Related papers: Random Matrix Theory and Classical Statistical Mec…
Extending the argument of Ref.\citen{[4]} to the long-range spectral statistics of classically integrable quantum systems, we examine the level number variance, spectral rigidity and two-level cluster function. These observables are…
The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude…
Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on…
A random matrix ensemble incorporating both GUE and Poisson level statistics while respecting $U(N)$ invariance is proposed and shown to be equivalent to a system of noninteracting, confined, one dimensional fermions at finite temperature.
Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang--Baxter equation, from which…
We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses $U_q\big(\mathfrak{sl}(2)\big)$ invariance due to the choice of open boundary conditions imposed. An…
It is described how one comes to the Wigner-Dyson random matrix theory (RMT) starting from a model of a disordered metal. The lectures start with a historical introduction where basic ideas of the RMT and theory of disordered metals are…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the fundamental $U_q[G_2]$ vertex model. We find four distinct classes of reflection matrices such that half of them are diagonal while the other half…
We suggest that the spectral properties near zero virtuality of three dimensional QCD, follow from a Hermitean random matrix model. The exact spectral density is derived for this family of random matrix models both for even and odd number…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
A new type of quantum transfer matrix, arising as a Cholesky factor for the steady state density matrix of a dissipative Markovian process associated with the boundary-driven Lindblad equation for the isotropic spin-1/2 Heisenberg (XXX)…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend…
We compute the boundary scattering amplitudes of the breathers of the supersymmetric sine-Gordon model using the fusion of the soliton-antisoliton pair scattering with the boundary with a known result of the soliton boundary scattering…
We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…
We study a one-dimensional lattice model of interacting spinless fermions. This model is integrable for both periodic and open boundary conditions, the latter case includes the presence of Grassmann valued non-diagonal boundary fields…
We explain the concepts of computational statistical physics which have proven very helpful in the study of Yang-Mills integrals, an ubiquitous new class of matrix models. Issues treated are: Absolute convergence versus Monte Carlo…
Quantum systems with discrete symmetries can usually be desymmetrized, but this strategy fails when considering transport in open systems with a symmetry that maps different openings onto each other. We investigate the joint probability…
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…
We study statistical properties of the energy spectra of two-dimensional quasiperiodic tight-binding models. The multifractal nature of the eigenstates of these models is corroborated by the scaling of the participation numbers with the…