相关论文: Energy-level correlations in chiral symmetric diso…
We study level correlations of disordered systems with chiral unitary symmetry (AIII symmetry). We use a random matrix model with a finite correlation length to derive a supersymmetric nonlinear sigma model. The result is compared with…
We calculate two-point energy level correlation function in weakly disorderd metallic grain with taking account of localization corrections to the universal random matrix result. Using supersymmetric nonlinear sigma model and exactly…
We compute energy level correlations in weakly disordered metallic grains using the fermionic replica method. We use the standard sigma-model approach and show that non--trivial saddle points, which break replica symmetry, must be included…
Parametric energy-level correlation describes the response of the energy-level statistics to an external parameter such as the magnetic field. Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the parametric…
We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the…
The main elements and methods of chiral perturbation theory, the effective field theory of the Standard Model below the scale of spontaneous chiral symmetry breaking, are summarized. Applications to the interactions of mesons and baryons at…
Numerical study of the parametric motion of energy levels in a model system built on Random Matrix Theory is presented. The correlation function of levels' slopes (the so called velocity correlation function) is determined numerically and…
We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
Contrary to conventional wisdom, level repulsion in semiclassical spectrum is not just a feature of classically chaotic systems, but classically integrable systems as well. While in chaotic systems level repulsion develops on a scale of the…
We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…
A brief introduction to the low-energy effective field theory of the standard model, chiral perturbation theory, is presented.
We use the semiclassical approach combined with the scaling results for the diffusion coefficient to consider the two-level correlation function $R(\varepsilon)$ for a disordered electron system in the crossover region, characterized by the…
Energy spectra of disordered systems share a common feature: if the entropy of the quenched disorder is larger than the entropy of the dynamical variables, the spectrum is locally that of a random energy model and the correlation between…
The critical behaviour of three-dimensional disordered systems is investigated by analysing the spectral fluctuations of the energy spectrum. Our results suggest that the initial symmetries (orthogonal, unitary and symplectic) are broken by…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
Chiral perturbation theory is a very general expansion method which can be applied to any dynamical system which has continuous global symmetries and in which the ground state breaks some of these spontaneously. In these lectures we explain…
We use a combination of perturbation theory, holography, supersymmetric localization, integrability, and numerical conformal bootstrap methods to constrain the energy-energy correlator in $\text{SU}(N_c)$ ${\mathcal N}=4$ SYM at finite…
We study the correlation between the energy spectra of two disordered Hamiltonians of the form $H_a=H_{0a}+s_{a}\varphi$ ($a=1,2$) with $H_{0a}$ and $\varphi$ drawn from random distributions. We calculate this correlation function…
We resolve an apparent contradiction between numeric and analytic results for one-dimensional disordered systems with power-law spectral correlations. The conflict arises when considering rigorous results that constrain the set of…