Related papers: Correlation Functions in Disordered Systems
This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary conditions. A sharp convergence rate is obtained for isolated…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is…
The autocorrelation function of spectral determinants is proposed as a convenient tool for the characterization of spectral statistics in general, and for the study of the intimate link between quantum chaos and random matrix theory, in…
This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed) linear autonomous differential equations, and the associate ones of…
We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…
We study a diagonalizable Hamiltonian that is not at first hermitian. Requirement that a measurement shall not change one Hamiltonian eigenstate into another one with a different eigenvalue imposes that an inner product must be defined so…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of…
We study one-parametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semi-conical…
We present here a general iterative formula which gives a (formal) series expansion for the time autocorrelation of smooth dynamical variables, for all Hamiltonian systems endowed with an invariant measure. We add some criteria, theoretical…
Exact eigenvalue correlation functions are computed for large $N$ hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support…
We investigate the effects of randomness in a strongly correlated electron model in one-dimension at half-filling. The ground state correlation functions are exactly written by products of 3$\times$3 transfer matrices and are evaluated…
In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the…
The constraints imposed by asymptotic freedom and analyticity on the large-order behavior of perturbation theory for the electromagnetic current-current correlation function are examined. By suitably applying the renormalization group, the…
Many coordination phenomena are based on a synchronisation process, whose global behaviour emerges from the interactions among the individual parts. Often in Nature, such self-organising mechanism allows the system to behave as a whole and…
We show that eigenvalue correlations in unitary-invariant ensembles of large random matrices adhere to novel universal laws that only depend on a multicriticality of the bulk density of states near the soft edge of the spectrum. Our…
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible…
Identifying the spectrum of the sum of two given Hermitian matrices with fixed eigenvalues is the famous Horn's problem.In this note, we investigate a variant of Horn's problem, i.e., we identify the probability density function (abbr. pdf)…
This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original…