Publications

Order by: publication date number of citations

• Quantum Chirikov criterion: Two particles in a box as a toy model for a quantum gas

  Dmitry Yampolsky, N. L. Harshman, Vanja Dunjko, Zaijong Hwang, Maxim Olshanii

  SciPost Phys. 12, 035 (2022) · published 24 January 2022 | Toggle abstract · pdf

  We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter represented by two equal mass particles. To that system, we apply a quantum generalization of Chirikov's criterion for the onset of chaos, i.e. the criterion of overlapping resonances. There, classical nonlinear resonances translate almost verbatim to the quantum language. Quantum mechanics intervenes at a later stage: the resonances occupying less than one Hamiltonian eigenstate are excluded from the chaos criterion. Resonances appear as contiguous patches of low purity unperturbed eigenstates, separated by the groups of undestroyed states---the quantum analogues of the classical KAM tori.

  3 citations

• High-low pressure domain wall for the classical Toda lattice

  Christian B. Mendl, Herbert Spohn

  SciPost Phys. Core 5, 002 (2022) · published 24 January 2022 | Toggle abstract · pdf

  We study the classical Toda lattice with domain wall initial conditions, for which left and right half lattice are in thermal equilibrium but with distinct parameters of pressure, mean velocity, and temperature. In the hydrodynamic regime the respective space-time profiles scale ballisticly. The particular case of interest is a jump from low to high pressure at uniform temperature and zero mean velocity. Thereby the scaling function for the average stretch (also free volume) is forced to change sign. By direct inspection, the hydrodynamic equations for the Toda lattice seem to be singular at zero stretch. In our contribution we report on numerical solutions and convincingly establish that nevertheless the self-similar solution exhibits smooth behavior.

  4 citations

• Particle fluctuations and the failure of simple effective models for many-body localized phases

  Maximilian Kiefer-Emmanouilidis, Razmik Unanyan, Michael Fleischhauer, Jesko Sirker

  SciPost Phys. 12, 034 (2022) · published 21 January 2022 | Toggle abstract · pdf

  We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions with those in the non-interacting case (Anderson localization) and in effective models where only interaction terms diagonal in the Anderson basis are kept. We demonstrate that these types of simple effective models cannot account for the particle number fluctuations observed in the MBL phase of the microscopic model. This implies that assisted and pair hopping terms---generated when transforming the microscopic Hamiltonian into the Anderson basis---cannot be neglected even at strong disorder and weak interactions. As a consequence, it appears questionable if the microscopic model possesses an exponential number of exactly conserved {\it local} charges. If such a set of conserved local charges does not exist, then particles are expected to ultimately delocalize for any finite disorder strength.

  10 citations

• Persistent current of SU(N) fermions

  Wayne J. Chetcuti, Tobias Haug, Leong-Chuan Kwek, Luigi Amico

  SciPost Phys. 12, 033 (2022) · published 21 January 2022 | Toggle abstract · pdf

  We study the persistent current in a system of SU($N$) fermions with repulsive interaction confined in a ring-shaped potential and pierced by an effective magnetic flux. By applying a combination of Bethe ansatz and numerical analysis, we demonstrate that, as a combined effect of spin correlations, interactions and applied flux a specific phenomenon can occur in the system: spinon creation in the ground state. As a consequence, peculiar features in the persistent current arise. The elementary flux quantum, which fixes the persistent current periodicity, is observed to evolve from a single particle one to an extreme case of fractional flux quantum, in which one quantum is shared by all the particles. We show that the persistent current depends on the number of spin components $N$, number of particles and interaction in a specific way that in certain physical regimes has universality traits. At integer filling fractions, the persistent current is suppressed above a threshold of the repulsive interaction by the Mott spectral gap. Despite its mesoscopic nature, the current displays a clear finite size scaling behavior. Specific parity effects in the persistent current landscape hold.

  20 citations

• Generalized dilaton gravity in 2d

  Daniel Grumiller, Romain Ruzziconi, Céline Zwikel

  SciPost Phys. 12, 032 (2022) · published 21 January 2022 | Toggle abstract · pdf

  Generalized dilaton gravity in 2d is the most general consistent deformation of the Jackiw-Teitelboim model that maintains local Lorentz invariance. The action is generically not power-counting renormalizable, thus going beyond the class of models typically studied. Nevertheless, all these models are exactly soluble. We focus on a subclass of dilaton scale invariant models. Within this subclass, we identify a 3-parameter family of models that describe black holes asymptoting to AdS2 in the UV and to dS2 in the IR. Since these models could be interesting for holography, we address thermodynamics and boundary issues, including boundary charges, asymptotic symmetries and holographic renormalization.

  39 citations

• Non-equilibrium Sachdev-Ye-Kitaev model with quadratic perturbation

  Aleksey V. Lunkin, Mikhail V. Feigel’man

  SciPost Phys. 12, 031 (2022) · published 20 January 2022 | Toggle abstract · pdf

  We consider a non-equilibrium generalization of the mixed SYK$_4$+SYK$_2$ model and calculate the energy dissipation rate $W(\omega)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the polaron energy splitting $\omega_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $\omega_R$ and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.

  2 citations

• Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models

  Yacine Ikhlef, Alexi Morin-Duchesne

  SciPost Phys. 12, 030 (2022) · published 20 January 2022 | Toggle abstract · pdf

  In two-dimensional loop models, the scaling properties of critical random curves are encoded in the correlators of connectivity operators. In the dense O($n$) loop model, any such operator is naturally associated to a standard module of the periodic Temperley-Lieb algebra. We introduce a new family of representations of this algebra, with connectivity states that have two marked points, and argue that they define the fusion of two standard modules. We obtain their decomposition on the standard modules for generic values of the parameters, which in turn yields the structure of the operator product expansion of connectivity operators.

  6 citations

• Sterile neutrinos as dark matter candidates

  Joachim Kopp

  SciPost Phys. Lect. Notes 36 (2022) · published 19 January 2022 | Toggle abstract · pdf

  In these brief lecture notes, we introduce sterile neutrinos as dark matter candidates. We discuss in particular their production via oscillations, their radiative decay, as well as possible observational signatures and constraints.

  6 citations

• Magnetisation and Mean Field Theory in the Ising Model

  Dalton A R Sakthivadivel

  SciPost Phys. Lect. Notes 35 (2022) · published 19 January 2022 | Toggle abstract · pdf

  In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine a magnetisation function, and the results of the derivation are interpreted graphically, physically, and mathematically. We give a new interpretation of the self-consistency condition in terms of intersecting surfaces and constrained solution sets. We also include some more general comments on the thermodynamics of the phase transition. We end by evaluating symmetry considerations in magnetisation, and some more subtle features of the Ising model. Together, a self-contained overview of the mean field Ising model is given, with some novel presentation of important results.

  13 citations

• Half-wormholes in SYK with one time point

  Baur Mukhametzhanov

  SciPost Phys. 12, 029 (2022) · published 19 January 2022 | Toggle abstract · pdf

  In this note we study the SYK model with one time point, recently considered by Saad, Shenker, Stanford, and Yao. Working in a collective field description, they derived a remarkable identity: the square of the partition function with fixed couplings is well approximated by a "wormhole" saddle plus a "pair of linked half-wormholes" saddle. It explains factorization of decoupled systems. Here, we derive an explicit formula for the half-wormhole contribution. It is expressed through a hyperpfaffian of the tensor of SYK couplings. We then develop a perturbative expansion around the half-wormhole saddle. This expansion truncates at a finite order and gives the exact answer. The last term in the perturbative expansion turns out to coincide with the wormhole contribution. In this sense the wormhole saddle in this model does not need to be added separately, but instead can be viewed as a large fluctuation around the linked half-wormholes.

  19 citations