Publications

Order by: publication date number of citations

• Matrix method and the suppression of Runge's phenomenon

  Shui-Fa Shen, Wei-Liang Qian, Jie Zhang, Yu Pan, Yu-Peng Yan, Cheng-Gang Shao

  SciPost Phys. Core 7, 034 (2024) · published 5 June 2024 | Toggle abstract · pdf

  Higher-degree polynomial interpolations carried out on uniformly distributed nodes are often plagued by overfitting, known as Runge's phenomenon. This work investigates Runge's phenomenon and its suppression in various versions of the matrix method for black hole quasinormal modes. It is shown that an appropriate choice of boundary conditions gives rise to desirable suppression of oscillations associated with the increasing Lebesgue constant. For the case of discontinuous effective potentials, where the application of the above boundary condition is not feasible, the recently proposed scheme with delimited expansion domain also leads to satisfactory results. The onset of Runge's phenomenon and its effective suppression are demonstrated by evaluating the relevant waveforms. Furthermore, we argue that both scenarios are either closely related to or practical imitations of the Chebyshev grid. The implications of the present study are also addressed.

  1 citation

• Renormalization group and effective potential: a simple non-perturbative approach

  Jose Gaite

  SciPost Phys. Core 5, 044 (2022) · published 26 September 2022 | Toggle abstract · pdf

  We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It yields a simple second order differential equation for the effective potential. The equation can be solved and its solution is compared with other non-perturbative results and with results of perturbation theory. In three dimensions, we are led to study the sextic field theory ($\lambda\phi^4+g\phi^6$). We work out this theory at two-loop perturbative order and find the non-perturbative approach to be superior.

  1 citation

• Precise predictions for boosted Higgs production

  Kathrin Becker, Fabrizio Caola, Andrea Massironi, Bernhard Mistlberger, Pier F. Monni, Xuan Chen, Stefano Frixione, Thomas Gehrmann, Nigel Glover, Keith Hamilton, Alexander Huss, Stephen P. Jones, Alexander Karlberg, Matthias Kerner, Kirill Kudashkin, Jonas M. Lindert, Gionata Luisoni, Michelangelo L. Mangano, Stefano Pozzorini, Emanuele Re, Gavin P. Salam, Eleni Vryonidou, Christopher Wever

  SciPost Phys. Core 7, 001 (2024) · published 4 January 2024 | Toggle abstract · pdf

  Inclusive Higgs boson production at large transverse momentum is induced by different production channels. We focus on the leading production mechanism through gluon fusion, and perform a consistent combination of the state of the art calculations obtained in the infinite-top-mass effective theory at next-to-next-to-leading order (NNLO) and in the full Standard Model (SM) at next-to-leading order (NLO). We thus present approximate QCD predictions for this process at NNLO, and a study of the corresponding perturbative uncertainties. This calculation is then compared with those obtained with commonly used event generators, and we observe that the description of the considered kinematic regime provided by these tools is in good agreement with state of the art calculations. Finally, we present accurate predictions for other production channels such as vector boson fusion, and associated production with a gauge boson, and with a $t\bar{t}$ pair. We find that, at large transverse momentum, the contribution of other production modes is substantial, and therefore must be included for a precise theory prediction of this observable.

  1 citation

• Surface-acoustic-wave-induced unconventional superconducting pairing

  Viktoriia Kornich

  SciPost Phys. Core 5, 005 (2022) · published 27 January 2022 | Toggle abstract · pdf

  Unconventional superconductivity is usually associated with symmetry breaking in the system. Here we consider a simple setup consisting of a solid state material with conduction electrons and an applied surface acoustic wave (SAW), that can break time and spatial translation symmetries. We study the symmetries of the possible SAW-induced order parameters, showing that even-frequency spin-triplet odd-parity order parameter can occur. We suggest different methods of how to engineer the symmetries of the order parameters using SAWs and the applications of such setups.

  1 citation

• The high-temperature expansion of the thermal sunset

  Andreas Ekstedt, Johan Löfgren

  SciPost Phys. Core 3, 008 (2020) · published 22 October 2020 | Toggle abstract · pdf

  We give a prescription for calculating the high-temperature expansion of the thermal sunset integral to arbitrary order. We derive all terms odd in $T$, and rederive previous results up to $\mathcal{O}(T^0) $ for both bosonic and fermionic thermal sunsets in dimensional regularisation. We perform analytical and numerical cross-checks. Intermediate steps involve integrals over three Bessel functions.

  1 citation

• Excitations and ergodicity of critical quantum spin chains from non-equilibrium classical dynamics

  Stéphane Vinet, Gabriel Longpré, William Witczak-Krempa

  SciPost Phys. Core 5, 035 (2022) · published 7 July 2022 | Toggle abstract · pdf

  We study a quantum spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. The Hamiltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic, and depends on the Ising couplings normalized by the bath's temperature. We give its exact ground states. Proceeding with uniform couplings, we study the one- and two-magnon excitations. Solutions for the latter are derived via a Bethe Ansatz scheme. In the antiferromagnetic regime, the two-magnon branch states show intricate behavior, especially regarding their hybridization with the continuum. We find that that the gapless chain hosts multiple dynamics at low energy as seen through the presence of multiple dynamical critical exponents. Finally, we analyze the full energy level spacing distribution as a function of the Ising coupling. We conclude that the system is non-integrable for generic parameters, or equivalently, that the corresponding non-equilibrium classical dynamics are ergodic.

  1 citation

• Analytic thermodynamic properties of the Lieb-Liniger gas

  Matthew L. Kerr, Giulia De Rosi, Karen V. Kheruntsyan

  SciPost Phys. Core 7, 047 (2024) · published 30 July 2024 | Toggle abstract · pdf

  We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact repulsive interactions. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics-thanks to its integrability and possible experimental realization using, e.g., ensembles of ultracold bosonic atoms confined to quasi-1D geometries. The thermodynamics of the uniform Lieb-Liniger gas can be obtained numerically using the exact thermal Bethe ansatz (TBA) method, first derived in 1969 by Yang and Yang. However, the TBA numerical calculations do not allow for the in-depth understanding of the underlying physical mechanisms that govern the thermodynamic behavior of the Lieb-Liniger gas at finite temperature. Our work is then motivated by the insights that emerge naturally from the transparency of closed-form analytic results, which are derived here in six different regimes of the gas and which exhibit an excellent agreement with the TBA numerics. Our findings can be further adopted for characterising the equilibrium properties of inhomogeneous (e.g., harmonically trapped) 1D Bose gases within the local density approximation and for the development of improved hydrodynamic theories, allowing for the calculation of breathing mode frequencies which depend on the underlying thermodynamic equation of state. Our analytic approaches can be applied to other systems including impurities in a quantum bath, liquid helium-4, and ultracold Bose gas mixtures.

  1 citation

• Entanglement Rényi entropies from ballistic fluctuation theory: The free fermionic case

  Giuseppe del Vecchio del Vecchio, Benjamin Doyon, Paola Ruggiero

  SciPost Phys. Core 7, 005 (2024) · published 14 February 2024 | Toggle abstract · pdf

  The large-scale behaviour of entanglement entropy in finite-density states, in and out of equilibrium, can be understood using the physical picture of particle pairs. However, the full theoretical origin of this picture is not fully established yet. In this work, we clarify this picture by investigating entanglement entropy using its connection with the large-deviation theory for thermodynamic and hydrodynamic fluctuations. We apply the universal framework of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the model, to correlation functions of branch-point twist fields, the starting point for computing Rényi entanglement entropies within the replica approach. Focusing on free fermionic systems in order to illustrate the ideas, we show that both the equilibrium behavior and the dynamics of Rényi entanglement entropies can be fully derived from the BFT. In particular, we emphasise that long-range correlations develop after quantum quenches, and accounting for these explain the structure of the entanglement growth. We further show that this growth is related to fluctuations of charge transport, generalising to quantum quenches the relation between charge fluctuations and entanglement observed earlier. The general ideas we introduce suggest that the large-scale behaviour of entanglement has its origin within hydrodynamic fluctuations.

  1 citation

• A new derivation of the relationship between diffusion coefficient and entropy in classical Brownian motion by the ensemble method

  Yi Liao, Xiao-Bo Gong

  SciPost Phys. Core 4, 015 (2021) · published 2 June 2021 | Toggle abstract · pdf

  The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the correlation is often strongly non-linear. To understand this complex dependence, we consider the classical Brownian diffusion in this work. Under certain rational assumption, i.e. in the bi-component fluid mixture, the mass of the Brownian particle $M$ is far greater than that of the bath molecule $m$, we can adopt the weakly couple limit. Only considering the first-order approximation of the mass ratio $m/M$, we obtain a linear motion equation in the reference frame of the observer as a Brownian particle. Based on this equivalent equation, we get the Hamiltonian at equilibrium. Finally, using canonical ensemble method, we define a new entropy that is similar to the Kolmogorov-Sinai entropy. Further, we present an analytic expression of the relationship between the diffusion coefficient $D$ and the entropy $S$ in the thermal equilibrium, that is to say, $D =\frac{\hbar}{eM} \exp{[S/(k_Bd)]}$, where $d$ is the dimension of the space, $k_B$ the Boltzmann constant, $\hbar $ the reduced Planck constant and $e$ the Euler number. This kind of scaling relation has been well-known and well-tested since the similar one for single component is firstly derived by Rosenfeld with the expansion of volume ratio.

  1 citation

• A general learning scheme for classical and quantum Ising machines

  Ludwig Schmid, Enrico Zardini, Davide Pastorello

  SciPost Phys. Core 7, 013 (2024) · published 14 March 2024 | Toggle abstract · pdf

  An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is based on the Ising structure and can be efficiently trained using gradient descent. We provide a mathematical characterization of the training process, which is based upon optimizing a loss function whose partial derivatives are not explicitly calculated but estimated by the Ising machine itself. Moreover, we present some experimental results on the training and execution of the proposed learning model. These results point out new possibilities offered by Ising machines for different learning tasks. In particular, in the quantum realm, the quantum resources are used for both the execution and the training of the model, providing a promising perspective in quantum machine learning.

  1 citation