Related papers: Fortuity with a single matrix
In this project, we will develop the foundations of quantum mechanics using the methods of supersymmetry. We will discuss the use of the superpotential to derive the supersymmetric partner of a potential in one dimension, and explore…
It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…
Let $A$ be an $n \times n$ random matrix with iid entries over a finite field of order $q$. Suppose that the entries do not take values in any additive coset of the field with probability greater than $1 - \alpha$ for some fixed $0 < \alpha…
We study the underlying extended supersymmetric structure in a system composed of fermions scattered off an infinitely extended static domain wall in the $xz$-plane. As we shall demonstrate, the fermionic scattered states are associated to…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore…
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…
We study some sorts of dimensionally-deconstructed models for supersymmetric (Euclidean) quantum mechanics, or zero-dimensional field theory. In these models, we assign bosonic and fermionic variables to vertices and edges of a graph. We…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
The $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(2)$ and $SU(3)$ gauge symmetry groups is studied. A numerical method to find finite matrix representation of the Hamiltonian is presented in detail. It is used to find spectrum…
We study numerically various wave functions in a gauged matrix quantum mechanics of six commuting hermitian $N\times N$ matrices. Our simulations span ranges of $N$ up to 10000. This system is a truncated and quenched version of N=4 SYM…
I review some recent works on the Hermitean one-matrix and d-dimensional gauge-invariant matrix models. Special attention is paid to solving the models at large-N by the loop equations. For the one-matrix model the main result concerns…
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite, leading to a severe reduction of the free parameters. We review the investigation of FUTs based on SU(5) in the context of…
We study N=1 supersymmetric U(N) gauge theory coupled to an adjoint scalar superfiled with a cubic superpotential containing a multi trace term. We show that the field theory results can be reproduced from a matrix model which its potential…
We propose a new and intuitive metric for aleatoric uncertainty quantification (UQ), the prevalence of class collisions defined as the same input being observed in different classes. We use the rate of class collisions to define the…
We study the phase diagram of the two-dimensional N=1 Wess-Zumino model on the lattice using Wilson fermions and the fermion loop formulation. We give a complete nonperturbative determination of the ground state structure in the continuum…
The lowest representatives of the Form Factors relative to the trace operators of N=1 Super Sinh-Gordon Model are exactly calculated. The novelty of their determination consists in solving a coupled set of unitarity and crossing equations.…
When spatial boundaries are inserted, SUSY can be broken. We show that in an $\mathcal{N}=2$ supersymmetric theory, all the boundary conditions allowed by self-adjointness of the Hamiltonian break $\mathcal{N}=2$ SUSY while only a few of…
We study and classify $SU(5)$-GUT completions of accidental composite dark matter models. These theories postulate new vectorlike confining dark color dynamics and give an accidentally stable baryonic dark matter candidate. In realistic…
Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such…