Publications

Order by: publication date number of citations

• Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions

  Jiaxin Qiao

  SciPost Phys. 13, 093 (2022) · published 12 October 2022 | Toggle abstract · pdf

  We analyze the convergence properties of operator product expansions (OPE) for Lorentzian CFT four-point functions of scalar operators. We give a complete classification of Lorentzian four-point configurations. All configurations in each class have the same OPE convergence properties in s-, t- and u-channels. We give tables including the information of OPE convergence for all classes. Our work justifies that in a subset of the configuration space, Lorentzian CFT four-point functions are genuine analytic functions. Our results are valid for unitary CFTs in $d\geq2$. Our work also provides some Lorentzian regions where one can do bootstrap analysis in the sense of functions.

  1 citation

• Invariant approach to the driven Jaynes-Cummings model

  Ivan Alejandro Bocanegra-Garay, L. Hernández-Sánchez, Irán Ramos-Prieto, Francisco Soto-Eguibar, Héctor Manuel Moya-Cessa

  SciPost Phys. 16, 007 (2024) · published 8 January 2024 | Toggle abstract · pdf

  We investigate the dynamics of the driven Jaynes-Cummings model, where a two-level atom interacts with a quantized field and both, atom and field, are driven by an external classical field. Via an invariant approach, we are able to transform the corresponding Hamiltonian into the one of the standard Jaynes-Cummings model. Subsequently, the exact analytical solution of the Schrödinger equation for the driven system is obtained and employed to analyze some of its dynamical variables.

  1 citation

• Non-invertible symmetries and higher representation theory II

  Thomas Bartsch, Mathew Bullimore, Andrea E. V. Ferrari, Jamie Pearson

  SciPost Phys. 17, 067 (2024) · published 26 August 2024 | Toggle abstract · pdf

  In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete applications we provide a unified description of the symmetry categories of gauge theories in three and four dimensions based on the Lie algebra $\mathfrak{so}(N)$, and a fully categorical description of non-invertible symmetries obtained by gauging a 1-form symmetry with a mixed 't Hooft anomaly. We also discuss the effect of discrete torsion on symmetry categories, based a series of obstructions determined by spectral sequence arguments.

  1 citation

• Topological interpretation of color exchange invariants: hexagonal lattice on a torus

  Olivier Cépas, Peter M. Akhmetiev

  SciPost Phys. 10, 042 (2021) · published 18 February 2021 | Toggle abstract · pdf

  We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a special surface with Arf-Kervaire invariant one, and is interpreted as resulting from an obstruction to transform the surface into its chiral image with special continuous deformations. We also consider additional constraints on the dynamics and see how the surface is modified.

  1 citation

• Hyperquaternions and physics

  Patrick R. Girard, Romaric Pujol, Patrick Clarysse, Philippe Delachartre

  SciPost Phys. Proc. 14, 030 (2023) · published 24 November 2023 | Toggle abstract · pdf

  The paper develops, within a new representation of Clifford algebras in terms of tensor products of quaternions called hyperquaternions, several applications. The first application is a quaternion 2D representation in contradistinction to the frequently used 3D one. The second one is a new representation of the conformal group in (1+2) space (signature $+--$) within the Dirac algebra $C_(2,3) \simeq $$\mathbb{C\otimes H\otimes H}$ subalgebra of $\mathbb{H\otimes H\otimes H}$. A numerical example and a canonical decomposition into simple planes are given. The third application is a classification of all hyperquaternion algebras into four types, providing the general formulas of the signatures and relating them to the symmetry groups of physics.

  1 citation

• Particle dynamics on torsional galilean spacetimes

  José Figueroa-O'Farrill, Can Görmez, Dieter Van den Bleeken

  SciPost Phys. 14, 059 (2023) · published 4 April 2023 | Toggle abstract · pdf

  We study free particle motion on homogeneous kinematical spacetimes of galilean type. The three well-known cases of Galilei and (A)dS-Galilei spacetimes are included in our analysis, but our focus will be on the previously unexplored torsional galilean spacetimes. We show how in well-chosen coordinates free particle motion becomes equivalent to the dynamics of a damped harmonic oscillator, with the damping set by the torsion. The realization of the kinematical symmetry algebra in terms of conserved charges is subtle and comes with some interesting surprises, such as a homothetic version of hamiltonian vector fields and a corresponding generalization of the Poisson bracket. We show that the Bargmann extension is universal to all galilean kinematical symmetries, but also that it is no longer central for nonzero torsion. We also present a geometric interpretation of this fact through the Eisenhart lift of the dynamics.

  1 citation

• Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings

  Wenxuan Zou, Haiping Huang

  SciPost Phys. Lect. Notes 79 (2024) · published 20 February 2024 | Toggle abstract · pdf

  Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners to access the essence of this tool and the underlying physics. Here, we give a pedagogical introduction of this method in a particular example of random neural networks, where neurons are randomly and fully connected by correlated synapses and therefore the network exhibits rich emergent collective dynamics. We also review related past and recent important works applying this tool. In addition, a physically transparent and alternative method, namely the dynamical cavity method, is also introduced to derive exactly the same results. The numerical implementation of solving the integro-differential mean-field equations is also detailed, with an illustration of exploring the fluctuation dissipation theorem.

  1 citation

• Fusion and monodromy in the Temperley-Lieb category

  Jonathan Belletête, Yvan Saint-Aubin

  SciPost Phys. 5, 041 (2018) · published 31 October 2018 | Toggle abstract · pdf

  Graham and Lehrer (1998) introduced a Temperley-Lieb category $\mathsf{\widetilde{TL}}$ whose objects are the non-negative integers and the morphisms in $\mathsf{Hom}(n,m)$ are the link diagrams from $n$ to $m$ nodes. The Temperley-Lieb algebra $\mathsf{TL}_{n}$ is identified with $\mathsf{Hom}(n,n)$. The category $\mathsf{\widetilde{TL}}$ is shown to be monoidal. We show that it is also a braided category by constructing explicitly a commutor. A twist is also defined on $\mathsf{\widetilde{TL}}$. We introduce a module category ${\text{ Mod}_{\mathsf{\widetilde{TL}}}}$ whose objects are functors from $\mathsf{\widetilde{TL}}$ to $\mathsf{Vect}_{\mathbb C}$ and define on it a fusion bifunctor extending the one introduced by Read and Saleur (2007). We use the natural morphisms constructed for $\mathsf{\widetilde{TL}}$ to induce the structure of a ribbon category on ${\text{ Mod}_{\mathsf{\widetilde{TL}}}}(\beta=-q-q^{-1})$, when $q$ is not a root of unity. We discuss how the braiding on $\mathsf{\widetilde{TL}}$ and integrability of statistical models are related. The extension of these structures to the family of dilute Temperley-Lieb algebras is also discussed.

  1 citation

• Quantum cylindrical integrability in magnetic fields

  Ondřej Kubů, Libor Šnobl

  SciPost Phys. Proc. 14, 032 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We present the classification of quadratically integrable systems of the cylindrical type with magnetic fields in quantum mechanics. Following the direct method used in classical mechanics by [F Fournier et al 2020 J. Phys. A: Math. Theor. 53 085203] to facilitate the comparison, the cases which may a priori differ yield 2 systems without any correction and 2 with it. In all of them the magnetic field B coincides with the classical one, only the scalar potential W may contain a $\hbar^2$-dependent correction. Two of the systems have both cylindrical integrals quadratic in momenta and are therefore not separable. These results form a basis for a prospective study of superintegrability.

  1 citation

• A simple coin for a 2d entangled walk

  Ahmadullah Zahed, Kallol Sen

  SciPost Phys. Core 6, 048 (2023) · published 10 July 2023 | Toggle abstract · pdf

  We analyze the effect of a simple coin operator, built out of Bell pairs, in a 2d Discrete Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find analytical and closed form solutions to the recursion relations of the DQRW. The coin induces entanglement between the spin and position degrees of freedom, which oscillates with time and reaches a constant value asymptotically. We probe the entangling properties of the coin operator further, by two different measures. First, by integrating over the space of initial tensor product states, we determine the Entangling Power of the coin operator. Secondly, we compute the Generalized Relative Rényi Entropy between the corresponding density matrices for the entangled state and the initial pure unentangled state. Both the Entangling Power and Generalized Relative Rényi Entropy behaves similar to the entanglement with time. Finally, in the continuum limit, the specific coin operator reduces the 2d DQRW into two 1d massive fermions coupled to synthetic gauge fields, where both the mass term and the gauge fields are built out of the coin parameters.

  1 citation