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Journal articles on the topic 'Pfaffian structure'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Mizusaki, Takahiro, and Peter Schuck. "Alpha correlations in terms of the hyper-Pfaffian." EPJ Web of Conferences 223 (2019): 01040. http://dx.doi.org/10.1051/epjconf/201922301040.

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We find that the overlap between alpha-like four-body condensation wave function and m-scheme basis state can be represented by the hyper-Pfaffian, which is a natural extension of the Pfaffian for thepair-condensation wave function. This overlap is useful for nuclear structure calculations with the variational Monte Carlo method. As the hyper-Pfaffian has, however, only a few mathematical relations, it is quite difficult to use for numerical computations. We also find that a specific case of hyper-Pfaffian can be expressed by the sum of standard Pfaffians.

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2

Xie, Xi-Yang, Bo Tian, Wen-Rong Sun, and Yun-Po Wang. "Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids." Zeitschrift für Naturforschung A 71, no. 4 (2016): 337–43. http://dx.doi.org/10.1515/zna-2015-0490.

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AbstractIn this article, the prolongation structure technique is applied to a generalised inhomogeneous Gardner equation, which can be used to describe certain physical situations, such as the stratified shear flows in ocean and atmosphere, ion acoustic waves in plasmas with a negative ion, interfacial solitary waves over slowly varying topographies, and wave motion in a non-linear elastic structural element with large deflection. The Lax pairs, which are derived via the prolongation structure, are more general than the Lax pairs published before. Under the Painlevé conditions, the linear-damp

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3

Speissegger, Patrick. "The Pfaffian closure of an o-minimal structure." Journal für die reine und angewandte Mathematik (Crelles Journal) 1999, no. 508 (1999): 189–211. http://dx.doi.org/10.1515/crll.1999.508.189.

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4

Miller, Chris, and Patrick Speissegger. "Pfaffian differential equations over exponential o-minimal structures." Journal of Symbolic Logic 67, no. 1 (2002): 438–48. http://dx.doi.org/10.2178/jsl/1190150053.

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In this paper, we continue investigations into the asymptotic behavior of solutions of differential equations over o-minimal structures.Let ℜ be an expansion of the real field (ℝ, +, ·).A differentiable map F = (F1,…, F1): (a, b) → ℝi is ℜ-Pfaffian if there exists G: ℝ1+l → ℝl definable in ℜ such that F′(t) = G(t, F(t)) for all t ∈ (a, b) and each component function Gi: ℝ1+l → ℝ is independent of the last l − i variables (i = 1, …, l). If ℜ is o-minimal and F: (a, b) → ℝl is ℜ-Pfaffian, then (ℜ, F) is o-minimal (Proposition 7). We say that F: ℝ → ℝl is ultimately ℜ-Pfaffian if there exists r ∈

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5

Speissegger, Patrick, and Jean-Marie Lion. "Analytic stratification in the Pfaffian closure of an o-minimal structure." Duke Mathematical Journal 103, no. 2 (2000): 215–31. http://dx.doi.org/10.1215/s0012-7094-00-10322-5.

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6

Wang, L. J., F. Q. Chen, Y. Sun, T. Mizusaki, and M. Oi. "Application of the Pfaffian Algorithm in the Nuclear Structure Study at High Spins." Acta Physica Polonica B 46, no. 3 (2015): 497. http://dx.doi.org/10.5506/aphyspolb.46.497.

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7

Jones, G. O. "Zero sets of smooth functions in the Pfaffian closure of an o-minimal structure." Proceedings of the American Mathematical Society 136, no. 11 (2008): 4019–25. http://dx.doi.org/10.1090/s0002-9939-08-09373-8.

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8

Akemann, Gernot, and Eugene Kanzieper. "Integrable Structure of Ginibre’s Ensemble of Real Random Matrices and a Pfaffian Integration Theorem." Journal of Statistical Physics 129, no. 5-6 (2007): 1159–231. http://dx.doi.org/10.1007/s10955-007-9381-2.

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9

Sun, Yang, Jiaqi Wang, Saumi Dutta, and Long-Jun Wang. "A novel projected shell model method for nuclear level density." EPJ Web of Conferences 329 (2025): 02002. https://doi.org/10.1051/epjconf/202532902002.

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We introduce a shell model method for calculating nuclear level density (NLD) generally applicable for arbitrarily heavy deformed nuclei. The method is novel because of our use of physical guidance for the construction of its configuration space and the computational breakthrough with the Pfaffian algorithm. Taking a well deformed even-even 164 Dy nucleus as an example, we solve exactly the eigenvalue equation to obtain a large ensemble of eigenstates of angular momentum and parity. Our results indicate a potential need to revise some common understanding of the structural behavior in the pair

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10

Shevchenko, Yu. "Сurvature-torsion tensor for Cartan connection". Differential Geometry of Manifolds of Figures, № 50 (2019): 155–68. http://dx.doi.org/10.5922/0321-4796-2019-50-18.

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A Lie group containing a subgroup is considered. Such a group is a principal bundle, a typical fiber of this principal bundle is the subgroup and a base is a homogeneous space, which is obtained by factoring the group by the subgroup. Starting from this group, we constructed structure equations of a space with Cartan connection, which generalizes the Cartan point projective connection, Akivis’s linear projective connection, and a plane projective connection. Structure equations of this Cartan connection, containing the components of the curvature-torsion object, allowed: 1) to show that the cu

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11

Byun, Sung-Soo, Markus Ebke, and Seong-Mi Seo. "Wronskian structures of planar symplectic ensembles." Nonlinearity 36, no. 2 (2022): 809–44. http://dx.doi.org/10.1088/1361-6544/aca3f4.

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Abstract We consider the eigenvalues of non-Hermitian random matrices in the symmetry class of the symplectic Ginibre ensemble, which are known to form a Pfaffian point process in the plane. It was recently discovered that the limiting correlation kernel of the symplectic Ginibre ensemble in the vicinity of the real line can be expressed in a unified form of a Wronskian. We derive scaling limits for variations of the symplectic Ginibre ensemble and obtain such Wronskian structures for the associated universality classes. These include almost-Hermitian bulk/edge scaling limits of the elliptic s

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12

Barletta, Elisabetta, Sorin Dragomir, and Francesco Esposito. "On the Canonical Foliation of an Indefinite Locally Conformal Kähler Manifold with a Parallel Lee Form." Mathematics 9, no. 4 (2021): 333. http://dx.doi.org/10.3390/math9040333.

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We study the semi-Riemannian geometry of the foliation F of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is the Lee form of M). If M is conformally flat then every leaf of F is shown to be a totally geodesic semi-Riemannian hypersurface in M, and a semi-Riemannian space form of sectional curvature c/4, carrying an indefinite c-Sasakian structure. As a corollary of the result together with a semi-Riemannian version of the de Rham decomposition theorem any geodesically complete, conformally flat, indefinite Vais

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13

Berraho, M. "Плюригармонические определимые функции в некоторых $o$-минимальных расширениях вещественного поля". Владикавказский математический журнал, № 4 (23 грудня 2021): 35–40. http://dx.doi.org/10.46698/w9805-4567-8091-g.

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In this paper, we first try to solve the following problem: If a pluriharmonic function $f$ is definable in an arbitrary o-minimal expansion of the structure of the real field $\overline{\mathbb{R}}:=(\mathbb{R},+,-,.,0,1,<)$, does this function be locally the real part of a holomorphic function which is definable in the same expansion? In Proposition 2.1 below, we prove that this problem has a positive answer if the Weierstrass division theorem holds true for the system of the rings of real analytic definable germs at the origin of $\mathbb{R}^n$. We obtain the same answer for an o-minimal

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14

Ryazanov, N. "About differential equations of the curvature tensors of a fundamental group and affine connections." Differential Geometry of Manifolds of Figures, no. 50 (2019): 133–40. http://dx.doi.org/10.5922/0321-4796-2019-50-15.

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The principal bundle is considered, the base of which is an n-dimensional smooth manifold, and the typical fiber is an r-fold Lie group. Structure equations for the forms of the fundamental group and affine connections are given, each of which contains the corresponding components of the curvature tensor. For each connection, an approach is shown that allows to find the differential equations for the components of the curvature tensor of the corresponding connection in a faster way than by differentiating the expressions of these objects in terms of the connection objects and their Pfaffian de

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15

Machado, A. R., D. B. Pinho, M. Silva, and O. L. Pereira. "First Report of Leaf Spot Disease Caused by Cercosporella pfaffiae on Brazilian Ginseng (Pfaffia glomerata) in Brazil." Plant Disease 96, no. 11 (2012): 1702. http://dx.doi.org/10.1094/pdis-06-12-0614-pdn.

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Pfaffia glomerata (Spreng) Pedersen (Amaranthaceae) and other species in this genus, popularly known as “Brazilian ginseng,” have been marketed and used for many years in folk medicine for the treatment of various diseases (1). In January 2012, samples of P. glomerata with leaf spots were collected in the city of Viçosa, state of Minas Gerais, Brazil. Two samples were deposited in the herbarium at the Universidade Federal de Viçosa (VIC31849 and VIC31851). The diseased leaves were examined using a stereomicroscope (75×). The fungal structures were scraped with a scalpel from the plant surface

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16

Spera, Mauro, and Tilmann Wurzbacher. "Determinants, Pfaffians and Quasi-Free Representations of the CAR Algebra." Reviews in Mathematical Physics 10, no. 05 (1998): 705–21. http://dx.doi.org/10.1142/s0129055x98000227.

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In this paper we apply the theory of quasi-free states of CAR algebras and Bogolubov automorphisms to give an alternative C*-algebraic construction of the Determinant and Pfaffian line bundles discussed by Pressley and Segal and by Borthwick. The basic property of the Pfaffian of being the holomorphic square root of the Determinant line bundle (after restriction from the Hilbert space Grassmannian to the Siegel manifold, or isotropic Grassmannian, consisting of all complex structures on an associated Hilbert space) is derived from a Fock–anti-Fock correspondence and an application of the Power

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17

Zhitomirskii, M. Ya. "Degeneracies of differential 1-forms and Pfaffian structures." Russian Mathematical Surveys 46, no. 5 (1991): 53–90. http://dx.doi.org/10.1070/rm1991v046n05abeh002843.

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18

Fornasiero, Antongiulio, and Tamara Servi. "Relative Pfaffian closure for definably complete Baire structures." Illinois Journal of Mathematics 55, no. 3 (2011): 1203–19. http://dx.doi.org/10.1215/ijm/1369841803.

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19

Bunke, Ulrich. "String Structures and Trivialisations of a Pfaffian Line Bundle." Communications in Mathematical Physics 307, no. 3 (2011): 675–712. http://dx.doi.org/10.1007/s00220-011-1348-0.

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20

Kung, Joseph P. S. "Pfaffian structures and critical problems in finite symplectic spaces." Annals of Combinatorics 1, no. 1 (1997): 159–72. http://dx.doi.org/10.1007/bf02558472.

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21

BARCO, M. A. "Solvable structures and their application to a class of Cauchy problem." European Journal of Applied Mathematics 13, no. 5 (2002): 449–77. http://dx.doi.org/10.1017/s0956792501004697.

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We examine how symmetry and computer algebra can assist in solving the Cauchy problem for Pfaffian systems. We use recent results on integrating Frobenius integrable distributions via solvable symmetry structures to develop two techniques that when used in conjunction with symmetry determination software DIMSYM, allow us to solve the Cauchy problem for the special situation when there exists a one-dimensional Cauchy characteristic space. We also illustrate how our work can assist in extracting local solutions of a certain class of first and second order non-linear partial differential equation

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22

BRANSON, THOMAS, and A. ROD GOVER. "PONTRJAGIN FORMS AND INVARIANT OBJECTS RELATED TO THE Q-CURVATURE." Communications in Contemporary Mathematics 09, no. 03 (2007): 335–58. http://dx.doi.org/10.1142/s0219199707002460.

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It was shown by Chern and Simons that the Pontrjagin forms are conformally invariant. We show them to be the Pontrjagin forms of the conformally invariant tractor connection. The Q-curvature is intimately related to the Pfaffian. Working on even-dimensional manifolds, we show how the k-form operators Qk of [12], which generalize the Q-curvature, retain a key aspect of the Q-curvature's relation to the Pfaffian, by obstructing certain representations of natural operators on closed forms. In a closely related direction, we show that the Qk give rise to conformally invariant quadratic forms Θk on

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23

Kieburg, Mario, and Thomas Guhr. "A new approach to derive Pfaffian structures for random matrix ensembles." Journal of Physics A: Mathematical and Theoretical 43, no. 13 (2010): 135204. http://dx.doi.org/10.1088/1751-8113/43/13/135204.

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24

Hu, Lei, Yi-Tian Gao, Shu-Liang Jia, Jing-Jing Su, and Gao-Fu Deng. "Solitons for the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid via the Pfaffian technique." Modern Physics Letters B 33, no. 30 (2019): 1950376. http://dx.doi.org/10.1142/s0217984919503767.

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Fluids are common in nature, the study of which helps the design of the related industries. Under investigation in this letter is the (2[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid. Pfaffian solutions have been obtained based on the Pfaffian technique with the assistance of the real auxiliary function [Formula: see text]. N-soliton solutions with [Formula: see text] are constructed, where y is the scaled space coordinate and [Formula: see text] is the steady stream function in the irrotational incompressible

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25

Chang, Xiang-Ke. "Hermite–Padé approximations with Pfaffian structures: Novikov peakon equation and integrable lattices." Advances in Mathematics 402 (June 2022): 108338. http://dx.doi.org/10.1016/j.aim.2022.108338.

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26

Genovese, Claudio, Tomonori Shirakawa, Kousuke Nakano, and Sandro Sorella. "General Correlated Geminal Ansatz for Electronic Structure Calculations: Exploiting Pfaffians in Place of Determinants." Journal of Chemical Theory and Computation 16, no. 10 (2020): 6114–31. http://dx.doi.org/10.1021/acs.jctc.0c00165.

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27

Bornemann, Folkmar, and Michael La Croix. "The singular values of the GOE." Random Matrices: Theory and Applications 04, no. 02 (2015): 1550009. http://dx.doi.org/10.1142/s2010326315500094.

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As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ensemble (GOE): the even-location singular values are distributed as the positive eigenvalues of a Gaussian ensemble with chiral unitary symmetry, while the odd-location singular values, conditioned on the even-location ones, can be algebraically transformed into a set of independent χ-distributed random variables. We discuss three applications of this structure: first, there is a pair of bidiagonal square matrices, who

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28

Caleffi, Edilainy Rizzieri, Gabriela Krausová, Ivana Hyršlová, et al. "Isolation and prebiotic activity of inulin-type fructan extracted from Pfaffia glomerata (Spreng) Pedersen roots." International Journal of Biological Macromolecules 80 (September 2015): 392–99. http://dx.doi.org/10.1016/j.ijbiomac.2015.06.053.

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29

Slemmons, Krista EH, Aaron Medford, Brenda L. Hall, et al. "Changes in glacial meltwater alter algal communities in lakes of Scoresby Sund, Renland, East Greenland throughout the Holocene: Abrupt reorganizations began 1000 years before present." Holocene 27, no. 7 (2016): 929–40. http://dx.doi.org/10.1177/0959683616678468.

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We investigated the response of lake algal communities to changes in glacial meltwater from the Renland Ice Cap (Greenland) through the Holocene to assess whether influxes always elicit consistent responses or novel responses. We measured sedimentary algal pigments in two proximal lakes, snow-fed Raven and glacier- and snow-fed Bunny Lake, and diatom community structure and turnover in Bunny Lake. Diatom data were not available in Raven Lake. We also modeled lake-level change in Bunny Lake to identify how glacial meltwater may have altered diatom habitat availability through time. Through a se

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30

Silva, Eric Keven, Matheus A. Bargas, Henrique S. Arruda, Renata Vardanega, Glaucia M. Pastore, and M. Angela A. Meireles. "Supercritical CO2 Processing of a Functional Beverage Containing Apple Juice and Aqueous Extract of Pfaffia glomerata Roots: Fructooligosaccharides Chemical Stability after Non-Thermal and Thermal Treatments." Molecules 25, no. 17 (2020): 3911. http://dx.doi.org/10.3390/molecules25173911.

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The effects of supercritical CO2 processing on the chemical stability of fructooligosaccharides (FOS) and other functional and nutritional compounds were evaluated employing non-thermal and thermal approaches. Apple juice was enriched with Pfaffia glomerata roots aqueous extract due to its high content of short-chain FOS and then subjected to different levels of temperature (40 and 60 °C), pressure (8 and 21 MPa), and CO2 volume ratio (20 and 50%). The percentage of CO2 volume was evaluated concerning the total volume of the high-pressure reactor. Also, the functional beverage was thermally tr

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31

Krahe, Nina-Katharina, Ralf G. Berger, and Franziska Ersoy. "A DyP-Type Peroxidase of Pleurotus sapidus with Alkene Cleaving Activity." Molecules 25, no. 7 (2020): 1536. http://dx.doi.org/10.3390/molecules25071536.

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Alkene cleavage is a possibility to generate aldehydes with olfactory properties for the fragrance and flavor industry. A dye-decolorizing peroxidase (DyP) of the basidiomycete Pleurotus sapidus (PsaPOX) cleaved the aryl alkene trans-anethole. The PsaPOX was semi-purified from the mycelium via FPLC, and the corresponding gene was identified. The amino acid sequence as well as the predicted tertiary structure showed typical characteristics of DyPs as well as a non-canonical Mn2+-oxidation site on its surface. The gene was expressed in Komagataella pfaffii GS115 yielding activities up to 142 U/L

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32

Pan-Collantes, Antonio J., Adrián Ruiz Serván, Concepcion Muriel, and Juan Luis Romero. "C∞-structures in the integration of involutive distributions." Physica Scripta, July 4, 2023. http://dx.doi.org/10.1088/1402-4896/ace403.

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Abstract For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution of vector fields, the problem of its integration is considered. Among the many approaches to this problem, solvable structures provide a systematic procedure of integration via Pfaffian equations that are integrable by quadratures. In this paper structures more general than solvable structures (named cinf-structures) are considered. The symmetry condition in the concept of solvable structure is weakened for cinf-structures by requiring their vector fields be just cinf-symmetries. For

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33

Binyamini, Gal, and Nicolai Vorobjov. "Effective Cylindrical Cell Decompositions for Restricted Sub-Pfaffian Sets." International Mathematics Research Notices, November 24, 2020. http://dx.doi.org/10.1093/imrn/rnaa285.

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Abstract The o-minimal structure generated by the restricted Pfaffian functions, known as restricted sub-Pfaffian sets, admits a natural measure of complexity in terms of a format ${{\mathcal{F}}}$, recording information like the number of variables and quantifiers involved in the definition of the set, and a degree $D$, recording the degrees of the equations involved. Khovanskii and later Gabrielov and Vorobjov have established many effective estimates for the geometric complexity of sub-Pfaffian sets in terms of these parameters. It is often important in applications that these estimates are

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34

Grimm, Thomas W., Arno Hoefnagels, and Mick van Vliet. "Structure and complexity of cosmological correlators." Physical Review D 110, no. 12 (2024). https://doi.org/10.1103/physrevd.110.123531.

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Cosmological correlators capture the spatial fluctuations imprinted during the earliest episodes of the Universe. While they are generally very nontrivial functions of the kinematic variables, they are known to arise as solutions to special sets of differential equations. In this work we use this fact to uncover the underlying tame structure for such correlators and argue that they admit a well-defined notion of complexity. In particular, building upon the recently proposed kinematic flow algorithm, we show that tree-level cosmological correlators of a generic scalar field theory in a Friedman

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35

Panagou, Dimitra, Herbert G. Tanner, and Kostas J. Kyriakopoulos. "Control Design for a Class of Nonholonomic Systems Via Reference Vector Fields and Output Regulation." Journal of Dynamic Systems, Measurement, and Control 137, no. 8 (2015). http://dx.doi.org/10.1115/1.4030335.

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This paper presents procedural guidelines for the construction of discontinuous state feedback controllers for driftless, kinematic nonholonomic systems, with extensions to a class of dynamic nonholonomic systems with drift. Given an n-dimensional kinematic nonholonomic system subject to κ Pfaffian constraints, system states are partitioned into “leafwise” and “transverse,” based on the structure of the Pfaffian constraint matrix. A reference vector field F is defined as a function of the leafwise states only in a way that it is nonsingular everywhere except for a submanifold containing the or

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36

Bajdich, M., L. Mitas, G. Drobný, L. K. Wagner, and K. E. Schmidt. "Pfaffian Pairing Wave Functions in Electronic-Structure Quantum Monte Carlo Simulations." Physical Review Letters 96, no. 13 (2006). http://dx.doi.org/10.1103/physrevlett.96.130201.

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Akemann, Gernot, Sung-Soo Byun, and Kohei Noda. "Pfaffian Structure of the Eigenvector Overlap for the Symplectic Ginibre Ensemble." Annales Henri Poincaré, May 10, 2025. https://doi.org/10.1007/s00023-025-01575-x.

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Abstract We study the integrable structure and scaling limits of the conditioned eigenvector overlap of the symplectic Ginibre ensemble of Gaussian non-Hermitian random matrices with independent quaternion elements. The average of the overlap matrix elements constructed from left and right eigenvectors, conditioned to x, are derived in terms of a Pfaffian determinant. Regarded as a two-dimensional Coulomb gas with the Neumann boundary condition along the real axis, it contains a kernel of skew-orthogonal polynomials with respect to the weight function $$\omega ^\mathrm{(over)}(z)=|z-\overline{

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38

Crainic, Marius, and Ori Yudilevich. "Lie Pseudogroups à la Cartan." Memoirs of the American Mathematical Society 303, no. 1527 (2024). http://dx.doi.org/10.1090/memo/1527.

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We present a modern formulation of Élie Cartan’s structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan’s systatic system. The monograph is divided into three parts. In part one, using notions coming from the theory of Lie groupoids and algebroids, we introduce the framework of Cartan algebroids and realizations, structures that encode Cartan’s structure equations and notion of a pseudogroup in normal form. In part two, we present a novel proof of Cartan’s Second Fundamental Theorem which states that any Lie pseudogroup is equivalent to a pseudogr

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39

Bajdich, M., L. Mitas, L. K. Wagner, and K. E. Schmidt. "Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods." Physical Review B 77, no. 11 (2008). http://dx.doi.org/10.1103/physrevb.77.115112.

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40

Koshida, Shinji. "Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures." Symmetry, Integrability and Geometry: Methods and Applications, January 26, 2021. http://dx.doi.org/10.3842/sigma.2021.008.

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The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a positive contraction acting on a ''doubled'' one-particle space with an additional structure defines a unique PfPP. Recently, Olshanski inverted the direction from free fermions to DPPs, proposed a scheme to construct a fermionic state from a quasi-invariant probability measure, and introduced the notion of perfectness of a probability measure. We propose a method

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41

Palm, F. A., C. Repellin, N. Goldman, and F. Grusdt. "Absence of gapless Majorana edge modes in few-leg bosonic flux ladders." Physical Review Research 7, no. 1 (2025). https://doi.org/10.1103/physrevresearch.7.l012001.

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The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions are topologically ordered non-Abelian phases of matter, such as certain fractional quantum Hall states. Quantum simulators provide unprecedented controllability and versatility to investigate such states, and developing experimentally feasible schemes to realize and identify them is of immediate relevance. Motivated by recent experiments, we consider bosons

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42

Grimm, Thomas W., Lorenz Schlechter, and Mick van Vliet. "Complexity in tame quantum theories." Journal of High Energy Physics 2024, no. 5 (2024). http://dx.doi.org/10.1007/jhep05(2024)001.

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Abstract Inspired by the notion that physical systems can contain only a finite amount of information or complexity, we introduce a framework that allows for quantifying the amount of logical information needed to specify a function or set. We then apply this methodology to a variety of physical systems and derive the complexity of parameter-dependent physical observables and coupling functions appearing in effective Lagrangians. In order to implement these ideas, it is essential to consider physical theories that can be defined in an o-minimal structure. O-minimality, a concept from mathemati

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43

He, Jimmy. "Boundary current fluctuations for the half‐space ASEP and six‐vertex model." Proceedings of the London Mathematical Society 128, no. 2 (2024). http://dx.doi.org/10.1112/plms.12585.

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AbstractWe study fluctuations of the current at the boundary for the half‐space asymmetric simple exclusion process (ASEP) and the height function of the half‐space six‐vertex model at the boundary at large times. We establish a phase transition depending on the effective density of particles at the boundary, with Gaussian symplectic ensemble (GSE) and Gaussian orthogonal ensemble (GOE) limits as well as the Baik–Rains crossover distribution near the critical point. This was previously known for half‐space last‐passage percolation, and recently established for the half‐space log‐gamma polymer

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Tokmachev, Andrey M. "Separation of metric in Wick’s theorem." Journal of Chemical Physics 159, no. 19 (2023). http://dx.doi.org/10.1063/5.0174998.

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In quantum chemistry, Wick’s theorem is an important tool to reduce products of fermionic creation and annihilation operators. It is especially useful in computations employing reference states. The original theorem has been generalized to tackle multiconfigurational wave functions or nonorthogonal orbitals. One particular issue of the resulting structure is that the metric and density matrices are intertwined despite their different origin. Here, an alternative, rather general tensorial formulation of Wick’s theorem is proposed. The main difference is the separation of the metric—the coeffici

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Deffayet, Cédric, Burt A. Ovrut, and Paul J. Steinhardt. "Moduli axions, stabilizing moduli, and the large field swampland conjecture in heterotic M-theory." Physical Review D 109, no. 12 (2024). http://dx.doi.org/10.1103/physrevd.109.126004.

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We compute the F- and D-term potential energy for the dilaton, complex structure, and Kähler moduli of realistic vacua of heterotic M-theory compactified on Calabi-Yau threefolds where, for simplicity, we choose h1,1=h2,1=1. However, the formalism is immediately applicable to the “universal” moduli of Calabi-Yau threefolds with h1,1=h1,2>1 as well. The F-term potential is computed using the nonperturbative complex structure, gaugino condensate and “world sheet instanton” superpotentials in theories in which the hidden sector contains an anomalous U(1) structure group. The Green-Schwarz anom

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Akemann, Gernot, Sung-Soo Byun, and Markus Ebke. "Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases." Journal of Statistical Physics 190, no. 1 (2022). http://dx.doi.org/10.1007/s10955-022-03005-2.

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AbstractAn exact map was established by Lacroix-A-Chez-Toine et al. in (Phys Rev A 99(2):021602, 2019) between the N complex eigenvalues of complex non-Hermitian random matrices from the Ginibre ensemble, and the positions of N non-interacting Fermions in a rotating trap in the ground state. An important quantity is the statistics of the number of Fermions $$\mathcal {N}_a$$ N a in a disc of radius a. Extending the work (Lacroix-A-Chez-Toine et al., in Phys Rev A 99(2):021602, 2019) covering Gaussian and rotationally invariant potentials Q, we present a rigorous analysis in planar complex and

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Binyamini, Gal, Dmitry Novikov, and Benny Zak. "Wilkie's conjecture for Pfaffian structures." Annals of Mathematics 199, no. 2 (2024). http://dx.doi.org/10.4007/annals.2024.199.2.5.

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Galluccio, Anna, and Martin Loebl. "On the Theory of Pfaffian Orientations. II. $T$-joins, $k$-cuts, and Duality of Enumeration." Electronic Journal of Combinatorics 6, no. 1 (1998). http://dx.doi.org/10.37236/1439.

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This is a continuation of our paper "A Theory of Pfaffian Orientations I: Perfect Matchings and Permanents". We present a new combinatorial way to compute the generating functions of $T$-joins and $k$-cuts of graphs. As a consequence, we show that the computational problem to find the maximum weight of an edge-cut is polynomially solvable for the instances $(G,w)$ where $G$ is a graph embedded on an arbitrary fixed orientable surface and the weight function $w$ has only a bounded number of different values. We also survey the related results concerning a duality of the Tutte polynomial, and pr

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Loebl, Martin, and Petr Somberg. "Discrete Dirac Operators, Critical Embeddings and Ihara-Selberg Functions." Electronic Journal of Combinatorics 22, no. 1 (2015). http://dx.doi.org/10.37236/3741.

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The aim of the paper is to formulate a discrete analogue of the claim made by Alvarez-Gaume et al., realizing the partition function of the free fermion on a closed Riemann surface of genus $g$ as a linear combination of $2^{2g}$ Pfaffians of Dirac operators. Let $G=(V,E)$ be a finite graph embedded in a closed Riemann surface $X$ of genus $g$, $x_e$ the collection of independent variables associated with each edge $e$ of $G$ (collected in one vector variable $x$) and $\S$ the set of all $2^{2g}$ spin-structures on $X$. We introduce $2^{2g}$ rotations $rot_s$ and $(2|E|\times 2|E|)$ matrices $

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Bajdich, Michal, and Lubos Mitas. "Electronic structure quantum Monte Carlo." Acta Physica Slovaca. Reviews and Tutorials 59, no. 2 (2009). http://dx.doi.org/10.2478/v10155-010-0095-7.

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Electronic structure quantum Monte CarloQuantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. The QMC approaches combine analytical insights with stochastic computational techniques for efficient solution of several classes of important many-body problems such as the stationary Schrödinger equation. QMC methods of various flavors have been applied to a great variety of systems spanning continuous and lattice quantum models, molecular and condensed systems, BEC-BCS ultracold condensates, nuclei, etc. In this review, we focus on the electronic s

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