Related papers: Random matrix ensembles with random interactions: …
A known result in random matrix theory states the following: Given a random Wigner matrix $X$ which belongs to the Gaussian Orthogonal Ensemble (GOE), then such matrix $X$ has an invariant distribution under orthogonal conjugations. The…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…
Recent developments [Kamenev and Mezard, cond-mat/9901110, cond-mat/9903001; Yurkevich and Lerner, cond-mat/9903025; Zirnbauer, cond-mat/9903338] have revived a discussion about applicability of the replica approach to description of…
We prove that the asymptotic behavior of the recoupling coefficients of the symmetric group is characterized by a quantum marginal problem -- namely, by the existence of quantum states of three particles with given eigenvalues for their…
Two problems of the Standard Model, associated with the introduction of non-gauge interactions and with the introduction of an electromagnetic field as a linear combination of fields on which various gauge groups are implemented, are…
An attempt is made to describe random matrix ensembles with unitary invariance of measure (UE) in a unified way, using a combination of Tracy-Widom (TW) and Adler-Shiota-Van Moerbeke (ASvM) approaches to derivation of partial differential…
Random matrix theory has proven very successful in the understanding of the spectra of chaotic systems. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles, the Gaussian…
We propose a model based on the gauge group $SU(4)\times SU(2)_L\times SU(2)_R$ where the Dirac masses of all the known fermions are generated as one-loop radiative corrections. We are able to generate realistic quark and lepton masses and…
We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble…
We apply concepts of random differential geometry connected to the random matrix ensembles of the random linear operators acting on finite dimensional Hilbert spaces. The values taken by random linear operators belong to the Liouville…
Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study…
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by…
One of the necessary steps in constructing high precision option of KKMC was to install the double bremsstrahlung matrix element for the process e+ e- to nu_e bar nu_e into the scheme of Coherent Exclusive Exponentiation. The process is…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…
A SUSY SO(10) $\times A_4$ GUT model is constructed for fermion masses and mixing by introducing a minimal set of low dimensional Higgs representations needed to break the guage symmetry down to $SU(3)_c \times U(1)_{em}$. The hierarchy of…
We study the effective matrix model for for gauge fields and fermions on a quantum computer. We use the Variational Quantum Eigensolver (VQE) using IBM QISKit for the effective matrix model for SU(2) and SU(3) including fermions in the…
The pattern of quark and lepton mass matrices is unexplained in the standard model of particle interactions. I propose the novel idea of a progressive gauge U(1) symmetry where it is a reflection of the regressive electroweak symmetry…
Several phenomenological features of fermion masses and mixings can be accounted for by a simple model for fermion mass matrices, which suggests an underlying U(2) horizontal symmetry. In this context, it is also proposed how an approximate…
We study the renormalizable group equations (RGEs) of the extended strong and weak gauge couplings in an ${\rm SU}(8)$ theory, where three-generational SM fermions are non-trivially embedded. This framework was previously found to generate…
We study low energy implications of F-theory GUT models based on $SU(5)$ extended by a $U(1)'$ symmetry which couples non-universally to the three families of quarks and leptons. This gauge group arises naturally from the maximal…