Related papers: On the large $D$ expansion of Hermitian multi-matr…
The commonly used spatial entropy $h_{r}(\mathcal{U})$ of the multi-dimensional shift space $\mathcal{U}$ is the limit of growth rate of admissible local patterns on finite rectangular sublattices which expands to whole space…
We study finite $N$ aspects of the $O(m)\times O(N-m)$ vector model with quartic interactions in general $2\leq d \leq 6$ spacetime dimensions. This model has recently been shown to display the phenomenon of persistent symmetry breaking at…
We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green functions, we outline…
We study the asymptotic shape of the occupied region for monotone deterministic dynamics in d-dimensional Euclidean space parametrized by a threshold theta, and a Borel set N with positive and finite Lebesgue measure. If A_n denotes the…
Let $L$ be a negative holomorphic line bundle over an $(n-1)$-dimensional complex torus $D$. Let $h$ be a Hermitian metric on $L$ such that the curvature form of the dual Hermitian metric defines a flat K\"ahler metric on $D$. Then $h$ is…
In this paper, our main goal is to achieve the high-order asymptotic expansion of solutions to $\sigma$-evolution equations with different damping types in the $L^2$ framework. Throughout this, we observe the influence of parabolic like…
In order for non-Hermitian (NH) topological effects to be relevant for practical applications, it is necessary to study disordered systems. In the absence of disorder, certain driven-dissipative cavity arrays with engineered non-local…
We analyze the exact formulae for the resistance between two arbitrary notes in a rectangular network of resistors under free, periodic and cylindrical boundary conditions obtained by Wu [J. Phys. A 37, 6653 (2004)]. Based on such…
As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $\mathcal N=2$ 4d superconformal models we consider two special theories with gauge groups $SU(N)$ and…
The Hamming graph $H(d,n)$ is the Cartesian product of $d$ complete graphs on $n$ vertices. Let $m=d(n-1)$ be the degree and $V = n^d$ be the number of vertices of $H(d,n)$. Let $p_c^{(d)}$ be the critical point for bond percolation on…
The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to…
The mobility edge (ME) is a critical energy delineates the boundary between extended and localized states within the energy spectrum, and it plays a crucial role in understanding the metal-insulator transition in disordered or quasiperiodic…
The Dicke model, which describes the collective interaction between an ensemble of atoms and a single-mode photon field, serves as a fundamental framework for studying light-matter interactions and quantum electrodynamic phenomena. In this…
We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices, i.e. of the hermitian matrices $H_n$ with independent Gaussian entries such that $<…
Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems: The topological invariant of the bulk in $d$ dimensions corresponds to the number of $(d-1)$-dimensional boundary…
We define a new large $N$ limit for general $\text{O}(N)^{R}$ or $\text{U}(N)^{R}$ invariant tensor models, based on an enhanced large $N$ scaling of the coupling constants. The resulting large $N$ expansion is organized in terms of a…
Usually duality process keeps energy spectrum invariant. In this paper, we provide a duality, which keeps entanglement spectrum invariant, in order to diagnose quantum entanglement of non-Hermitian non-interacting fermionic systems. We…
Supersymmetric sectors of $\mathcal{N}=4$ super-Yang-Mills theory motivate the study of the partition function for the counting of gauge-invariant functions of $d=2,3$ matrices transforming under the adjoint action of $U(N)$. The partition…
We develop a systematically general theory of one-dimensional (1D) non-Hermitian systems, elaborating on the energy bands, the band degeneracy, and the defectiveness of eigenstates under open boundary conditions. We analyze the band…
We show that the large N expansion in the multi-trace 1 formal hermitian matrix model is governed by the topological recursion of [Eynard and Orantin, 2007] with initial conditions. In terms of a 1d gas of eigenvalues, this model includes -…