Journal articles: 'Gaussian ansatz'

1

Wang, Meng-Jong. "The Gaussian ansatz and beyond." Il Nuovo Cimento A 104, no. 3 (March 1991): 449–52. http://dx.doi.org/10.1007/bf02799149.

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GUPTA, SOURENDU, and A. IRBÄCK. "FINITE SIZE SCALING ON THE ISING COEXISTENCE LINE." International Journal of Modern Physics C 03, no. 05 (October 1992): 1119–24. http://dx.doi.org/10.1142/s0129183192000749.

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We report tests of finite-size scaling ansatzes in the low temperature phase of the two-dimensional Ising model. For moments of the magnetisation density, we find good agreement with the new ansatz of Borgs and Kotecký, and clear evidence of violations of the double Gaussian ansatz. We note that certain consequences of the convexity of the free energy are not adequately treated in either of these approaches.

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Dinda, P. Tchofo, K. Nakkeeran, and A. B. Moubissi. "Optimized Hermite-gaussian ansatz functions for dispersion-managed solitons." Optics Communications 187, no. 4-6 (January 2001): 427–33. http://dx.doi.org/10.1016/s0030-4018(00)01135-4.

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BISWAS, S., A. SHAW, and D. BISWAS. "SCHRÖDINGER–WHEELER–DEWITT EQUATION IN MULTIDIMENSIONAL COSMOLOGY." International Journal of Modern Physics D 10, no. 04 (August 2001): 585–93. http://dx.doi.org/10.1142/s0218271801001372.

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We study multidimensional cosmology to obtain the wavefunction of the universe using wormhole dominance proposal. Using a prescription for time we obtain the Schrödinger–Wheeler–DeWitt equation without any reference to WD equation and WKB ansatz for WD wavefunction. It is found that the Hartle–Hawking or wormhole-dominated boundary conditions serve as a seed for inflation as well as for Gaussian type ansatz to Schrödinger–Wheeler–DeWitt equation.

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BISWAS, S., A. SHAW, and B. MODAK. "TIME IN QUANTUM GRAVITY." International Journal of Modern Physics D 10, no. 04 (August 2001): 595–606. http://dx.doi.org/10.1142/s0218271801001384.

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The Wheeler–DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting from Wheeler–DeWitt equation and WKB ansatz for the WD wavefunction. The approach has some drawbacks. In this work, we obtain the time-contained Schrödinger–Wheeler–DeWitt equation without using the WD equation and the WKB ansatz for the wavefunction. We further show that a Gaussian ansatz for SWD wavefunction is consistent with the Hartle–Hawking or wormhole dominance proposal boundary condition. We thus find an answer to the small scale boundary conditions.

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Preuss, Roland, and Udo von Toussaint. "Outlier-Robust Surrogate Modeling of Ion–Solid Interaction Simulations." Entropy 25, no. 4 (April 19, 2023): 685. http://dx.doi.org/10.3390/e25040685.

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Data for complex plasma–wall interactions require long-running and expensive computer simulations. Furthermore, the number of input parameters is large, which results in low coverage of the (physical) parameter space. Unpredictable occasions of outliers create a need to conduct the exploration of this multi-dimensional space using robust analysis tools. We restate the Gaussian process (GP) method as a Bayesian adaptive exploration method for establishing surrogate surfaces in the variables of interest. On this basis, we expand the analysis by the Student-t process (TP) method in order to improve the robustness of the result with respect to outliers. The most obvious difference between both methods shows up in the marginal likelihood for the hyperparameters of the covariance function, where the TP method features a broader marginal probability distribution in the presence of outliers. Eventually, we provide first investigations, with a mixture likelihood of two Gaussians within a Gaussian process ansatz for describing either outlier or non-outlier behavior. The parameters of the two Gaussians are set such that the mixture likelihood resembles the shape of a Student-t likelihood.

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Wu, Shu-Guang, and Yang Zhang. "The Nonlinear Field Equation of the Three-point Correlation Function of Galaxies: to the Second Order of Density Perturbation." Research in Astronomy and Astrophysics 22, no. 4 (March 31, 2022): 045015. http://dx.doi.org/10.1088/1674-4527/ac55ff.

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Abstract Based on the field theory of density fluctuation under Newtonian gravity, we obtain analytically the nonlinear equation of 3-pt correlation function ζ of galaxies in a homogeneous, isotropic, static universe. The density fluctuation has been kept up to second order. By the Fry–Peebles ansatz and the Groth-Peebles ansatz, the equation of ζ becomes closed and differs from the Gaussian approximate equation. Using the boundary condition inferred from the data of SDSS, we obtain the solution ζ(r, u, θ) at fixed u = 2, which exhibits a shallow U-shape along the angle θ and, nevertheless, decreases monotonously along the radial r. We show its difference with the Gaussian solution. As a direct criterion of non-Gaussianity, the reduced Q(r, u, θ) deviates from the Gaussianity plane Q = 1, exhibits a deeper U-shape along θ and varies weakly along r, agreeing with the observed data.

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Raab, Benedikt, Thomas Srdinko, and Helmut Leeb. "Formulation of Model Defects Suitable for the Resonance Regime." EPJ Web of Conferences 211 (2019): 07006. http://dx.doi.org/10.1051/epjconf/201921107006.

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A method to account for model deficiencies in nuclear data evaluations in the resonance regime is proposed. The method follows the ideas of Schnabel and coworkers and relies on Gaussian processes with a novel problemadapted ansatz for the covariance matrix of model uncertainties extending the formalism to the energy region of resonances. The method was used to evaluate a set of schematic but realistic neutron reaction data generated by an R-matrix code and a well defined model defect. Using the extended ansatz for model defects the Bayesian evaluation successfully recovered the built-in model defect in size and structure thus demonstrating the applicability of the method.

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Darewych, J. W., and A. D. Polozov. "Variational solution of bound states in a charged interacting scalar-field theory." Canadian Journal of Physics 66, no. 11 (November 1, 1988): 969–71. http://dx.doi.org/10.1139/p88-155.

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Two interacting [Formula: see text] scalar fields in N spatial dimensions are investigated using the Gaussian variational approximation. The interaction is taken to be in the form [Formula: see text]. Two-particle bound-state solutions are obtained in the domain g < 2λ for N = 1 and 2. The nonrelativistic limit, which is also the weak-coupling limit, is shown to correspond to an attractive delta-function interaction. For N = 3, the Gaussian ansatz suggests triviality of the theory, in that the renormalized coupling constant is identically zero.

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PERCUS, J. K. "INTERFACE STRUCTURE." International Journal of Modern Physics B 13, no. 05n06 (March 10, 1999): 659–66. http://dx.doi.org/10.1142/s0217979299000552.

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Phase-separated fluids are analyzed from several viewpoints: local thermodynamic, in which all density correlations are ignored; mean field, which correctly treats those at medium range; and a modified Kac-Siegert form which only coarse-grains those at short range. The last form appears as an ensemble average over tail potential fields, and is treated variationally with a Gaussian ansatz. Application to a planar interface shows the anticipated surface softening as any confining field is removed, and in statistically homogeneous condensation, a form of the familiar level set description assumes relevance. Suggestions are made as to removing the Gaussian assumption.

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Leone, Lorenzo, Salvatore F. E. Oliviero, Lukasz Cincio, and M. Cerezo. "On the practical usefulness of the Hardware Efficient Ansatz." Quantum 8 (July 3, 2024): 1395. http://dx.doi.org/10.22331/q-2024-07-03-1395.

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Variational Quantum Algorithms (VQAs) and Quantum Machine Learning (QML) models train a parametrized quantum circuit to solve a given learning task. The success of these algorithms greatly hinges on appropriately choosing an ansatz for the quantum circuit. Perhaps one of the most famous ansatzes is the one-dimensional layered Hardware Efficient Ansatz (HEA), which seeks to minimize the effect of hardware noise by using native gates and connectives. The use of this HEA has generated a certain ambivalence arising from the fact that while it suffers from barren plateaus at long depths, it can also avoid them at shallow ones. In this work, we attempt to determine whether one should, or should not, use a HEA. We rigorously identify scenarios where shallow HEAs should likely be avoided (e.g., VQA or QML tasks with data satisfying a volume law of entanglement). More importantly, we identify a Goldilocks scenario where shallow HEAs could achieve a quantum speedup: QML tasks with data satisfying an area law of entanglement. We provide examples for such scenario (such as Gaussian diagonal ensemble random Hamiltonian discrimination), and we show that in these cases a shallow HEA is always trainable and that there exists an anti-concentration of loss function values. Our work highlights the crucial role that input states play in the trainability of a parametrized quantum circuit, a phenomenon that is verified in our numerics.

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BARAN, A., A. STASZCZAK, J. DOBACZEWSKI, and W. NAZAREWICZ. "COLLECTIVE INERTIA AND FISSION BARRIERS WITHIN THE SKYRME-HARTREE-FOCK THEORY." International Journal of Modern Physics E 16, no. 02 (February 2007): 443–51. http://dx.doi.org/10.1142/s0218301307005879.

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Spontaneous fission barriers, quadrupole inertia tensor, and zero-point quadrupole correlation energy are calculated for 252,256,258 Fm in the framework of the self-consistent Skyrme-Hartree-Fock+BCS theory. Two ways of computing collective inertia are employed: the Gaussian Overlap Approximation to the Generator Coordinate Method and cranking ansatz. The Skyrme results are compared with those of the Gogny-Hartree-Fock-Bogolyubov model.

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Wai, P. K. A., and K. Nakkeeran. "On the uniqueness of Gaussian ansatz parameters equations: generalized projection operator method." Physics Letters A 332, no. 3-4 (November 2004): 239–43. http://dx.doi.org/10.1016/j.physleta.2004.09.075.

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Iacob, Theodor-Felix, Marina Lute, and Felix Iacob. "A Numerical Approach for the Solution of Schrödinger Equation With Pseudo-Gaussian Potentials." Annals of West University of Timisoara - Physics 58, no. 1 (December 1, 2015): 1–6. http://dx.doi.org/10.1515/awutp-2015-0201.

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Abstract The Schrödinger equation with pseudo-Gaussian potential is investigated. The pseudo-Gaussian potential can be written as an infinite power series. Technically, by an ansatz to the wave-functions, exact solutions can be found by analytic approach [12]. However, to calculate the solutions for each state, a condition that will stop the series has to be introduced. In this way the calculated energy values may suffer modifications by imposing the convergence of series. Our presentation, based on numerical methods, is to compare the results with those obtained in the analytic case and to determine if the results are stable under different stopping conditions.

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Dai, J., and R. V. Krems. "Quantum Gaussian process model of potential energy surface for a polyatomic molecule." Journal of Chemical Physics 156, no. 18 (May 14, 2022): 184802. http://dx.doi.org/10.1063/5.0088821.

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With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PESs in the energy domain.

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Boulougouris, Georgios C. "Free energy calculations, enhanced by a gaussian ansatz, for the “chemical work” distribution." Journal of Computational Chemistry 35, no. 13 (March 24, 2014): 1024–35. http://dx.doi.org/10.1002/jcc.23590.

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Aydogmus, Fatma. "Numeric Solutions of Dirac–Gursey Spinor Field Equation Under External Gaussian White Noise." Fluctuation and Noise Letters 15, no. 02 (June 2016): 1650018. http://dx.doi.org/10.1142/s0219477516500188.

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In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.

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Spychala, Kai J., Zeeshan H. Amber, Lukas M. Eng, and Michael Ruesing. "Modeling nonlinear optical interactions of focused beams in bulk crystals and thin films: A phenomenological approach." Journal of Applied Physics 133, no. 12 (March 28, 2023): 123105. http://dx.doi.org/10.1063/5.0136252.

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Coherent nonlinear optical [Formula: see text]-spectroscopy is a frequently used tool in modern material science as it is sensitive to many different local observables, which comprise, among others, crystal symmetry and vibrational properties. The richness in information, however, may come with challenges in data interpretation, as one has to disentangle the many different effects like multiple reflections, phase jumps at interfaces, or the influence of the Guoy-phase. In order to facilitate interpretation, the work presented here proposes an easy-to-use semi-analytical modeling Ansatz, which bases upon known analytical solutions using Gaussian beams. Specifically, we apply this Ansatz to compute nonlinear optical responses of (thin film) optical materials. We try to conserve the meaning of intuitive parameters like the Gouy-phase and the nonlinear coherent interaction length. In particular, the concept of coherence length is extended, which is a must when using focal beams. The model is subsequently applied to exemplary cases of second- and third-harmonic generation. We observe a very good agreement with experimental data, and furthermore, despite the constraints and limits of the analytical Ansatz, our model performs similarly well as when using more rigorous simulations. However, it outperforms the latter in terms of computational power, requiring more than three orders less computational time and less performant computer systems.

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Rusin, Rahmi, Rudy Kusdiantara, and Hadi Susanto. "Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schrödinger lattices." Journal of Physics A: Mathematical and Theoretical 51, no. 47 (October 31, 2018): 475202. http://dx.doi.org/10.1088/1751-8121/aae4be.

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Wang, Hui, and Tian-Tian Zhang. "Stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 3 (March 4, 2019): 878–89. http://dx.doi.org/10.1108/hff-08-2018-0448.

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Purpose The purpose of this paper is to study stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms, which can be used to describe the propagation properties of optical soliton solutions. Design/methodology/approach The authors apply the ansatz method and the Hamiltonian system technique to find its bright, dark and Gaussian wave solitons and analyze its modulation instability analysis and stability analysis solution. Findings The results imply that the generalized nonlinear Schrödinger equation has bright, dark and Gaussian wave solitons. Meanwhile, the authors provide the graphical analysis of such solutions to better understand their dynamical behavior. Some constraint conditions are provided which can guarantee the existence of solitons. The authors analyze its modulation instability analysis and stability analysis solution. Originality/value These results may help us to further study the local structure and the interaction of solutions in generalized nonlinear Schrödinger -type equations. The authors hope that the results provided in this work can help enrich the dynamic behavior of the generalized nonlinear Schrödinger--type equations.

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Barna, Imre F., Gabriella Bognár, Mohammed Guedda, László Mátyás, and Krisztián Hriczó. "ANALYTIC SELF-SIMILAR SOLUTIONS OF THE KARDAR-PARISI-ZHANG INTERFACE GROWING EQUATION WITH VARIOUS NOISE TERMS." Mathematical Modelling and Analysis 25, no. 2 (March 18, 2020): 241–56. http://dx.doi.org/10.3846/mma.2020.10459.

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The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the self-similar ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as various noise distribution functions. Six different cases were investigated among others Gaussian, Lorentzian, white or even pink noise. Analytic solutions are evaluated and analyzed for all cases. All results are expressible with various special functions like Kummer, Heun, Whittaker or error functions showing a very rich mathematical structure with some common general characteristics.

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YAMAGUCHI, SATOSHI. "BUBBLING GEOMETRIES FOR HALF-BPS WILSON LINES." International Journal of Modern Physics A 22, no. 07 (March 20, 2007): 1353–74. http://dx.doi.org/10.1142/s0217751x07035070.

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We consider the supergravity backgrounds that correspond to supersymmetric Wilson line operators in the context of AdS/CFT correspondence. We study the gravitino and dilatino conditions of the IIB supergravity under the appropriate ansatz, and obtain some necessary conditions for a supergravity background that preserves the same symmetry as the supersymmetric Wilson lines. The supergravity solutions are characterized by continuous version of Maya diagrams. This diagram is related to the eigenvalue distribution of the Gaussian matrix model. We also consider the similar backgrounds of the 11-dimensional supergravity.

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Ruban, V. P. "Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation." Journal of Experimental and Theoretical Physics 120, no. 5 (May 2015): 925–32. http://dx.doi.org/10.1134/s1063776115050179.

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Sattary Nikkhoo, Negin, and Mohammad Reza Shojaei. "Electromagnetic and gravitational form factors by using the modified Gaussian ansatz for Hq(x,t)." Nuclear Physics A 969 (January 2018): 138–50. http://dx.doi.org/10.1016/j.nuclphysa.2017.09.010.

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Putra, Gusrian, Hanifah Septaningtiyas, Elsa Nabila, and Lisa Arianti Br Tarigan. "Analisis Kestabilan Solusi Soliton pada Persamaan Schrodinger Nonlinier Diskrit Nonlokal." Indonesian Journal of Applied Mathematics 2, no. 1 (April 15, 2022): 17. http://dx.doi.org/10.35472/indojam.v2i1.730.

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In this paper, the Nonlocal Discrete Nonlinear Schrodinger (DNLS) equation that interpolates the Nonlocal Ablowitz-Ladik DNLS and the Nonlocal Cubic DNLS equations and its stability are studied in detail. The solution of the Nonlocal SNLD equation is a soliton wave in the form of a Gaussian ansatz obtained using the method of Variational Approximation (VA). The stability of the solution is also analyzed using the VA. These semi-analytical results are then compared to numerical results. The soliton and its stability obtained via VA is concluded to be having a fairly good conformity with numerical results.

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ANTONOV, D. V. "AN EXACT SOLUTION OF THE LOOP EQUATION IN STRONG TURBULENCE." Modern Physics Letters A 11, no. 39n40 (December 28, 1996): 3113–18. http://dx.doi.org/10.1142/s021773239600309x.

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The Hamilton–Jacobi equation for the loop effective action in strong turbulence with Gaussian random forces1,2 is solved by making use of the smearing procedure for the loop space functional Laplacian, proposed in Ref. 3. The solution obtained satisfies tensor- or scalar area law ansatz and depends on the initial data and the potential term in the loop Hamiltonian, averaged over loops. In the lowest order in the viscosity this average may be eliminated, and the solution is given by a certain linear combination of the initial data and the potential term and their functional derivatives.

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Nse Biyoghe, S., Th B. Ekogo, and A. B. Moubissi. "Collective variable analysis of the nonlinear Schrödinger equation for soliton molecules in fibers." Journal of Nonlinear Optical Physics & Materials 26, no. 02 (June 2017): 1750023. http://dx.doi.org/10.1142/s0218863517500230.

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We present a description of soliton molecules in terms of its collective variables namely temporal separation between two consecutive pulses, peak-power of each pulse, center-of-mass, chirp, frequency and phase of the whole molecule. Assuming the Hermite–Gaussian ansatz to represent the temporal profile of the molecule, we derive a set of six differential equations for the evolution of the collective variables in the limit of the bare or variational approximation. Then we perform numerical experiments to confirm the ability of the proposed approach for two-soliton molecule propagating along a Dispersion-managed fiber for anomalous, zero or normal averaged dispersion.

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Mardonov, Shukhrat N., and Bobomurat J. Ahmedov. "Rabi Frequency Management of Collapsing Quasi-Two-Dimensional Bose-Einstein Condensates with Pseudospin-1/2." Particles 5, no. 2 (April 28, 2022): 135–45. http://dx.doi.org/10.3390/particles5020012.

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The collapse of quasi-two-dimensional pseudospin-1/2 Bose-Einstein condensate of attracting atoms with intra- and cross-spin interaction is studied in the presence of the Rabi coupling. The condensate dynamics is presented as a function of the self-interaction and Rabi frequency. The evolution of two components of the condensate by using the Gross-Pitaevskii equations is investigated. The initial Gaussian ansatz for two-component wave functions is selected for the better interpretation of the numerical results. The intra-spin-coupling modifies the critical number of atoms causing the collapse while the collapse is observed only in a single pseudospin component. It is demonstrated that for cross-spin-coupling only double spin-components collapse can occur.

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DE AVELLAR, MARCIO G. B., and J. E. HORVATH. "EXACT AND QUASI-EXACT MODELS OF STRANGE STARS." International Journal of Modern Physics D 19, no. 12 (October 2010): 1937–55. http://dx.doi.org/10.1142/s0218271810018128.

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We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

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Piela, Lucjan. "Search for the Most Stable Structures on Potential Energy Surfaces." Collection of Czechoslovak Chemical Communications 63, no. 9 (1998): 1368–80. http://dx.doi.org/10.1135/cccc19981368.

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Smoothing techniques for global optimization in search for the most stable structures (clusters or conformers) have been a novel possibility for the last decade. The techniques turned out to be related to a variety of fundamental laws: Fick's diffusion equation, time-dependent and time-independent Schrodinger equations, Smoluchowski dynamics equation, Bloch equation of canonical ensemble evolution with temperature, Gibbs free-energy principle. The progress indicator of global optimization in those methods takes different physical meanings: time, imaginary time, Planck constant, or the inverse absolute temperature. Despite this large spectrum of physical phenomena, the resulting global optimization procedures have a remarkable common feature. In the case of the Gaussian Ansatz for the wave function or density distribution, the underlying differential equations of motion for the Gaussian position and width are similar for all these phenomena. In all techniques the smoothed potential energy function plays a central role rather than the potential energy function itself. The smoothed potential results from a Gaussian convolution or filtering out high frequency Fourier components of the original potential energy function. During the minimization, the Gaussian position moves according to the negative gradient of the smoothed potential energy function. The Gaussian width is position dependent through the curvature of the potential energy function, and evolves according to the following rule. For sufficiently positive curvatures (close to minima of the smoothed potential) the width decreases, thus leading to a smoothed potential approaching the original potential energy function, while for negative curvatures (close to maxima) the width increases leading eventually to the disappearance of humps of the original potential energy function. This allows for crossing barriers separating the energy basins. Some methods result in an additional term, which increases the width, when the potential becomes flat. This may be described as a feature allowing hunting for distant minima.

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Çakmak, Burak, Yue M. Lu, and Manfred Opper. "Analysis of random sequential message passing algorithms for approximate inference." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 7 (July 1, 2022): 073401. http://dx.doi.org/10.1088/1742-5468/ac764a.

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Abstract We analyze the dynamics of a random sequential message passing algorithm for approximate inference with large Gaussian latent variable models in a student–teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices drawn from rotation invariant ensembles. Moreover, we consider a model mismatching setting, where the teacher model and the one used by the student may be different. By means of dynamical functional approach, we obtain exact dynamical mean-field equations characterizing the dynamics of the inference algorithm. We also derive a range of model parameters for which the sequential algorithm does not converge. The boundary of this parameter range coincides with the de Almeida Thouless (AT) stability condition of the replica-symmetric ansatz for the static probabilistic model.

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Song, Yu-Kun. "Azimuthal Asymmetries for eA/eN Semi-Inclusive DIS and Its Nuclear Dependence." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660036. http://dx.doi.org/10.1142/s2010194516600363.

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We applied collinear expansion to the semi-inclusive deeply inelastic lepton-nucleon (nucleus) scattering process [Formula: see text] with both polarized beam and polarized target up to twist-3, and unpolarized process up to twist-4. The differential cross section and azimuthal asymmetries are expressed in terms of gauge invariant twist-3 and twist-4 TMD parton distribution/correlation functions. Measurements of such azimuthal asymmetries provide methods to study different spin and transverse momentum aspects of the partonic structure of nucleon. We further study the nuclear dependence of azimuthal asymmetries and adopt Gaussian ansatz for TMD distribution/correlation functions to estimat the semi-quantitive behaviour of the nuclear dependence. We predict the A-dependence of azimuthal asymmetries which can be tested in the planned EIC’s.

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Prestipino, Santi, Alessandro Sergi, Ezio Bruno, and Paolo V. Giaquinta. "A variational mean-field study of clusterization in a zero-temperature system of soft-core bosons." EPJ Web of Conferences 230 (2020): 00008. http://dx.doi.org/10.1051/epjconf/202023000008.

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We work out the ground-state diagram of weakly-repulsive penetrable bosons, using mean-field theory with a Gaussian ansatz on the single-particle wave function. Upon compression, the fluid transforms into a cluster supersolid, whose structure is characterized for various choices of the embedding space. In Euclidean space, the stable crystals are those with the most compact structure, i.e., triangular and fcc in two and three dimensions, respectively. For particles confined in a spherical surface, as the sphere radius increases we observe a sequence of transitions between different cluster phases, all having a regular or semiregular polyhedron as supporting frame for the clusters. The present results are relevant for the behavior of ultracold bosons weakly coupled to a Rydberg state.

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Kadam, Guru Prakash. "Transport properties of hadronic matter in magnetic field." Modern Physics Letters A 30, no. 10 (March 25, 2015): 1550031. http://dx.doi.org/10.1142/s0217732315500315.

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We study the effect of magnetic field on the transport properties like shear and bulk viscosities of hot and dense hadronic matter within hadron resonance gas model. We estimate the bulk viscosity using low energy theorems for bilocal correlators of the energy–momentum tensor generalized to finite temperature, density and magnetic field. We use Gaussian ansatz for the spectral function at low frequency. We estimate shear viscosity coefficient using molecular kinetic theory. We find that vacuum contribution due to finite magnetic field dominates the bulk viscosity (ζ) for the temperatures up to 0.1 GeV and increases with magnetic field while ratio ζ/s decreases with magnetic field. We also find that shear viscosity coefficient of hadronic matter decreases with magnetic field.

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ABOBAKER, ABDOSLLAM M., A. B. MOUBISSI, TH B. EKOGO, and K. NAKKEERAN. "ANALYTICAL SOLUTIONS FOR THE VARIATIONAL EQUATIONS DERIVED FOR THE NONLINEAR SCHRÖDINGER EQUATION: DISPERSION-MANAGED FIBER SYSTEM." Journal of Nonlinear Optical Physics & Materials 17, no. 03 (September 2008): 285–97. http://dx.doi.org/10.1142/s0218863508004226.

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We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse, we derive the variational equations. For a particular case of DM fiber systems when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses, we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

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Campa, Alessandro. "The study of the dynamics of the order parameter of coupled oscillators in the Ott–Antonsen scheme for generic frequency distributions." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 8 (August 2022): 083104. http://dx.doi.org/10.1063/5.0093577.

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The Ott–Antonsen ansatz shows that, for certain classes of distribution of the natural frequencies in systems of [Formula: see text] globally coupled Kuramoto oscillators, the dynamics of the order parameter, in the limit [Formula: see text], evolves, under suitable initial conditions, in a manifold of low dimension. This is not possible when the frequency distribution, continued in the complex plane, has an essential singularity at infinity; this is the case, for example, of a Gaussian distribution. In this work, we propose a simple approximation scheme that allows one to extend also to this case the representation of the dynamics of the order parameter in a low dimensional manifold. Using the Gaussian frequency distribution as a working example, we compare the dynamical evolution of the order parameter of the system of oscillators, obtained by the numerical integration of the [Formula: see text] equations of motion, with the analogous dynamics in the low dimensional manifold obtained with the application of the approximation scheme. The results confirm the validity of the approximation. The method could be employed for general frequency distributions, allowing the determination of the corresponding phase diagram of the oscillator system.

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Convy, Ian, William Huggins, Haoran Liao, and K. Birgitta Whaley. "Mutual information scaling for tensor network machine learning." Machine Learning: Science and Technology 3, no. 1 (January 20, 2022): 015017. http://dx.doi.org/10.1088/2632-2153/ac44a9.

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Abstract Tensor networks have emerged as promising tools for machine learning, inspired by their widespread use as variational ansatze in quantum many-body physics. It is well known that the success of a given tensor network ansatz depends in part on how well it can reproduce the underlying entanglement structure of the target state, with different network designs favoring different scaling patterns. We demonstrate here how a related correlation analysis can be applied to tensor network machine learning, and explore whether classical data possess correlation scaling patterns similar to those found in quantum states, which might indicate the best network to use for a given dataset. We utilize mutual information (MI) as measure of correlations in classical data, and show that it can serve as a lower-bound on the entanglement needed for a probabilistic tensor network classifier. We then develop a logistic regression algorithm to estimate the MI between bipartitions of data features, and verify its accuracy on a set of Gaussian distributions designed to mimic different correlation patterns. Using this algorithm, we characterize the scaling patterns in the Modified National Institute of Standards and Technology and Tiny Images datasets, and find clear evidence of boundary-law scaling in the latter. This quantum-inspired classical analysis offers insight into the design of tensor networks that are best suited for specific learning tasks.

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De, Bitan, Piotr Sierant, and Jakub Zakrzewski. "On intermediate statistics across many-body localization transition." Journal of Physics A: Mathematical and Theoretical 55, no. 1 (December 3, 2021): 014001. http://dx.doi.org/10.1088/1751-8121/ac39cd.

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Abstract The level statistics in the transition between delocalized and localized phases of many body interacting systems is considered. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically via Monte Carlo method. The resulting higher order spacing ratios are compared with data coming from different quantum many body systems. It is found that this Pechukas–Yukawa distribution compares favorably with β–Gaussian ensemble—a single parameter model of level statistics proposed recently in the context of disordered many-body systems. Moreover, the Pechukas–Yukawa distribution is also only slightly inferior to the two-parameter β–h ansatz shown earlier to reproduce level statistics of physical systems remarkably well.

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Wang, Guoming, Sukin Sim, and Peter D. Johnson. "State Preparation Boosters for Early Fault-Tolerant Quantum Computation." Quantum 6 (October 6, 2022): 829. http://dx.doi.org/10.22331/q-2022-10-06-829.

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Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum algorithms for quantum simulation, including VQE and many of its variants. However, for such algorithms to be useful, they need to overcome several critical barriers including the inability to prepare high-quality approximations of the ground state. Current challenges to state preparation, including barren plateaus and the high-dimensionality of the optimization landscape, make state preparation through ansatz optimization unreliable. In this work, we introduce the method of ground state boosting, which uses a limited-depth quantum circuit to reliably increase the overlap with the ground state. This circuit, which we call a booster, can be used to augment an ansatz from VQE or be used as a stand-alone state preparation method. The booster converts circuit depth into ground state overlap in a controllable manner. We numerically demonstrate the capabilities of boosters by simulating the performance of a particular type of booster, namely the Gaussian booster, for preparing the ground state of N2 molecular system. Beyond ground state preparation as a direct objective, many quantum algorithms, such as quantum phase estimation, rely on high-quality state preparation as a subroutine. Therefore, we foresee ground state boosting and similar methods as becoming essential algorithmic components as the field transitions into using early fault-tolerant quantum computers.

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Seo, Sambu, and Klaus Obermayer. "Soft Learning Vector Quantization." Neural Computation 15, no. 7 (July 1, 2003): 1589–604. http://dx.doi.org/10.1162/089976603321891819.

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Learning vector quantization (LVQ) is a popular class of adaptive nearest prototype classifiers for multiclass classification, but learning algorithms from this family have so far been proposed on heuristic grounds. Here, we take a more principled approach and derive two variants of LVQ using a gaussian mixture ansatz. We propose an objective function based on a likelihood ratio and derive a learning rule using gradient descent. The new approach provides a way to extend the algorithms of the LVQ family to different distance measure and allows for the design of “soft” LVQ algorithms. Benchmark results show that the new methods lead to better classification performance than LVQ 2.1. An additional benefit of the new method is that model assumptions are made explicit, so that the method can be adapted more easily to different kinds of problems.

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Singh, Sudhir, R. Sakthivel, M. Inc, A. Yusuf, and K. Murugesan. "Dynamics of optical solitons and conservation laws of a new (2+1)-dimensional integrable nonlinear evolution equation in deep water oceanic waves." Modern Physics Letters B 34, no. 05 (January 2, 2020): 2050068. http://dx.doi.org/10.1142/s0217984920500682.

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An integrable extension of the famous Schrödinger equation in (2[Formula: see text]+[Formula: see text]1) dimension, named Kundu–Mukherjee–Naskar (KMN) equation, governing the evolution of ion-acoustic wave in magnetized plasma and oceanic rogue waves is considered, and dark/black as well as gray optical soliton solutions are constructed by using a complex envelope ansatz approach with appropriate conditions for the existence of solitons. Also, a new class of combined gray and black optical soliton solutions is obtained by applying Chupin Liu’s theorem, and it is found to be anti-dark solitons. Additionally, Gaussian wave solutions are derived. Further, the investigation of symmetry analysis, nonlinear self-adjointness and conservation laws (Cls) for the KMN equation are carried out. These results further enrich and deepen the understanding of the dynamics of a higher-dimensional soliton propagation.

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Lasar, Christian, and Thorsten Klüner. "Explicitly correlated orbital optimized contracted pair correlation methods: Foundations and applications." Journal of Theoretical and Computational Chemistry 17, no. 04 (June 2018): 1850024. http://dx.doi.org/10.1142/s0219633618500244.

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Pair correlation methods are able to achieve highly accurate solutions for chemical problems. Unfortunately, their applicability is generally restricted to medium-sized molecules due to storage requirements and computational costs. These restrictions can be partly overcome by local correlation methods. These methods use physical and mathematical criteria to decide which interactions are of such a long range that they do not have to be computed and saved. In our new ansatz, we define an alternative way towards local correlation. The range of interactions is strictly bound to the decay of integrals over Gaussian type geminals in the atomic orbital basis. The number of variables is reduced by orders of magnitude applying an efficient contraction scheme, leading to a naturally local representation of correlation effects. This scheme is extended by orbital optimization to describe multi-reference problems and explicit correlation to improve the basis set convergence.

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Sarkar, Mrinal, and Shamik Gupta. "Synchronization in the Kuramoto model in presence of stochastic resetting." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (July 2022): 073109. http://dx.doi.org/10.1063/5.0090861.

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What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated interruptions of its dynamics with a reset to the initial condition? While resetting to a synchronized state, it may happen between two successive resets that the system desynchronizes, which depends on the duration of the random time interval between the two resets. Here, we unveil how such a protocol of stochastic resetting dramatically modifies the phase diagram of the bare model, allowing, in particular, for the emergence of a synchronized phase even in parameter regimes for which the bare model does not support such a phase. Our results are based on an exact analysis invoking the celebrated Ott–Antonsen ansatz for the case of the Lorentzian distribution of natural frequencies and numerical results for Gaussian frequency distribution. Our work provides a simple protocol to induce global synchrony in the system through stochastic resetting.

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Jahn, A., M. Gluza, F. Pastawski, and J. Eisert. "Holography and criticality in matchgate tensor networks." Science Advances 5, no. 8 (August 2019): eaaw0092. http://dx.doi.org/10.1126/sciadv.aaw0092.

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The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand these bulk-boundary correspondences, shedding light on connections between geometry and entanglement. We introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1 + 1 dimensions. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk lattices, obtaining highly accurate critical data. Within our framework, we also produce translation-invariant critical states by an efficiently contractible tensor network with the geometry of the multiscale entanglement renormalization ansatz. Furthermore, we establish a link between holographic quantum error–correcting codes and tensor networks. This work is expected to stimulate a more comprehensive study of tensor network models capturing bulk-boundary correspondences.

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MENGESHA, ELIAS, and SHASHANK BHATNAGAR. "RADIATIVE DECAYS OF EQUAL MASS VECTOR MESONS IN A BETHE–SALPETER EQUATION FRAMEWORK." International Journal of Modern Physics E 21, no. 10 (October 2012): 1250084. http://dx.doi.org/10.1142/s021830131250084x.

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In this work, we have employed Bethe–Salpeter equation (BSE) under Covariant Instantaneous Ansatz (CIA) to study radiative decays of light vector mesons through the process: h→h'γ, taking h and h' as equal mass light vector and pseudoscalar mesons, respectively. The decay widths calculated for these processes are in reasonable agreement with data. The motivation for this work was our intention to resolve the problems involved in calculations of triangle quark-loop diagrams which appear in processes such as radiative meson decays, meson form factors, strong decays of mesons, etc., in BSE under CIA, which give rise to complexities in amplitudes (as pointed out earlier in Ref. 1) due to the presence of the time-like momentum components in Gaussian factors associated with the vertex functions of the participating hadrons. In this work we try to highlight this problem and then demonstrate a mathematical procedure which might lead to calculations of such processes in BSE under CIA.

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EMRAN, M. S., and J. SCHUMACHER. "Fine-scale statistics of temperature and its derivatives in convective turbulence." Journal of Fluid Mechanics 611 (September 25, 2008): 13–34. http://dx.doi.org/10.1017/s0022112008002954.

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We study the fine-scale statistics of temperature and its derivatives in turbulent Rayleigh–Bénard convection. Direct numerical simulations are carried out in a cylindrical cell with unit aspect ratio filled with a fluid with Prandtl number equal to 0.7 for Rayleigh numbers between 107 and 109. The probability density function of the temperature or its fluctuations is found to be always non-Gaussian. The asymmetry and strength of deviations from the Gaussian distribution are quantified as a function of the cell height. The deviations of the temperature fluctuations from the local isotropy, as measured by the skewness of the vertical derivative of the temperature fluctuations, decrease in the bulk, but increase in the thermal boundary layer for growing Rayleigh number, respectively. Similarly to the passive scalar mixing, the probability density function of the thermal dissipation rate deviates significantly from a log-normal distribution. The distribution is fitted well by a stretched exponential form. The tails become more extended with increasing Rayleigh number which displays an increasing degree of small-scale intermittency of the thermal dissipation field for both the bulk and the thermal boundary layer. We find that the thermal dissipation rate due to the temperature fluctuations is not only dominant in the bulk of the convection cell, but also yields a significant contribution to the total thermal dissipation in the thermal boundary layer. This is in contrast to the ansatz used in scaling theories and can explain the differences in the scaling of the total thermal dissipation rate with respect to the Rayleigh number.

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Manzhos, Sergei, and Manabu Ihara. "Advanced Machine Learning Methods for Learning from Sparse Data in High-Dimensional Spaces: A Perspective on Uses in the Upstream of Development of Novel Energy Technologies." Physchem 2, no. 2 (March 29, 2022): 72–95. http://dx.doi.org/10.3390/physchem2020006.

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Machine learning (ML) has found increasing use in physical sciences, including research on energy conversion and storage technologies, in particular, so-called sustainable technologies. While often ML is used to directly optimize the parameters or phenomena of interest in the space of features, in this perspective, we focus on using ML to construct objects and methods that help in or enable the modeling of the underlying phenomena. We highlight the need for machine learning from very sparse and unevenly distributed numeric data in multidimensional spaces in these applications. After a brief introduction of some common regression-type machine learning techniques, we focus on more advanced ML techniques which use these known methods as building blocks of more complex schemes and thereby allow working with extremely sparse data and also allow generating insight. Specifically, we will highlight the utility of using representations with subdimensional functions by combining the high-dimensional model representation ansatz with machine learning methods such as neural networks or Gaussian process regressions in applications ranging from heterogeneous catalysis to nuclear energy.

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BOONSERM, PETARPA, and MATT VISSER. "BUCHDAHL-LIKE TRANSFORMATIONS FOR PERFECT FLUID SPHERES." International Journal of Modern Physics D 17, no. 01 (January 2008): 135–63. http://dx.doi.org/10.1142/s0218271808011912.

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In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007) and Phys. Rev. D76 (2006) 0440241 (gr-qc/0607001)] we have discussed several "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general-relativistic static perfect fluid spheres. Working in Schwarzschild curvature coordinates, we used these algorithmic ideas to prove several "solution-generating theorems" of varying levels of complexity. In the present article we consider the situation in other coordinate systems. In particular, in general diagonal coordinates we shall generalize our previous theorems, in isotropic coordinates we shall encounter a variant of the so-called "Buchdahl transformation," and in other coordinate systems (such as Gaussian polar coordinates, Synge isothermal coordinates, and Buchdahl coordinates) we shall find a number of more complex "Buchdahl-like transformations" and "solution-generating theorems" that may be used to investigate and classify the general-relativistic static perfect fluid sphere. Finally, by returning to general diagonal coordinates and making a suitable ansatz for the functional form of the metric components, we place the Buchdahl transformation in its most general possible setting.

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Mamis, K. I., G. A. Athanassoulis, and Z. G. Kapelonis. "A systematic path to non-Markovian dynamics: new response probability density function evolution equations under Gaussian coloured noise excitation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2226 (June 2019): 20180837. http://dx.doi.org/10.1098/rspa.2018.0837.

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Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic dynamics, advanced statistical physics and uncertainty quantification of macroscopic systems. In the present work, such equations are derived for a scalar, nonlinear RDE under additive coloured Gaussian noise excitation, through the stochastic Liouville equation. The latter is an exact, yet non-closed equation, involving averages over the time history of the non-Markovian response. This non-locality is treated by applying an extension of the Novikov–Furutsu theorem and a novel approximation, employing a stochastic Volterra–Taylor functional expansion around instantaneous response moments, leading to efficient, closed, approximate equations for the response pdf. These equations retain a tractable amount of non-locality and nonlinearity, and they are valid in both the transient and long-time regimes for any correlation function of the excitation. Also, they include as special cases various existing relevant models, and generalize Hänggi's ansatz in a rational way. Numerical results for a bistable nonlinear RDE confirm the accuracy and the efficiency of the new equations. Extension to the multidimensional case (systems of RDEs) is feasible, yet laborious.

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Tsuchida, Satoshi, and Hiroshi Kuratsuji. "Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation." International Journal of Modern Physics B 32, no. 12 (May 3, 2018): 1850147. http://dx.doi.org/10.1142/s0217979218501473.

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A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker–Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

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Journal articles on the topic 'Gaussian ansatz'

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