Publications

Order by: publication date number of citations

• Localization control born of intertwined quasiperiodicity and non-Hermiticity

  Junmo Jeon, SungBin Lee

  SciPost Phys. Core 6, 077 (2023) · published 9 November 2023 | Toggle abstract · pdf

  Quasiperiodic systems are neither randomly disordered nor translationally invariant in the absence of periodic length scales. Based on their incommensurate order, novel physical properties such as critical states and self-similar wavefunctions have been actively discussed. However, in open systems generally described by the non-Hermitian Hamiltonians, it is hardly known how such quasiperiodic order would lead to new phenomena. In this work, we show that the intertwined quasiperiodicity and non-Hermiticity can give rise to striking effects: perfect delocalization of the critical and localized states to the extended states. In particular, we explore the wave function localization character in the Aubry-André-Fibonacci (AAF) model where non-reciprocal hopping phases are present. Here, the AAF model continuously interpolates the two different limits between metal to insulator transition and the critical states, and the non-Hermiticity is encoded in the hopping phase factors. Surprisingly, their interplay results in the perfect delocalization of the states, which is never allowed in quasiperiodic systems with Hermiticity. By quantifying the localization via the inverse participation ratio and the fractal dimension, we discuss that the non-Hermitian hopping phase leads to delicate control of localization characteristics of the wave function. Our work offers (1) emergent delocalization transition in quasiperiodic systems via non-Hermitian hopping phase and (2) detailed localization control of the critical states. In addition, we suggest an experimental realization of controllable localized, critical and delocalized states, using photonic crystals.

• Massive particle interferometry with lattice solitons

  Piero Naldesi, Juan Polo, Peter D. Drummond, Vanja Dunjko, Luigi Amico, Anna Minguzzi, Maxim Olshanii

  SciPost Phys. 15, 187 (2023) · published 8 November 2023 | Toggle abstract · pdf

  We discuss an interferometric scheme employing interference of bright solitons formed as specific bound states of attracting bosons on a lattice. We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102, 010403 (2009)] for using the scattering of a quantum matter-wave soliton on a barrier in order to create a coherent superposition state of the soliton being entirely to the left of the barrier and being entirely to the right of the barrier. In that proposal, it was assumed that the scattering is perfectly elastic, i.e. that the center-of-mass kinetic energy of the soliton is lower than the chemical potential of the soliton. Here we relax this assumption: By employing a combination of Bethe ansatz and DMRG-based analysis of the dynamics of the appropriate many-body system, we find that the interferometric fringes persist even when the center-of-mass kinetic energy of the soliton is above the energy needed for its complete dissociation into constituent atoms.

• Vacuum-field-induced state mixing

  Diego Fernández de la Pradilla, Esteban Moreno, Johannes Feist

  SciPost Phys. 15, 252 (2023) · published 22 December 2023 | Toggle abstract · pdf

  By engineering the electromagnetic vacuum field, the induced Casimir-Polder shift (also known as Lamb shift) and spontaneous emission rates of individual atomic levels can be controlled. When the strength of these effects becomes comparable to the energy difference between two previously uncoupled atomic states, an environment-induced interaction between these states appears after tracing over the environment. This interaction has been previously studied for degenerate levels and simple geometries involving infinite, perfectly conducting half-spaces or free space. Here, we generalize these studies by developing a convenient description that permits the analysis of these non-diagonal perturbations to the atomic Hamiltonian in terms of an accurate non-Hermitian Hamiltonian. Applying this theory to a hydrogen atom close to a dielectric nanoparticle, we show strong vacuum-field-induced state mixing that leads to drastic modifications in both the energies and decay rates compared to conventional diagonal perturbation theory. In particular, contrary to the expected Purcell enhancement, we find a surprising decrease of decay rates within a considerable range of atom-nanoparticle separations. Furthermore, we quantify the large degree of mixing of the unperturbed eigenstates due to the non-diagonal perturbation. Our work opens new quantum state manipulation possibilities in emitters with closely spaced energy levels.

• Higher-order corrections to the kinetic mass definition for the bottom and the charm quarks

  Matteo Fael

  SciPost Phys. Proc. 7, 026 (2022) · published 21 June 2022 | Toggle abstract · pdf

  In these proceedings we discuss the relation between the kinetic and the on-shell schemes for the bottom and the charm quarks and present the methods for the calculation of the mass relation to higher orders in perturbative QCD. The bottom mass in the kinetic scheme is a pivotal input parameter in the inclusive determination of $|V_{cb}|$ from $B\to X_c \ell \nu_\ell$ decays. By combining the relation between the kinetic and the on-shell mass with well-know results for the $\overline{\mathrm{MS}}$-on-shell conversion, we obtain a prediction for $m_b^\mathrm{kin}$ based on precise determinations of $\overline{m}_b(\overline{m}_b)$.

• Comments on the negative grade KdV hierarchy

  Y. F. Adans, Jose F. Gomes, G. V. Lobo, A. H. Zimerman

  SciPost Phys. Proc. 14, 014 (2023) · published 23 November 2023 | Toggle abstract · pdf

  The construction of negative grade KdV hierarchy is proposed in terms of a Miura-gauge transformation. Such gauge transformation is employed within the zero curvature representation and maps the Lax operator of the mKdV into its couterpart within the KdV setting. Each odd negative KdV flow is obtained from an odd and its subsequent even negative mKdV flows. The negative KdV flows are shown to inherit the two different vacua structure that characterizes the associated mKdV flows.

• Newton mechanics, Galilean relativity, and special relativity in $\alpha$-deformed binary operation setting

  Won S. Chung, Mahouton N. Hounkonnou

  SciPost Phys. Proc. 14, 024 (2023) · published 23 November 2023 | Toggle abstract · pdf

  We define new velocity and acceleration having dimension of $(Length)^{\alpha}/(Time)$ and $(Length)^{\alpha}/(Time)^2,$ respectively, based on the fractional addition rule. We discuss the formulation of fractional Newton mechanics, Galilean relativity and special relativity in the same setting. We show the conservation of the fractional energy, characterize the Lorentz transformation and group, and derive the expressions of the energy and momentum. The two body decay is discussed as a concrete illustration.

• Classifying irreducible fixed points of five scalar fields in perturbation theory

  Junchen Rong, Slava Rychkov

  SciPost Phys. 16, 040 (2024) · published 1 February 2024 | Toggle abstract · pdf

  Classifying perturbative fixed points near upper critical dimensions plays an important role in understanding the space of conformal field theories and critical phases of matter. In this work, we consider perturbative fixed points of N=5 scalar bosons coupled with quartic interactions preserving an arbitrary subgroup $G\subset O(5)$. We perform an exhaustive algorithmic search over the symmetry groups G which are irreducible and satisfy the Landau condition, so that the fixed point can be reached by fine-tuning a single mass term and there is no need to tune the cubic couplings. We also impose stability of the RG flow in the space of quartic couplings, and reality. We thus prove that there exist no new stable fixed points in d=4-$\epsilon$ dimensions beyond the two known ones: namely the O(5) nvariant fixed point and the Cubic(5) fixed point. This work is a continuation of the classification of such fixed points with N=4 scalars by Toledano, Michel, Toledano and Brézin in 1985 [Phys. Rev. B 31, 7171 (1985)].

• A differential-geometry approach to operator mixing in massless QCD-like theories and Poincaré-Dulac theorem

  Matteo Becchetti

  SciPost Phys. Proc. 7, 032 (2022) · published 21 June 2022 | Toggle abstract · pdf

  We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) = -\frac{\gamma(g)}{\beta(g)} =\frac{\gamma_0}{\beta_0}\frac{1}{g} + \cdots $ determines which different cases of operator mixing can occur, and we review their classification. We derive a sufficient condition for $A(g)$ to be set in the one-loop exact form $A(g) = \frac{\gamma_0}{\beta_0}\frac{1}{g}$. Finally, we discuss the consequences of the unitarity requirement in massless QCD-like theories, and we demonstrate that $\gamma_0$ is always diagonalizable if the theory is conformal invariant and unitary in its free limit at $g =0$.

• Interfacially adsorbed bubbles determine the shape of droplets

  Alessio Squarcini, Antonio Tinti

  SciPost Phys. 15, 164 (2023) · published 16 October 2023 | Toggle abstract · pdf

  The characterization of density correlations in the presence of strongly fluctuating interfaces has always been considered a difficult problem in statistical mechanics. Here we study - by using recently developed exact field-theoretical techniques - density correlations for an interface with endpoints on a wall forming a droplet in 2D. Our framework applies to interfaces entropically repelled by a hard wall as well as to wetting transitions. In the former case bubbles adsorbed on the interface are taken into account by the theory which yields a systematic treatment of finite-size corrections to one- and two-point functions and show how these are related to Brownian excursions. Our analytical predictions are confirmed by Monte Carlo simulations without free parameters. We also determine one- and two-point functions at wetting by using integrable boundary field theory. We show that correlations are long ranged for entropic repulsion and at wetting. For both regimes we investigate correlations in momentum space by generalizing the notion of interface structure factor to semi-confined systems. Distinctive signatures of the two regimes manifest in the structure factor through a term that we identify on top of the capillary-wave one.

• Stochastic representation of the quantum quartic oscillator

  Gennaro Tucci, Stefano De Nicola, Sascha Wald, Andrea Gambassi

  SciPost Phys. Core 6, 029 (2023) · published 14 April 2023 | Toggle abstract · pdf

  Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.