无序系统与神经网络
Tensor networks provide discrete representations of quantum many-body systems, yet their precise connection to continuum field theories remains relatively poorly understood. Invoking a notion of typicality, we develop a continuum…
The correlation properties of the nonaffine elastic response in strongly disordered materials are investigated using the theory of correlated random matrices and supported by numerical models. While the nonaffine displacement field itself…
We demonstrate a mechanism for the production of massive excitations in graphs. We treat the number of neighbors at each vertex in the graph (degree) as a scalar field. Then we introduce a mechanism inspired by the Higgs mechanism in…
Utilizing the intrinsic history-dependence and nonlinearity of hardware, physical reservoir computing is a promising neuromorphic approach to encode time-series data for in-sensor computing. The accuracy of this encoding critically depends…
Characterizing crystalline energy landscapes is essential to predicting thermodynamic stability, electronic structure, and functional behavior. While machine learning (ML) enables rapid property predictions, the "black-box" nature of most…
We present a systematic numerical investigation of the "entanglement geometry gravity" chain in random tensor networks (RTN) established by the ER EPR conjecture and Jacobson's thermodynamic derivation. First, we verify the kinematic…
The Bott index has become an indispensable tool to probe the topology of quantum matter, particularly in systems lacking translational symmetry. Constructed from a plaquette operator, it retains the phase information while discarding the…
We introduce a solvable spherical model of coupled oscillators with fully random interactions and distributed natural frequencies. Using the dynamical mean-field theory, we derive self-consistent equations for the steady-state response and…
We explore quantum localization phenomena in a system of two coupled tight-binding chains with incommensurate periods. Employing the inverse participation ratio as a measure of localization, we investigate the effects of geometric…
Many data-science applications involve detecting a shared signal between two high-dimensional variables. Using random matrix theory methods, we determine when such signal can be detected and reconstructed from sample correlations, despite…
We analyze the one-pass stochastic gradient descent dynamics of a two-layer neural network with quadratic activations in a teacher--student framework. In the high-dimensional regime, where the input dimension $N$ and the number of samples…
We investigate dense higher-order associative memories in the high storage regime when the stored patterns are biased, namely when the entries of the patterns are not symmetrically distributed around zero. In this setting, the standard…
We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as $1/r^{a}$ with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument.…
We demonstrate that wave amplification enables even weak nonlinearities to reshape linear wave-packet transport in nonreciprocal systems. We study the dynamics of bulk Gaussian wave packets in the Hatano--Nelson model with onsite cubic…
We investigate the localization properties of a generalized SSH model. Numerical and analytical results indicate the emergence of extended states protected by unbounded hopping in this model. Moreover, this protection effect is disrupted by…
We investigate a classical formulation of the Quantum Approximate Optimization Algorithm (QAOA), realized as a Hamiltonian dynamical system of classical kicked tops, which we call the Variational Iterative Rotation Algorithm (VIRAL). The…
Recently, purpose-built analog hardware that can efficiently minimize the Ising energy and thereby solve a variety of combinatorial optimization problems has been receiving widespread attention. In this work, we show how multidimensional,…
It is a folklore belief in the theory of spin glasses and disordered systems that out-of-equilibrium dynamics fail to find stable local optima exhibiting e.g. local strict convexity on physical time-scales. In the context of the…
We introduce a systematic method for expanding general spin-glass Hamiltonians in terms of Mattis interactions, providing a novel perspective for understanding the fundamental differences between short-range Edwards-Anderson (EA) and…
This study investigates the spatial confinement of topological $\pi$-modes in one-dimensional chiral-symmetric systems. In conventional periodic and quasiperiodic structures, edge-mode wave functions inevitably penetrate the bulk. To…