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1
Ong, Perkins Jon, i Danilo M. Yanga. "Damping of spin waves in high-Tc superconductors in the spin polaron formulation". International Journal of Modern Physics B 32, nr 15 (18.06.2018): 1850190. http://dx.doi.org/10.1142/s0217979218501904.
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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.
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BRESSLOFF, P. C., J. G. TAYLOR i A. RESTUCCIA. "A FUNCTIONAL LIGHT-CONE GAUGE CONSTRUCTION OF A BOSONIC STRING COMPACTIFIED ON A TORUS". International Journal of Modern Physics A 03, nr 02 (luty 1988): 451–86. http://dx.doi.org/10.1142/s0217751x88000175.
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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.
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Ng, K. K. "Bilayered Spin-S Heisenberg Model in Fractional Dimensions". International Journal of Modern Physics B 12, nr 18 (20.07.1998): 1809–12. http://dx.doi.org/10.1142/s0217979298001034.
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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.
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MANDAL, GAUTAM, ANIRVAN M. SENGUPTA i SPENTA R. WADIA. "INTERACTIONS AND SCATTERING IN d = 1 STRING THEORY". Modern Physics Letters A 06, nr 16 (30.05.1991): 1465–77. http://dx.doi.org/10.1142/s0217732391001585.
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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.
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Ostrovska, Sofiya. "On the properties of the limit q-Bernstein operator". Studia Scientiarum Mathematicarum Hungarica 48, nr 2 (1.06.2011): 160–79. http://dx.doi.org/10.1556/sscmath.48.2011.2.1164.
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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.
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Feng, Xin, Xu Wang i Yue Zhang. "Research on public emotional polarization and public opinion evolution of OTC and learning during the COVID-19 epidemic: taking the topic of OTC on Zhihu as an example". Library Hi Tech 40, nr 2 (16.12.2021): 286–303. http://dx.doi.org/10.1108/lht-09-2021-0323.
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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.
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Nogaki, Kosuke, i Hiroshi Shinaoka. "Bosonic Nevanlinna Analytic Continuation". Journal of the Physical Society of Japan 92, nr 3 (15.03.2023). http://dx.doi.org/10.7566/jpsj.92.035001.
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Neuhaus, James, Nathan S. Nichols, Debshikha Banerjee, Benjamin Cohen-Stead, Thomas Maier, Adrian Del Maestro i Steven Johnston. "SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions". SciPost Physics Codebases, 12.11.2024. http://dx.doi.org/10.21468/scipostphyscodeb.39.
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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/.
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Neuhaus, James, Nathan S. Nichols, Debshikha Banerjee, Benjamin Cohen-Stead, Thomas Maier, Adrian Del Maestro i Steven Johnston. "Codebase release r1.1 for SmoQyDEAC.jl". SciPost Physics Codebases, 12.11.2024. http://dx.doi.org/10.21468/scipostphyscodeb.39-r1.1.
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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/.
10
Palermo, A., M. Buzzegoli i F. Becattini. "Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field". Journal of High Energy Physics 2021, nr 10 (październik 2021). http://dx.doi.org/10.1007/jhep10(2021)077.
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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.
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Beccaria, M., i A. Cabo-Bizet. "Large N Schur index of $$ \mathcal{N} $$ = 4 SYM from semiclassical D3 brane". Journal of High Energy Physics 2024, nr 4 (18.04.2024). http://dx.doi.org/10.1007/jhep04(2024)110.
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Abstract We consider the refined Schur superconformal index of 4d $$ \mathcal{N} $$ N = 4 U(N) SYM and the first term of its giant-graviton expansion, first predicted in arXiv:2001.11667 using indirect superconformal algebra considerations and analytic continuation of fugacities. This correction is the leading non-perturbative correction to the index at large N and we reproduce it from the semiclassical partition function of quantum D3 brane wrapped on S1 × S3 in a twisted modification of the AdS5 × S5 string background, depending on the index R-symmetry fugacity. Our calculation does not exploit directly supersymmetry. It is based on the determination of the partition function of the various bosonic and fermionic fluctuations on the wrapped brane whose action is conformal with specific constant holonomies along thermal cycle. We show how those partition functions may be obtained by adapting the operator counting method of Cardy to the twisted background.
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Abreu, Samuel, Harald Ita, Francesco Moriello, Ben Page, Wladimir Tschernow i Mao Zeng. "Two-loop integrals for planar five-point one-mass processes". Journal of High Energy Physics 2020, nr 11 (listopad 2020). http://dx.doi.org/10.1007/jhep11(2020)117.
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Abstract We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at leading color in QCD. We provide a set of pure integrals together with differential equations in canonical form. We obtain analytic differential equations efficiently from numerical samples over finite fields, fitting an ansatz built from symbol letters. The symbol alphabet itself is constructed from cut differential equations and we find that it can be written in a remarkably compact form. We comment on the analytic properties of the integrals and confirm the extended Steinmann relations, which govern the double discontinuities of Feynman integrals, to all orders in ϵ. We solve the differential equations in terms of generalized power series on single-parameter contours in the space of Mandelstam invariants. This form of the solution trivializes the analytic continuation and the integrals can be evaluated in all kinematic regions with arbitrary numerical precision.
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Capizzi, Luca, i Pasquale Calabrese. "Symmetry resolved relative entropies and distances in conformal field theory". Journal of High Energy Physics 2021, nr 10 (październik 2021). http://dx.doi.org/10.1007/jhep10(2021)195.
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Abstract We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory having an internal U(1) symmetry. We provide analytic expressions for the charged moments corresponding to the resolution of both relative entropies and distances for general integer n. For the relative entropies, these formulas are manageable and the analytic continuation to n = 1 can be worked out in most of the cases. Conversely, for the distances the corresponding charged moments become soon untreatable as n increases. A remarkable result is that relative entropies and distances are the same for all symmetry sectors, i.e. they satisfy entanglement equipartition, like the entropies. Moreover, we exploit the OPE expansion of composite twist fields, to provide very general results when the subsystem is a single interval much smaller than the total system. We focus on the massless compact boson and our results are tested against exact numerical calculations in the XX spin chain.
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Wetterich, C. "Pregeometry and spontaneous time-space asymmetry". Journal of High Energy Physics 2022, nr 6 (czerwiec 2022). http://dx.doi.org/10.1007/jhep06(2022)069.
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Abstract In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of a model. For short distances we formulate our model as a Yang-Mills theory with fermions and vector fields. For the local gauge symmetry we take the non-compact group SO(4, ℂ). The particular representation of the vector field permits us to implement diffeomorphism invariant kinetic terms. Geometry and general relativity emerge at large distances due to a spontaneous breaking of the gauge symmetry which induces masses for the gauge bosons. The difference between time and space arises directly from this spontaneous symmetry breaking. For a euclidean metric all fields have a standard propagator at high momenta. Analytic continuation to a Minkowski-metric is achieved by a change of field values. We conjecture that this type of model could be consistent with unitarity and well behaved in the short distance limit.
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Dorigoni, Daniele, i Philip Glass. "The grin of Cheshire cat resurgence from supersymmetric localization". SciPost Physics 4, nr 2 (27.02.2018). http://dx.doi.org/10.21468/scipostphys.4.2.012.
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First we compute the \mbox{S}^2S2 partition function of the supersymmetric \mathbb{CP}^{N-1}ℂℙN−1 model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the \mathbb{CP}^1ℂℙ1 case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instanton-anti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from NN to r\in\mathbb{R}r∈ℝ. Although for generic real rr supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer rr to recover the undeformed model.