Showing papers by "International School for Advanced Studies published in 2023"

Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model

Abstract: Quantum scrambling plays an important role in understanding thermalization in closed quantum systems. By this effect, quantum information spreads throughout the system and becomes hidden in the form of non-local correlations. Alternatively, it can be described in terms of the increase in complexity and spatial support of operators in the Heisenberg picture, a phenomenon known as operator growth. In this work, we study the disordered fully-connected Sachdev-Ye-Kitaev (SYK) model, and we demonstrate that scrambling is absent for disorder-averaged expectation values of observables. In detail, we adopt a formalism typical of open quantum systems to show that, on average and within charge-conserved sectors, operators evolve in a relatively simple way which is governed by their operator size. This feature only affects single-time correlation functions, and in particular it does not hold for out-of-time-order correlators, which are well-known to show scrambling behavior. Making use of these findings, we develop a cumulant expansion approach to approximate the evolution of equal-time observables. We employ this scheme to obtain analytic results that apply to arbitrary system size, and we benchmark its effectiveness by exact numerics. Our findings shed light on the structure of the dynamics of observables in the SYK model, and provide an approximate numerical description that overcomes the limitation to small systems of standard methods.

Free energy on the sphere for non-abelian gauge theories

Abstract: We compute the $S^d$ partition function of the fixed point of non-abelian gauge theories in continuous $d$, using the $\epsilon$-expansion around $d=4$. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in $d>4$ or $d<4$. In the first case we extrapolate to $d=5$ to test a recently proposed construction of the UV fixed point of $5d$ $SU(2)$ Yang-Mills via a susy-breaking deformation of the $E_1$ SCFT. We find that the $F$ theorem allows the proposed RG flow. In the second case we extrapolate to $d=3$ to test whether QCD$_3$ with gauge group $SU(n_c)$ and $n_f$ fundamental matter fields flows to a CFT or to a symmetry-breaking phase. We find that within the regime with a real gauge coupling near $d=4$ the CFT phase is always favored. For lower values of $n_f$ we compare the average of $F$ between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value $n_f^*$ below which the symmetry-breaking phase takes over.

Spin-Liquid Insulators Can Be Landau’s Fermi Liquids

Abstract: The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge---inspired by the neutral spin-$1/2$ excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state---seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.

Introduction

Abstract: This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book reviews the psycholinguistic field, and offers an integrated view that includes at least linguistics, cognitive neuroscience, and developmental psychology. Linguists tend to have a different reading of the phenomenon. The book indicates a mapping between a stored representation that is abstract in nature (i.e. not particularly tight to any combination of phonemes or graphemes) and the actual input. The representation of diversity doesn’t end with a contrast between the approaches taken by different academic communities. The book also offers a snapshot of the current state of the debate within individual disciplines. It describes several theories that have been proposed in theoretical linguistics to account for the morphological domain. The book discusses morphological awareness, a meta-linguistic task that is very popular in the literature connecting morphological processing and reading development.

Homogenization of discrete thin structures

Abstract: We consider graphs parameterized on a portion X⊂Zd×{1,…,M}k of a cylindrical subset of the lattice Zd×Zk, and perform a discrete-to-continuum dimension-reduction process for energies defined on X of quadratic type. Our only assumptions are that X be connected as a graph and periodic in the first d-directions. We show that, upon scaling of the domain and of the energies by a small parameter ɛ, the scaled energies converge to a d-dimensional limit energy. The main technical points are a dimension-reducing coarse-graining process and a discrete version of the p-connectedness approach by Zhikov.

Prions

Abstract: Prions are defined as proteinaceous infectious particles solely composed of an aberrantly folded endogenous protein devoid of nucleic acids. These novel molecular entities are responsible for numerous but rare neurodegenerative disorders in animals and humans collectively defined as prion diseases. In humans these disorders may have sporadic, genetic or acquired etiology. The aberrantly folded protein is derived from the physiological cellular prion protein ubiquitously expressed in all tissues and particularly abundant in the central nervous system. The molecular mechanisms by which prion proteins convert into prions and accumulate in the nervous system are still elusive. Novel techniques for early detection of prions in affected animals and humans have been recently developed and tested. Currently no cure is available for these fatal disorders.

Collective response to local perturbations: how to evade threats without losing coherence

Abstract: Living groups move in complex environments and are constantly subject to external stimuli, predatory attacks and disturbances. An efficient response to such perturbations is vital to maintain the group's coherence and cohesion. Perturbations are often local, i.e. they are initially perceived only by few individuals in the group, but can elicit a global response. This is the case of starling flocks, that can turn very quickly to evade predators. In this paper, we investigate the conditions under which a global change of direction can occur upon local perturbations. Using minimal models of self-propelled particles, we show that a collective directional response occurs on timescales that grow with the system size and it is, therefore, a finite-size effect. The larger the group is, the longer it will take to turn. We also show that global coherent turns can only take place if i) the mechanism for information propagation is efficient enough to transmit the local reaction undamped through the whole group; and if ii) motility is not too strong, to avoid that the perturbed individual leaves the group before the turn is complete. No compliance with such conditions results in the group's fragmentation or in a non-efficient response.

Shedding light on human olfaction: electrophysiological recordings from sensory neurons in acute slices of olfactory epithelium

Abstract: Abstract The COVID-19 pandemic brought attention to our limited understanding of human olfactory physiology. While the cellular composition of the human olfactory epithelium is similar to that of other vertebrates, its functional properties are largely unknown. We prepared acute slices of human olfactory epithelium from nasal biopsies and used the whole-cell patch-clamp technique to record electrical properties of cells. We measured voltage-gated currents in human olfactory sensory neurons and supporting cells, and action potentials in neurons. Additionally, inward currents and action potentials responses of neurons to a phosphodiesterase inhibitor indicated that the transduction cascade involves cAMP as a second messenger. Furthermore, responses to odorant mixtures demonstrated that the transduction cascade was intact in this preparation. This study provides the first electrophysiological characterization of olfactory sensory neurons in acute slices of the human olfactory epithelium, paving the way for future research to expand our knowledge of human olfactory physiology.

An extended physics informed neural network for preliminary analysis of parametric optimal control problems

Abstract: In this work we propose an application of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many research fields, they can be computationally expensive most of all in a real-time and many-query setting. Thus, our main goal is to provide a physics informed learning paradigm to simulate parametrized phenomena in a small amount of time. The physics information will be exploited in many ways, in the loss function (standard physics informed neural networks), as an augmented input (extra feature employment) and as a guideline to build an effective structure for the neural network (physics informed architecture). These three aspects, combined together, will lead to a faster training phase and to a more accurate parametric prediction. The methodology has been tested for several equations and also in an optimal control framework.

Explicit reconstruction of the entanglement wedge via the Petz map

Abstract: We revisit entanglement wedge reconstruction in AdS/CFT using the Petz recovery channel. In the case of a spherical region on the boundary, we show that the Petz map reproduces the AdS-Rindler HKLL reconstruction. Moreover, for a generic subregion of the boundary, we could obtain the same boundary representation of a local bulk field lies in the entanglement wedge as the one proposed earlier in [1, 2] using properties of the modular flow.

Contact Interactions and Gamma Convergence

Abstract: We study contact interactions, a generalization of Albeverio’s point interactions. There are two types of contact interactions, weak and strong; the last type occurs only in a three particle system. Strong contact leads to systems that have an infinite number of bound states with eigenvalues that decrease with a scaling law. We prove that in both the strong and the weak contact cases the hamiltonians are strong resolvent limits of hamiltonians with potentials with support that vanishes with a given scaling law while the $$L^1$$ norm remains constant. In the weak contact case, the approximating hamiltonians must have a zero energy resonance. As applications we describe Bose-Einstein condensation in the low and high density regimes, the Fermi sea in solid state physics and the ground state of Nelson’s polaron.

Filtrations of numerically flat Higgs bundles and curve semistable Higgs bundles on Calabi–Yau varieties

Abstract: Abstract We consider Higgs bundles satisfying a notion of numerical flatness (H-nflatness) that was introduced in [5; 4], and show that they have Jordan-Hölder filtrations whose quotients are stable, locally free and H-nflat. This is applied to show that curve semistable Higgs bundles on simply connected Calabi–Yau varieties have vanishing discriminant.

Fermions

Abstract: Massless fermions (Dirac, Weyl and Majorana) and relevant formalisms are introduced: Lagrangians, equations of motion and spin states. Then they are canonically quantized and in particular the causal Green’s functions are introduced. Their symmetry properties are discussed, and the differences between Weyl and massless Majorana fermions are illustrated. Then follows a short introduction to Clifford algebras. Next the map from Minkowski to Euclidean background via a Wick rotation is described. The final section is devoted to a short introduction to Euclidean field theories.

On SYK traversable wormhole with imperfectly correlated disorders

Abstract: In this paper we study the phase structure of two Sachdev-Ye-Kitaev models (L-system and R-system) coupled by a simple interaction, with imperfectly correlated disorder. When the disorder of the two systems are perfectly correlated, $J_{i_1\cdots i_q}^{(L)}=J_{i_1\cdots i_q}^{(R)}$, this model is known to exhibit a phase transition at a finite temperature between the two-black hole phase at high-temperature and the traversable wormhole phase at low temperature. We find that, as the correlation $\langle J_{i_1\cdots i_q}^{(L)} J_{i_1\cdots i_q}^{(R)}\rangle$ is decreased, the critical temperature becomes lower. At the same time, the transmission between L-system and R-system in the low-temperature phase becomes more suppressed, while the chaos exponent of the whole system becomes larger. Interestingly we also observe that when the correlation is smaller than some q-dependent critical value the phase transition completely disappears in the entire parameter space. At zero temperature, the energy gap becomes larger as we decrease the correlation. We also use a generalized thermofield double state as a variational state. Interestingly, this state coincide with the ground state in the large q limit.