无序系统与神经网络

Dynamics of class II neurons, firing frequencies of which are strongly regulated by the inherent neuronal property, have been extensively studied since the formulation of the Hodgkin--Huxley model in 1952. However, how class II neurons…

We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards-Anderson Ising model of a spin glass in arbitrary dimension. Given a specific ground state, suppose the coupling value…

Spin qubits in quantum dots are a compelling platform for fault-tolerant quantum computing due to the potential to fabricate dense two-dimensional arrays with nearest neighbour couplings, a requirement to implement the surface code.…

During training, weight matrices in machine learning architectures are updated using stochastic gradient descent or variations thereof. In this contribution we employ concepts of random matrix theory to analyse the resulting stochastic…

We investigate the appearance of mobility edges in a one-dimensional non-Hermitian tight-banding model with alternating hopping constants and slowly varying quasi-periodic on-site potentials. Due to the presence of slowly varying exponent,…

We study the two-dimensional disordered topological superconductor with Hubbard interactions. When the magnitude of the pairing potential is tuned to special values, this interacting model is exactly solvable even when disorders are imposed…

In [arXiv:2311.08980], it was shown that if the limit of the free energy in a non-convex vector spin glass model exists, it must be a critical value of a certain functional. In this work, we extend this result to multi-species spin glass…

In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the…

Results regarding spin glass models are, to this day, mainly confined to models with Ising spins. Spin glass models with continuous spins exhibit interesting new physical behaviors related to the additional degrees of freedom, but have been…

In this paper, we study the critical behaviors in the non-Hermitian disorder Aubry-Andr\'{e} (DAA) model, and we assume the non-Hermiticity is introduced by nonreciprocal hopping. We employ the localization length $\xi$, the inverse…

The correlated Erd\"os-R\'enyi random graph ensemble is a probability law on pairs of graphs with $n$ vertices, parametrized by their average degree $\lambda$ and their correlation coefficient $s$. It can be used as a benchmark for the…

We demonstrate that slow growth of the number entropy following a quench from a local product state is consistent with many-body localization. To do this we construct a random circuit l-bit model with exponentially localized l-bits and…

The classification of gapped phases of non-interacting fermions hinges on the tenfold symmetries and on the spatial dimension. The notion of dimension leads to a well defined demarcation between bulk and edge. Here we explore the nature of…

Hyperbolic lattices, formed by tessellating the hyperbolic plane with regular polygons, exhibit a diverse range of exotic physical phenomena beyond conventional Euclidean lattices. Here, we investigate the impact of disorder on hyperbolic…

We study the behavior of spread complexity in the context of non-Hermitian many-body localization Transition (MBLT). Our analysis has shown that the singular value spread complexity is capable of distinguishing the ergodic and many-body…

Despite increasing demands for the thermodynamic data of liquids in a wide range of science and engineering fields, there is a still a considerable lack of reliable data over a wide range of temperature ($T$) and pressure conditions. The…

Disordered alloys of silver and gold have been in the interest of the condensed matter community for decades since they are the prototype of the ideal solid solution due to the chemical similarity of their constituents and due to their…

This paper introduces Gaussian disorder, characterized by two parameters:the expected value and the standard deviation.Studying this type of disorder enhances our understanding of how many-body localization (MBL) transition is influenced by…

Amorphous solids form an enormous and underutilized class of materials. In order to drive the discovery of new useful amorphous materials further we need to achieve a closer convergence between computational and experimental methods. In…

Charge transport in amorphous semiconductors is considerably more complicated than process in crystalline materials due to abundant localized states. In addition to device-scale characterization, spatially resolved measurements are…