Related papers: Unitary matrix models and random partitions: Unive…
The most general model with a magnetic impurity coupled to hybridizing and screening channels of a conduction band is considered. The partition function of the system is asymptotically equivalent to that of the multi-component kink plasma…
An expansion of row Markov matrices in terms of matrices related to permutations with repetitions, is introduced.It generalises the Birkhoff-von Neumann expansion of doubly stochastic matrices in terms of permutation matrices (without…
To illustrate the unitarity of the massive gauge field theory described in the foregoing papers, we calculate the scattering amplitudes up to the fourth order of perturbation by the optical theorem and the Landau-Cutkosky rule. In the…
Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such…
We review several problems of conventional Grand Unification and some new approaches. In particular, we discuss strongly coupled Grand Unified Theories. Standard Model may emerge as a low energy effective theory of composite particles in…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
We investigate a driven particle system, a multilane asymmetric exclusion process, where the particle number in every lane is conserved, and stationary state is fully uncorrelated. The phase space has, starting from three lanes and more, an…
The stochastic model of classical system of particles (partons), which dynamics includes random walk in plane as well as processes of death, splitting, annihilation and fusion of partons, is considered. A set of equations for multiparticle…
Concise review of the basic properties of unitary matrix integrals. They are studied with the help of the three matrix models: the ordinary unitary model, Brezin-Gross-Witten model and the Harish-Charndra-Itzykson-Zuber model. Especial…
We explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are…
We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble (CUE). Our study includes the full distribution…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
Many recent advancements in quantum computing leverage strong drives on nonlinear systems for state preparation, signal amplification, or gate operation. However, the interplay within such strongly driven system introduces multi-scale…
The unification of gauge couplings suggests that there is an underlying (supersymmetric) unification of the strong, electromagnetic and weak interactions. The prediction of the unification scale may be the first quantitative indication that…
In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the…
Using the geometric entanglement measure, we study the scaling of multipartite entanglement in several 1D models at criticality, specifically the linear harmonic chain and the XY spin chain encompassing both the Ising and XX critical…
We present an analytic expression of the nonperturbative free energy of a double-well supersymmetric matrix model in its double scaling limit, which corresponds to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…