Publications

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Random features and polynomial rules

Fabián Aguirre-López, Silvio Franz, Mauro Pastore

SciPost Phys. 18, 039 (2025) · published 31 January 2025 | · pdf

Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance of random features models for generic supervised learning problems with Gaussian data. Our approach, built with tools from the statistical mechanics of disordered systems, maps the random features model to an equivalent polynomial model, and allows us to plot average generalization curves as functions of the two main control parameters of the problem: the number of random features $N$ and the size $P$ of the training set, both assumed to scale as powers in the input dimension $D$. Our results extend the case of proportional scaling between $N$, $P$ and $D$. They are in accordance with rigorous bounds known for certain particular learning tasks and are in quantitative agreement with numerical experiments performed over many order of magnitudes of $N$ and $P$. We find good agreement also far from the asymptotic limits where $D\to ∞$ and at least one between $P/D^K$, $N/D^L$ remains finite.

3 citations
Exciton dissociation in organic solar cells: An embedded charge transfer state model

Jouda Jemaa Khabthani, Khouloud Chika, Alexandre Perrin, Didier Mayou

SciPost Phys. 18, 038 (2025) · published 31 January 2025 | · pdf

Organic solar cells are a promising avenue for renewable energy, and our study introduces a comprehensive model to investigate exciton dissociation processes at the donor-acceptor interface. Examining quantum efficiency and emitted phonons in the charge transfer state (CTS), we explore scenarios like variations of the environment beyond the CTS and repulsive/attractive potentials. The donor-acceptor interface significantly influences the injection process, with minimal impact from the environment beyond the CTS. Attractive potentials can create localized electron states at the interface, below the acceptor band, without necessarily hampering a good injection at higher energies. Exploring different recombination processes, including acceptor-side and donor-side recombination, presents distinct phases for the injection process versus the initial energy of the electron and the recombination rate. Our study highlights the important role of the type of recombination in determining the quantum efficiency and the existence of hot or cold charge transfer states. Finally, depending on the initial energy of the electron on the donor side, three distinct injection regimes are exhibited. The present model should be helpful for optimizing organic photovoltaic cell interfaces, highlighting the critical parameter interplay for enhanced performance.
Coalescing hardcore-boson condensate states with nonzero momentum

C. H. Zhang, Z. Song

SciPost Phys. Core 8, 013 (2025) · published 31 January 2025 | · pdf

Exceptional points (EPs), as an exclusive feature of a non-Hermitian system, support coalescing states to be alternative stable state beyond the ground state. In this work, we explore the influence of non-Hermitian impurities on the dynamic formation of condensate states in one-, two-, and three-dimensional extended Bose-Hubbard systems with strong on-site interaction. Based on the solution for the hardcore limit, we show exactly that condensate modes with off-diagonal long-range order (ODLRO) can exist when certain system parameters satisfy specific matching conditions. Under open boundary conditions, the condensate states become coalescing states when the non-Hermitian $\mathcal{PT}$-symmetric boundary gives rise to the EPs. The fundamental mechanism behind this phenomenon is uncovered through analyzing the scattering dynamics of many-particle wavepackets at the non-Hermitian boundaries. The EP dynamics facilitate the dynamic generation of condensate states with non-zero momentum. To further substantiate the theoretical findings, numerical simulations are conducted. This study not only unveils the potential condensation of interacting bosons but also offers an approach for the engineering of condensate states.

1 citation
Interaction and collision of skyrmions in chiral antiferromagnets

George Theodorou, Bruno Barton-Singer, Stavros Komineas

SciPost Phys. 18, 037 (2025) · published 30 January 2025 | · pdf

Skyrmions in an antiferromagnet can travel as solitary waves in stark contrast to the situation in ferromagnets. Traveling skyrmion solutions have been found numerically in chiral antiferromagnets. We study head-on collision events between two skyrmions. We find that the result of the collision depends on the initial velocity of the skyrmions. For small velocities, the skyrmions shrink as they approach, then bounce back and eventually acquire almost their initial speed. For larger velocities, the skyrmions approach each other and shrink until they become singular points at some finite separation and are eventually annihilated. Considering skyrmion energetics, we can determine the regimes of the different dynamical behaviors. Using a collective co-ordinate approach, we reproduce the dynamics of the collisions including the variation of the size of the skyrmions and collapse above a critical velocity.
Critical analysis of multiple reentrant localization in an antiferromagnetic helix with transverse electric field: Hopping dimerization-free scenario

Sudin Ganguly, Sourav Chattopadhyay, Kallol Mondal, Santanu K. Maiti

SciPost Phys. Core 8, 012 (2025) · published 30 January 2025 | · pdf

Reentrant localization (RL), a recently prominent phenomenon, traditionally links to the interplay of staggered correlated disorder and hopping dimerization, as indicated by prior research. Contrary to this paradigm, our present study demonstrates that hopping dimerization is not a pivotal factor in realizing RL. Considering a helical magnetic system with antiferromagnetic ordering, we uncover spin-dependent RL at multiple energy regions, in the absence of hopping dimerization. This phenomenon persists even in the thermodynamic limit. The correlated disorder in the form of Aubry-André-Harper model is introduced by applying a transverse electric field to the helical system, circumventing the use of traditional substitutional disorder. We conduct a finite-size scaling analysis on the observed reentrant phases to identify critical points, determine associated critical exponents, and examine the scaling behavior linked to localization transitions. Additionally, we explore the parameter space to identify the conditions under which the reentrant phases occur. Described within a tight-binding framework, present work provides a novel outlook on RL, highlighting the crucial role of electric field, antiferromagnetic ordering, and the helicity of the geometry. Potential applications and experimental realizations of RL phenomena are also explored.

3 citations
Free fermions with dephasing and boundary driving: Bethe Ansatz results

Vincenzo Alba

SciPost Phys. Core 8, 011 (2025) · published 30 January 2025 | · pdf

By employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe Ansatz to diagonalize the Liouvillian $\mathcal{L}^{(2)}$ governing the dynamics of the correlator. The majority of its eigenvalues are complex. Precisely, $L(L-1)/2$ complex eigenvalues do not depend on dephasing, apart from a trivial shift. The remaining complex levels are perturbatively related to the dephasing-independent ones for large $L$. The long-time dynamics is governed by a band of real eigenvalues, which contains an extensive number of levels. They give rise to diffusive scaling at intermediate times, when boundaries can be neglected. Moreover, they encode the breaking of diffusion at asymptotically long times. Interestingly, for large loss rate two boundary modes appear in the spectrum. The real eigenvalues correspond to string solutions of the Bethe equations, and can be treated effectively for large chains. This allows us to derive compact formulas for the dynamics of the fermionic density. We check our results against exact diagonalization, finding perfect agreement.

4 citations
Introduction to string theory

Carlo Maccaferri, Fabio Marino, Beniamino Valsesia

SciPost Phys. Lect. Notes 90 (2025) · published 29 January 2025 | · pdf

These are lecture notes of the introductory String Theory course held by one of the authors for the master program of Theoretical Physics at Turin University. The world-sheet approach to String Theory is pedagogically introduced in the framework of the bosonic string and of the superstring.
Closed-channel parameters of Feshbach resonances

Pascal Naidon

SciPost Phys. 18, 036 (2025) · published 29 January 2025 | · pdf

This work investigates how the closed channel of a Feshbach resonance is characterised by experimental observables. Surprisingly, it is found that the two-body observables associated with the Feshbach resonance can be insensitive to the properties of the closed channel. In particular, it is impossible in this situation to determine the energy of the bound state causing the resonance from the usual experimental data. This is the case for all magnetic Feshbach resonances in ultracold atoms, due to their deep two-body interaction potentials. This insensitivity highlights a major difference with Feshbach resonances that involve shallow interaction potentials, such as hadron resonances. It appears however that short-range two-body correlations and three-body observables are affected by a parameter of the closed channel called the "closed-channel scattering length". A photoassociation experiment is proposed to measure this parameter in ultracold atom systems.

1 citation
Gravitational higher-form symmetries and the origin of hidden symmetries in Kaluza-Klein compactifications

Carmen Gómez-Fayrén, Tomás Ortín, Matteo Zatti

SciPost Phys. Core 8, 010 (2025) · published 29 January 2025 | · pdf

We show that, in presence of isometries and non-trivial topology, the Einstein–Hilbert action is invariant under certain transformations of the metric which are not diffeomorphisms. These transformations are similar to the higher-form symmetries of field theories with $p$-form fields. In the context of toroidal Kaluza–Klein compactifications, we show that these symmetries give rise to some of the "hidden symmetries" (dualities) of the dimensionally-reduced theories.

4 citations
Codebase release 1.0 for kdotpy

Wouter Beugeling, Florian Bayer, Christian Berger, Jan Böttcher, Leonid Bovkun, Christopher Fuchs, Maximilian Hofer, Saquib Shamim, Moritz Siebert, Li-Xian Wang, Ewelina M. Hankiewicz, Tobias Kießling, Hartmut Buhmann, Laurens W. Molenkamp

SciPost Phys. Codebases 47-r1.0 (2025) · published 28 January 2025 | · src

The software project kdotpy provides a Python application for simulating electronic band structures of semiconductor devices with k·p theory on a lattice. The application implements the widely used Kane model, capable of reliable predictions of transport and optical properties for a large variety of topological and non-topological materials with a zincblende crystal structure. The application automates the tedious steps of simulating band structures. The user inputs the relevant physical parameters on the command line, for example materials and dimensions of the device, magnetic field, and temperature. The program constructs the appropriate matrix Hamiltonian on a discretized lattice of spatial coordinates and diagonalizes it. The physical observables are extracted from the eigenvalues and eigenvectors and saved as output. The program is highly customizable with a large set of configuration options and material parameters.

1 citation

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