相关论文: Ramp from Replica Trick

We study the dynamics of a quantum or classical particle in a two-dimensional rotating anisotropic harmonic potential. By a sequence of symplectic transformations for constant rotation velocity we find uncoupled normal generalized…

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form…

System reliability assessment(SRA) is a challenging task due to the limited experimental data and the complex nature of the system structures. Despite a long history dating back to \cite{buehler1957confidence}, exact methods have only been…

In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…

Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…

In this paper we discuss the $R$-matrix approach to treat the subthreshold resonances for the single-level and one channel, and for the single-level and two channel cases. In particular, the expression relating the ANC with the observable…

Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…

We introduce a new method to reconstruct the density matrix $\rho$ of a system of $n$-qubits and estimate its rank $d$ from data obtained by quantum state tomography measurements repeated $m$ times. The procedure consists in minimizing the…

Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…

In recent years, pi-conjugated polymers are attracting considerable interest in view of their light-dependent torsional reorganization around the pi-conjugated backbone, which determines peculiar light-emitting properties. Motivated by the…

The probability tomography approach developed for the scalar resistivity method is here extended to the 2D tensorial apparent resistivity acquisition mode. The rotational invariant derived from the trace of the apparent resistivity tensor…

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of…

We use a fully self-consistent Hartree$-$Fock (HF) based continuum random phase approximation (CRPA) to calculate strength functions $S(E)$ and transition densities $\rho_t(r)$ for isoscalar giant resonances with multipolarities $L = 0$, 1…

We study iterative methods based on Krylov subspaces for low-rank approximation under any Schatten-$p$ norm. Here, given access to a matrix $A$ through matrix-vector products, an accuracy parameter $\epsilon$, and a target rank $k$, the…

We study the long-time behaviour of the growth-fragmentation equation, a nonlocal linear evolution equation describing a wide range of phenomena in structured population dynamics. We show the existence of a spectral gap under conditions…

We consider a random walk in a truncated cone $K_N$, which is obtained by slicing cone $K$ by a hyperplane at a growing level of order $N$. We study the behaviour of the Green function in this truncated cone as $N$ increases. Using these…

We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…

We develop techniques to compute the k-th Moment of the Eigenvalue-statistic for a random Matrix M the entries of which do not have to be necessarily Independent. The dependence is controlled via an equivalence relation on the pairs of the…

It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time \tau using periodic-orbit theory. Two types of contributing pairs of orbits were…

A problem of statistical estimation of a Hermitian nonnegatively definite matrix of unit trace (for instance, a density matrix in quantum state tomography) is studied. The approach is based on penalized least squares method with a…