Auswahl der wissenschaftlichen Literatur zum Thema „Bosonic analytic continuation“

The damping of spin waves in high-T[Formula: see text] superconductors is investigated in this paper. We use the spin polaron formulation in the finite temperature (Matsubara) Green’s function method in a representation, where holes are described as spinless fermions (holons) and spins as normal bosons characterized by the hard-core bosonic operators in accordance with the Holstein–Primakoff transformation. The interaction of holes with spin waves is then described by a Hamiltonian, which resembles the conventional polaron problem and came to be known as the spin polaron Hamiltonian. The rate of the damping of spin waves is then obtained from the self-energy term of the spin wave Green’s function at finite temperature. In the limit of zero temperature and low frequency, the spin wave damping was subsequently determined. We evaluated the same quantity by analytic continuation to get the zero temperature result.

The closed bosonic string compactified on a torus is decomposed into two open strings corresponding to left and right movers respectively. Multiloop amplitudes are expressed as a product of a holomorphic and an anti-holomorphic function of the moduli of the world-sheet Riemann surface. Such a product is obtained by analytically continuing left and right open string amplitudes such that one is the complex conjugate of the other. A justification for this analytic continuation is provided using a second quantized field theory of strings. The extra parameters needed for complexification are shown to arise from the constraint expressing invariance under choice of origin for string parametrization. The chiral string is discussed.

The ground state and the phase transitions of the bilayered spin-S anti-ferromagnetic Heisenberg model were studied by Ng et al.1 by using the Schwinger boson mean field theory. In this paper, an analytic continuation of the self-consistent equations is carried out in order to study the extension of the model to fractional dimensions from 1 to 2. Decreasing the dimensionality from 2 has an effect similar to that of decreasing the spin S. The corresponding phase diagram and phase transition will also be discussed.

We discuss two results: (i) we calculate the two-point function of the density fluctuations to [Formula: see text] in the fermonic formulation of the d = 1 string theory and compare with the [Formula: see text] result from the candidate collective field Hamiltonian. The latter result is divergent, showing the inequivalence of the two theories. We find out the corrections to the collective field Hamiltonian (both in the form of infinite counterterms and additional finite pieces) needed to match with the fermion theory. (ii) We study tree-level scattering processes between bosons due to the localized interaction near the boundary (in a region of order [Formula: see text]). The reflection problem at the boundary is treated by an analytic continuation of the time-of-flight variable.

The limit q-Bernstein operator Bq = B∞,q: C[0, 1] → C[0, 1] emerges naturally as a q-version of the Szász-Mirakyan operator related to the q-deformed Poisson distribution. The latter is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state.The limit q-Bernstein operator has been widely studied lately. It has been shown that Bq is a positive shape-preserving linear operator on C[0, 1] with ‖Bq‖ = 1. Its approximation properties, probabilistic interpretation, behavior of iterates, and the impact on the smoothness have been examined.In this paper, it is shown that the possibility of an analytic continuation of Bqf into {z: |z| < R}, R > 1, implies the smoothness of f at 1, which is stronger when R is greater. If Bqf can be extended to an entire function, then f is infinitely differentiable at 1, and a sufficiently slow growth of Bqf implies analyticity of f in {z: |z − 1| < δ}, where δ is greater when the growth is slower. Finally, there is a bound for the growth of Bqf which implies f to be an entire function.

PurposeThe outbreak and continuation of COVID-19 have spawned the transformation of traditional teaching models to a certain extent. The Chinese Ministry of Education’s guidance on “keep learning and teaching during class suspension” has made OTC and learning (OTC) become routinized, and the public’s emotional attitudes toward OTC have also evolved over time. The purpose of this study is to segment the emotional text data and introduce it into the topic model to reveal the evolution process and stage characteristics of public emotional polarity and public opinion of OTC topics during public health emergencies in the context of social media participation. The research has important guiding significance for the development of OTC and can influence and improve the efficiency and effect of OTC to a certain extent. The analysis of online public opinion can provide suggestions for the government and media to guide the trend of public opinion and optimize the OTC model.Design/methodology/approachThis paper takes the topic of “OTC” on Zhihu during the COVID-19 epidemic as an example, combined with the characteristics of public opinion changes, chooses Boson emotional dictionary and time series analysis method to build an OTC network public opinion theme evolution analysis framework that integrates emotional analysis and topic mining. Finally, an empirical analysis of the dynamic evolution of the communication network for each stage of the life cycle of a specific topic is realized.FindingsThis paper draws the following conclusions: (1) Through the emotional value table and the change trend chart of the number of comments, the analysis found that the number of positive comments is greater than the number of negative comments, which can be inferred that the public gradually accepts “OTC” and presents a positive emotional state. (2) By observing the changing trend of the average daily emotional value of the public, it is found that the overall emotional value shows a stable development trend after a large fluctuation. From the actual emotional value and the fitted emotional value curve, it can be seen that the overall curve fit is good, so ARIMA (12, 1, 6) can accurately predict the dynamic trend of the daily average emotional value in this paper. Therefore, based on the above-mentioned public opinion, emotional analysis research, relevant countermeasures and suggestions are put forward, which is conducive to guiding the development direction of public opinion in a positive way.Originality/valueTaking the topic of “OTC” in Zhihu as an example, this paper combines Boson emotional dictionary and time series to conduct a series of research analyses. Boson emotional dictionary can analyze the public’s emotional tendency, and time series can well analyze the intrinsic structure and complex features of the data to predict the future values. The combination of the two research methods allows for an adequate and unique study of public emotional polarization and the evolution of public opinion.

We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package’s output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package’s output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

Abstract We derive the general exact forms of the Wigner function, of mean values of conserved currents, of the spin density matrix, of the spin polarization vector and of the distribution function of massless particles for the free Dirac field at global thermodynamic equilibrium with rotation and acceleration, extending our previous results obtained for the scalar field. The solutions are obtained by means of an iterative method and analytic continuation, which lead to formal series in thermal vorticity. In order to obtain finite values, we extend to the fermionic case the method of analytic distillation introduced for bosonic series. The obtained mean values of the stress-energy tensor, vector and axial currents for the massless Dirac field are in agreement with known analytic results in the special cases of pure acceleration and pure rotation. By using this approach, we obtain new expressions of the currents for the more general case of combined rotation and acceleration and, in the pure acceleration case, we demonstrate that they must vanish at the Unruh temperature.

Cette thèse comprend deux projets distincts. Nous avons développé et testé un modèle d’intelligence artificielle pour résoudre des problèmes de prolongement analytique bosonique, c’est-à-dire pour générer la conductivité optique correcte à partir de la fonction de corrélation courant-courant. Des travaux récents ont démontré que les réseaux neuronaux peuvent surpasser les méthodes d’entropie maximale pour le prolongement analytique des fonctions de Green de Matsubara bruitées en physique des systèmes à plusieurs corps, tant en termes de précision que de coût de calcul. Ici, nous généralisons cette approche aux fonctions de réponse de la conductivité. Une combinaison de distributions Bêta est proposée comme moyen de générer des ensembles d’entraînement qui évitent les limitations associées aux paysages plats monotones, car elles offrent un ensemble large de spectres d’entraînement qualitativement différents. Nous constatons que les réseaux neuronaux sont particulièrement efficaces pour prédire la conductivité DC, une quantité notoirement difficile à prédire pour les méthodes d’entropie maximale. Nous précisons la procédure pour utiliser le modèle de manière indépendante de la température, ce qui signifie qu’un réseau neuronal entraîné à une température spécifique pourrait être utilisé à différentes températures via une routine de redimensionnement. Enfin, nous proposons une définition générale de la confiance à associer à la prédiction du profil de la conductivité optique, un élément manquant crucial dans le domaine du prolongement analytique par IA, et fournissons quelques perspectives sur son applicabilité. Le second projet se concentre sur les supraconducteurs à haute température à base de cuprates. Des travaux expérimentaux récents ont montré une forte anti-corrélation entre le paramètre d’ordre supraconducteur et ce que l’on appelle le gap de transfert de charge. Cela implique à la fois les orbitales de l’oxygène et du cuivre, et provient de la forte corrélation électronique typique de ces matériaux. En particulier, une mesure directe de ces observables et de leur anti-corrélation a été obtenue par des expériences de microscopie à effet tunnel (STM). En tirant parti de la modulation naturelle de la position de l’oxygène apical à la surface du BSCCO bi-couche, qui module également ces observables dans l’espace, l’anti-corrélation a pu être validée à différents sites du même matériau. En utilisant une méthode avancée de la théorie du champ moyen dynamique (DMFT) appliquée au modèle d’Emery-Hubbard inhomogène, qui prend en compte à la fois les orbitales du cuivre et de l’oxygène des plans de cuprates, nous sommes capables de simuler la situation expérimentale. En utilisant une méthode d’extrapolation par pseudo-inversion, nous pouvons montrer que l’anti-corrélation est présente et forte dans ce modèle, bien que la variation spatiale importante rapportée dans les expériences n’apparaisse pas. Cela appelle à une réévaluation critique de l’interprétation des résultats expérimentaux dans notre modélisation. Enfin, nous discutons de ces résultats en prolongement avec la température critique de transition, le paramètre d’ordre supraconducteur et le gap de transfert de charge de différents composés de cuprates connus
This thesis includes two projects. In the first one, we develop and bench-mark an A.I. model to solve bosonic analytic continuation problems, that is generating the right optical conductivity starting from the current-current correlation function. Recent work has demonstrated that Neural Network can outperform Maximum Entropy methods for the analytical continuation of noisy Matsubara Green’s function in many-body physics, both in accuracy and computational cost. Here we generalize this approach to the conductivity response functions. A combination of Beta distributions is proposed as way to generate training sets that avoid limitations associated with monotonous flat scenery, as they offer a broad set of qualitatively different training spectra. We find that Neural Networks are particularly efficient at predicting DC conductivity, a notoriously difficult quantity for Maximum Entropy methods. We clarify the procedure to use the model in a thermally agnostic fashion, meaning that a Neural Network trained at a specific temperature could be used at different ones through a rescaling routine. Finally, we propose a general definition of confidence to be associated with the prediction of the optical conductivity profile, a much needed missing tile in the A.I. analytic continuation landscape, and provide some insight on its applicability. The second project focuses on cuprate high temperature superconductors. Recent experimental work has shown a strong anticorrelation between superconducting order parameter and the so called charge transfer gap. This involves both oxygen and copper orbitals and originates from the strong electronic correlation typical of these materials. In particular, a direct measure of these observables and their anti-correlation has been obtained by scanning tunneling microscopy experiments. Taking advantage from the natural modulation of the apical oxygen position on the surface of bi-layered BSCCO, which also modulate these observable in space, the anti-correlation could be validated at different sites of the same material. Using an advanced Dynamical Mean Field Theory method applied to the inhomogeneous Emery-Hubbard model, which takes into account both the copper and the oxygen orbitals of the cuprate planes, we are able to simulate the experimental situation. By using a pseudoinversion extrapolation method, we can show that the anti-correlation is present and strong in this model, though the strong spatial variation reported in experiments does not occur. This calls for a critical re-evaluation of the interpretation of the experimental results within our modeling. We finally discuss these findings in relation with the critical transition temperature, the superconducting order parameter and charge transfer gap of various known cuprate compounds