Publications

Order by: publication date number of citations

• Ground state topology of a four-terminal superconducting double quantum dot

  Lev Teshler, Hannes Weisbrich, Jonathan Sturm, Raffael L. Klees, Gianluca Rastelli, Wolfgang Belzig

  SciPost Phys. 15, 214 (2023) · published 29 November 2023 | Toggle abstract · pdf

  In recent years, various classes of systems were proposed to realize topological states of matter. One of them are multiterminal Josephson junctions where topological Andreev bound states are constructed in the synthetic space of superconducting phases. Crucially, the topology in these systems results in a quantized transconductance between two of its terminals comparable to the quantum Hall effect. In this work, we study a double quantum dot with four superconducting terminals and show that it has an experimentally accessible topological regime in which the non-trivial topology can be measured. We also include Coulomb repulsion between electrons which is usually present in experiments and show how the topological region can be maximized in parameter space.

  8 citations

• A bound on thermal relativistic correlators at large spacelike momenta

  Souvik Banerjee, Kyriakos Papadodimas, Suvrat Raju, Prasant Samantray, Pushkal Shrivastava

  SciPost Phys. 8, 064 (2020) · published 20 April 2020 | Toggle abstract · pdf

  We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of these correlators is bounded by $e^{-\beta R}$, where $R$ is the radius of the smallest sphere that contains the polygon formed by the momenta. We show that perturbative quantum field theories can saturate this bound through suitably high-order loop diagrams. We also consider holographic theories in $d$-spacetime dimensions, where we show that the leading two-point function of generalized free-fields saturates the bound in $d = 2$ and is {\em below} the bound for $d > 2$. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.

  8 citations

• Harmonic chain far from equilibrium: Single-file diffusion, long-range order, and hyperuniformity

  Harukuni Ikeda

  SciPost Phys. 17, 103 (2024) · published 3 October 2024 | Toggle abstract · pdf

  In one dimension, particles can not bypass each other. As a consequence, the mean-squared displacement (MSD) in equilibrium shows sub-diffusion $MSD(t)\sim t^{1/2}$, instead of normal diffusion $MSD(t)\sim t$. This phenomenon is the so-called single-file diffusion. Here, we investigate how the above equilibrium behaviors are modified far from equilibrium. In particular, we want to uncover what kind of non-equilibrium driving force can suppress diffusion and achieve the long-range crystalline order in one dimension, which is prohibited by the Mermin-Wagner theorem in equilibrium. For that purpose, we investigate the harmonic chain driven by the following four types of driving forces that do not satisfy the detailed balance: (i) temporally correlated noise with the noise spectrum $D(\omega)\sim \omega^{-2\theta}$, (ii) conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $\theta>-1/4$, we observe $MSD(t)\sim t^{1/2+2\theta}$ for large $t$. On the other hand, for the driving forces (i) with $\theta<-1/4$ and (ii)-(iv), MSD remains finite. As a consequence, the harmonic chain exhibits the crystalline order even in one dimension. Furthermore, the density fluctuations of the model are highly suppressed in a large scale in the crystal phase. This phenomenon is known as hyperuniformity. We discuss that hyperuniformity of the noise fluctuations themselves is the relevant mechanism to stabilize the long-range crystalline order in one dimension and yield hyperuniformity of the density fluctuations.

  8 citations

• Out of equilibrium many-body expansion dynamics of strongly interacting bosons

  Rhombik Roy, Barnali Chakrabarti, Arnaldo Gammal

  SciPost Phys. Core 6, 073 (2023) · published 3 November 2023 | Toggle abstract · pdf

  We solve the Schrödinger equation from first principles to investigate the many-body effects in the expansion dynamics of one-dimensional repulsively interacting bosons released from a harmonic trap. We utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) to solve the many-body Schrödinger equation at high level of accuracy. The MCTDHB basis sets are explicitly time-dependent and optimised by variational principle. We probe the expansion dynamics by three key measures; time evolution of one-, two- and three-body densities. We observe when the mean-field theory results to unimodal expansion, the many-body calculation exhibits trimodal expansion dynamics. The many-body features how the initially fragmented bosons independently spreads out with time whereas the mean-field pictures the expansion of the whole cloud. We also present the three different time scale of dynamics of the inner core, outer core and the cloud as a whole. We analyze the key role played by the dynamical fragmentation during expansion. A Strong evidence of the many-body effects is presented in the dynamics of two- and three-body densities which exhibit correlation hole and pronounced delocalization effect.

  8 citations

• Introduction to Hamiltonian formulation of general relativity and homogeneous cosmologies

  Rishabh Jha

  SciPost Phys. Lect. Notes 73 (2023) · published 11 August 2023 | Toggle abstract · pdf

  We give a pedagogical introduction to the Hamiltonian formalism of general relativity at an advanced undergraduate and graduate levels. After covering the mathematical pre-requisites as well as the 3+1-decomposition of spacetime, we proceed to discuss the Arnowitt-Deser-Misner (ADM) formalism (a Hamiltonian approach) of general relativity. Then we proceed to give a brief but self-contained introduction to homogeneous (but not necessarily isotropic) universes and discuss the associated Bianchi classification. We first study their dynamics in the Lagrangian formulation, followed by the Hamiltonian formulation to show the equivalence of both approaches. We present a variety of examples to illustrate the ADM formalism: (i) free & massless scalar field coupled to homogeneous (in particular, Bianchi IX) universe, (ii) scalar field with a potential term coupled to Bianchi IX universe, (iii) electromagnetic field coupled to gravity in general, and (iv) electromagnetic field coupled to Bianchi IX universe.

  8 citations

• Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons

  Jakub Kopyciński, Maciej Łebek, Maciej Marciniak, Rafał Ołdziejewski, Wojciech Górecki, Krzysztof Pawłowski

  SciPost Phys. 12, 023 (2022) · published 14 January 2022 | Toggle abstract · pdf

  Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.

  7 citations

• Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity

  Gerben Oling, Juan F. Pedraza

  SciPost Phys. Core 8, 025 (2025) · published 27 February 2025 | Toggle abstract · pdf

  We demonstrate that the Carroll limit of general relativity coupled to matter captures the chaotic mixmaster dynamics of near-singularity limits. Zooming in on the behavior of general relativity close to spacelike singularities reveals rich and solvable ultra-local Belinski-Khalatnikov-Lifshitz (BKL) dynamics, which we show to be captured by a Carroll limit. Specifically, building on recent work on geometric Carroll expansions of general relativity, we establish that leading-order Carroll gravity, with suitable matter coupling, accurately describes well-known cosmological billiards behavior. Since the Carroll limit implements the ultra-local limit off shell, this opens up the door to a wide range of possible tractable applications, including spatially inhomogeneous setups and the emergence of spikes at late times. This further suggests that Carroll gravity, along with its subleading corrections, could serve as a valuable tool for studying deep infrared physics in AdS/CFT.

  7 citations

• Optimal control of a quantum sensor: A fast algorithm based on an analytic solution

  Santiago Hernández-Gómez, Federico Balducci, Giovanni Fasiolo, Paola Cappellaro, Nicole Fabbri, Antonello Scardicchio

  SciPost Phys. 17, 004 (2024) · published 4 July 2024 | Toggle abstract · pdf

  Quantum sensors can show unprecedented sensitivities, provided they are controlled in a very specific, optimal way. Here, we consider a spin sensor of time-varying fields in the presence of dephasing noise, and we show that the problem of finding the pulsed control field that optimizes the sensitivity (i.e., the smallest detectable signal) can be mapped to the determination of the ground state of a spin chain. We find an approximate but analytic solution of this problem, which provides a lower bound for the sensitivity and a pulsed control very close to optimal, which we further use as initial guess for realizing a fast simulated annealing algorithm. We experimentally demonstrate the sensitivity improvement for a spin-qubit magnetometer based on a nitrogen-vacancy center in diamond.

  7 citations

• Characteristic determinant and Manakov triple for the double elliptic integrable system

  A. Grekov, A. Zotov

  SciPost Phys. 10, 055 (2021) · published 4 March 2021 | Toggle abstract · pdf

  Using the intertwining matrix of the IRF-Vertex correspondence we propose a determinant representation for the generating function of the commuting Hamiltonians of the double elliptic integrable system. More precisely, it is a ratio of the normally ordered determinants, which turns into a single determinant in the classical case. With its help we reproduce the recently suggested expression for the eigenvalues of the Hamiltonians for the dual to elliptic Ruijsenaars model. Next, we study the classical counterpart of our construction, which gives expression for the spectral curve and the corresponding $L$-matrix. This matrix is obtained explicitly as a weighted average of the Ruijsenaars and/or Sklyanin type Lax matrices with the weights as in the theta function series definition. By construction the $L$-matrix satisfies the Manakov triple representation instead of the Lax equation. Finally, we discuss the factorized structure of the $L$-matrix.

  7 citations

• Quantum error correction and large $N$

  Alexey Milekhin

  SciPost Phys. 11, 094 (2021) · published 19 November 2021 | Toggle abstract · pdf

  In recent years quantum error correction (QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error correcting properties of the fermionic sector of various large $N$ theories. Specifically we examine $SU(N)$ matrix quantum mechanics and 3-rank tensor $O(N)^3$ theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large $N$ analysis and do not appeal to a particular form of Hamiltonian or holography.

  7 citations