无序系统与神经网络
Neurons in the brain show great diversity in their individual properties and their connections to other neurons. To develop an understanding of how neuronal diversity contributes to brain dynamics and function at large scales we start with…
Structural two level systems (TLSs) ubiquitous in amorphous solids are dramatically sensitive to thermal cycling to about $20$K and then back to low temperature, a process upon which the excitation energy of most TLSs is significantly…
We investigate the ergodicity-to-localization transition in interacting fermion systems subjected to a spatially uniform electric field. For that we employ the recently proposed Tensorflow Equations (TFE), a type of continuous unitary flow…
We present an analytical calculation of the local density of states correlation function $ \beta(\omega) $ in the L\'evy-Rosenzweig-Porter random matrix ensemble at energy scales larger than the level spacing but smaller than the bandwidth.…
Photonic and polaritonic systems offer a fast and efficient platform for accelerating machine learning (ML) through physics-based computing. To gain a computational advantage, however, polaritonic systems must: (1) exploit features that…
Non-Bloch band theory serves as a cornerstone for understanding intriguing non-Hermitian phenomena, such as the skin effect and extreme spectral sensitivity to boundary conditions. Yet this theory hinges on translational symmetry and thus…
We consider algorithmic determination of the $n$-dimensional Sherrington-Kirkpatrick (SK) spin glass model ground state free energy. It corresponds to a binary maximization of an indefinite quadratic form and under the \emph{worst case}…
We give a brief overview of the seminal paper which introduced the Kardar-Parisi-Zhang equation as a paradigmatic model for random growth in 1986. We describe some of the developments to which it gave rise in mathematics and physics over…
This paper develops a neural jamming phase diagram that interprets the emergence of consciousness in large language models as a critical phenomenon in high-dimensional disordered systems.By establishing analogies with jamming transitions in…
We study many-body localization (MBL) in a nearest-neighbor hopping 1D lattice with a slowly varying (SV) on-site potential $U_j = \lambda\cos(\pi\alpha j^s)$ with $0<s<1$. The corresponding non-interacting 1D lattice model is known to have…
Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can…
The detection of the top eigenvalue and its corresponding eigenvector in ensembles of random matrices has significant applications across various fields. An existing method, based on the linear stability of a complementary set of cavity…
Portfolio optimization is a routine asset management operation conducted in financial institutions around the world. However, under real-world constraints such as turnover limits and transaction costs, its formulation becomes a…
This monograph describes nine years of research carried out at the Institute for Electronics, Micro-electronics and Nanotechnologies (IEMN), developed around defining a generic concept for detection, filling a void between metrological…
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We contrast this motion with the motion of a quantum particle in a potential which varies randomly in space and in time,…
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We show that a freely moving particle measured in this way undergoes superdiffusion, while a charged particle moving in a…
We elucidate the different mechanisms of wave localisation in disordered finite systems of subwavelength resonators, where the disorder is in the spatial arrangement of the resonators. To do so, we employ the capacitance matrix formalism…
Quantum two-level systems (TLSs) commonly found at low temperature in amorphous and disordered materials are responsible for decoherence in superconducting Josephson junction qubits particularly because they absorb energy of coherent qubit…
We consider the spreading of a local operator $A$ in one-dimensional systems with Hamiltonian $H$ by calculating the $k$-fold commutator $[H,[H,[...,[H,A]]]]$. We derive bounds for the operator norm of this commutator in free and…
The global phase diagram of the Ashkin-Teller spin glass is calculated in d = 3 spatial dimensions by renormalization-group theory. Depending on the value of the positive or negative four-spin interaction, qualitatively different topologies…