission codes, can be obtained by fitting to experimental data.
Ma, Q.↗
Understanding the nature of mean-field semiclassical light-matter dynamics: An investigation of energy transfer, electron-electron correlations, external driving, and long-time detailed balance
Semiclassical electrodynamics (with quantum matter plus classical electrodynamics fields) is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be described instantaneously by static two-body interactions connecting two different molecules, while a classical transverse E field acts as a spectator at short distance; we will call this Hamiltonian no. I. On the other hand, intermolecular interactions can also be described as effects that are mediated exclusively through a classical one-body Ε field without any quantum effects at all (assuming we ignore electronic exchange); we will call this Hamiltonian no. II. Moreover, one can also mix these two different Hamiltonians into a third, hybrid Hamiltonian, which preserves quantum electron-electron correlations for lower excitations but describes higher excitations in a mean-field way. To investigate which semiclassical scheme is most reliable for practical use, here we study the real-time dynamics of a minimalistic many-site model—a pair of identical two-level systems (TLSs)—undergoing either resonance energy transfer (RET) or collectively driven dynamics. While both approaches (no. 1 and no. 2) perform reasonably well when there is no strong external excitation, we find that no single approach is perfect for all conditions (and all methods fail when a strong external field is applied). Each method has its own distinct problems: Hamiltonian no. I performs best for RET but behaves in a complicated manner for driven dynamics; Hamiltonian no. II is always stable, but obviously fails for RET at short distances. One key finding is that, for externally driven dynamics, a full configuration-interaction description of Hamiltonian no. I strongly overestimates the long-time electronic energy, highlighting the not obvious fact that, if one plans to merge quantum molecules with classical light, a full, exact treatment of electron-electron correlations can actually lead to worse results than a simple mean-field electronic structure treatment. Future work will need to investigate (i) how these algorithms behave in the context of more than a pair of TLSs and (ii) whether or not these algorithms can be improved in general by including crucial aspects of spontaneous emission.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
An archetype hydrogen atmosphere problem
Populations for the first three bound states and the continuum of hydrogen are determined for an isothermal hydrostatic atmosphere at 20,000 K. The atmosphere is treated as optically thin in the Balmer and Paschen continua and illuminated by continuum radiation at these wavelengths with prescribed radiation temperatures. The atmosphere is optically thick in the 2-1, 3-1, 3-2 and c-1 transitions. Three stages of approximation are treated: (1) radiative detailed balance in the 2-1, 3-1 and 3-2 transitions, (2) radiative detailed balance in the 3-1 and 3-2 transitions, and (3) all transitions out of detailed balance. The solution of this problem is nontrivial and presents sufficient difficulty to have caused the failure of at least one rather standard technique. The problem is thus a good archetype against which new methods or new implementations of old methods may be tested.
Athay, R. G.↗
Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind
The PI (Cranmer) and Co-I (A. van Ballegooijen) made significant progress toward the goal of building a "unified model" of the dominant physical processes responsible for the acceleration of the solar wind. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a one-dimensional and time-independent model of plasma heating and acceleration. The accomplishments in the report period are thus divided into these two categories: 1a. Focused Study of Kinetic MHD Turbulence. We have developed a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. A turbulent cascade is one possible way of generating small-scale fluctuations (easy to dissipate/heat) from a pre-existing population of low-frequency Alfven waves (difficult to dissipate/heat). We modeled the cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, though, there is insufficient power to heat protons and heavy ions. The dominant oblique waves undergo Landau damping, which implies strong parallel electron heating. We thus investigated the nonlinear evolution of the electron velocity distributions (VDFs) into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere) which are an alternate means of heating protons via stochastic interactions similar to particle-particle collisions. 1b. Focused Study of the Multi-Mode Detailed Balance Formalism. The PI began to explore the feasibility of using the "weak turbulence," or detailed-balance theory of Tsytovich, Melrose, and others to encompass the relevant physics of the solar wind. This study did not go far, however, because if the "strong" MHD turbulence discussed above is a dominant player in the wind's acceleration region, this formalism is inherently not applicable to the corona. We will continue to study the various published approaches to the weak turbulence formalism, especially with an eye on ways to parameterize nonlinear wave reflection rates. 2. Building the Unified Model Code Architecture. We have begun developing the computational model of a time-steady open flux tube in the extended corona. The model will be "unified" in the sense that it will include (simultaneously for the first time) as many of the various proposed physical processes as possible, all on equal footing. To retain this generality, we have formulated the problem in two interconnected parts: a completely kinetic model for the particles, using the Monte Carlo approach, and a finite-difference approach for the self-consistent fluctuation spectra. The two codes are run sequentially and iteratively until complete consistency is achieved. The current version of the Monte Carlo code incorporates gravity, the zero-current electric field, magnetic mirroring, and collisions. The fluctuation code incorporates WKJ3 wave action conservation and the cascade/dissipation processes discussed above. The codes are being run for various test problems with known solutions. Planned additions to the codes include prescriptions for nonlinear wave steepening, kinetic velocity-space diffusion, and multi-mode coupling (including reflection and refraction).
Cranmer, Steven R.↗
Hybrid Reduced Order Model for N2-N2 Interactions for Application to Dissociation and Energy Transfer Processes
Recent work in the aerothermodynamics community has focused on the development of reduced-order models for thermo-chemical non-equilibrium which avoid the restrictive assumptions of multi-temperature models and the prohibitive cost associated with State-to-State (StS) models. In the present work, this is accomplished by lumping energy states together and assuming groups of states are roughly in equilibrium. As a result, the non-equilibrium behavior of a gas can be captured at a reduced computational cost from a full StS simulation. In this work, we present a hybrid grouping model for studying energy transfer and dissociation in a mixture of nitrogen molecules due to N2-N2 reactions. This is accomplished by making use of a grouping strategy informed by data from the N2-N StS kinetic data. However, due to the massive computational cost associated with constructing StS data for the N2-N2 system, the kinetic data for the hybrid grouping model are calculated using the quasi-classical trajectory (QCT) method by sampling states for trajectory within the groups. This general framework is called the Maximum-Entropy Quasi-Classical Trajectory (ME-QCT) method. The primary challenge associated with this method is that rates for reverse grouped reactions cannot be obtained through detailed balance at a group level, due to the variation of group internal temperatures. To construct the full model for N2-N2 grouped kinetics using the ME-QCT method, detailed balance is invoked at the microscopic level, allowing for the calculation of the full kinetic data from QCT. Results will be presented using the full ME-QCT model for the N2-N2 system in an isothermal and isochoric reactor simulation. In addition, simple CFD test cases for a one-dimensional standing shock and for a quasi-one-dimensional nozzle will be used for demonstration of the ME-QCT method. This method allows for the calculation of non-equilibrium behavior for the N2-N2 system without the prohibitive cost of a full StS simulation. Moreover, it enables the construction of a unified model for the dissociating and recombining non-equilibrium flows.
nonequilibrium modeling↗
As‐Doped Polycrystalline CdSeTe: Localized Defects, Carrier Mobility and Lifetimes, and Impact on High‐Efficiency Solar Cells
Abstract The efficiency potential for single‐junction photovoltaics (PV) is described by the detailed balance model, which requires the elimination of nonradiative recombination and perfect minority carrier collection. Improvements in GaAs, Si, and perovskite PV follow this model. It might be more complex for CdTe, a leading thin‐film PV technology. While lifetime, passivation, and doping goals for 25% efficient CdTe solar cells are largely reached, voltage is ≈20% below the detailed balance limit. Why is that? In Se‐alloyed CdSe x Te 1‐x (Se is required for >20% efficiency) additional losses can occur due to electrostatic and bandgap fluctuations and due to electronic trap states. To understand mechanisms limiting CdSeTe solar cell performance and to suggest improvements, carrier dynamics, and transport in CdSe x Te 1‐x with variation in Se composition and as doping is analyzed. It is shown that trapping, likely due to anion‐site defects and their complexes, is correlated with low charge carrier mobility of 0.1–0.6 cm 2 (Vs) −1 . Even with 1000 ns charge carrier lifetimes, carrier diffusion length is less than the absorber thickness, reducing efficiency to ≈23%. Device simulations are used to analyze the performance of CdSe x Te 1‐x solar cells; thermodynamic models are not sufficient for absorbers with electronic disorder and trapping.
14 SOLAR ENERGY↗
Kramers' degeneracy for open systems in thermal equilibrium
Kramers' degeneracy theorem underpins many interesting effects in quantum systems with time-reversal symmetry. We show that the generator of dynamics for Markovian open fermionic systems can exhibit an analogous degeneracy, protected by a combination of time-reversal symmetry and the microreversibility (detailed balance) property of systems at thermal equilibrium—the degeneracy is lifted if either condition is not met. We provide simple examples of this phenomenon and show that the degeneracy is reflected in the single-particle Green's functions. Furthermore, we show that certain experimental signatures of topological edge modes in open many-body systems can be protected by microreversibility in the same way. Our results highlight the importance of detailed balance in characterizing open topological matter.
36 MATERIALS SCIENCE↗
Spatial profiles of photon chemical potential in near-field thermophotovoltaic cells
Emitted photons stemming from the radiative recombination of electron–hole pairs carry chemical potential in radiative energy converters. This luminescent effect can substantially alter the local net photogeneration in near-field thermophotovoltaic cells. Several assumptions involving the luminescent effect are commonly made in modeling photovoltaic devices; in particular, the photon chemical potential is assumed to be zero or a constant prescribed by the bias voltage. The significance of photon chemical potential depends upon the emitter temperature, the semiconductor properties, and the injection level. Hence, these assumptions are questionable in near-field thermophotovoltaic devices with nanoscale separation distances between the emitter and the cell. In the present work, an iterative solver that combines fluctuational electrodynamics with the drift-diffusion model is developed to tackle the coupled photon and charge transport problem, enabling the determination of the spatial profile of photon chemical potential beyond the detailed balance approach. Here, the difference between the results obtained by allowing the photon chemical potential to vary spatially and by assuming a constant value demonstrates the limitations of the conventional approaches. This study is critically important for performance evaluation of near-field thermophotovoltaic systems with nanoscale vacuum gaps.
30 DIRECT ENERGY CONVERSION↗