相关论文: On resumming periodic orbits in the spectra of int…

We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…

This study is concerned with the numerical solution of a class of infinite-horizon linear regulation problems with state equality constraints and output feedback control. We propose two numerical methods to convert the optimal control…

We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for…

We develop a spectral cut-off construction of real-time oscillatory integrals associated with non-autonomous Hamiltonian evolution equations. Let \(H_0\) be a positive self-adjoint reference operator on a Hilbert space \(\Hilb\), and let…

We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…

The Gutzwiller trace formula establishes a profound connection between the quantum spectrum and classical periodic orbits. However, its application is limited by its reliance on the semiclassical saddle point approximation. In this work, we…

Spectral reconstruction is a well studied numerically ill-posed problem which arises due to the relation of the Euclidean correlator to the spectral function via an inhomogeneous Fredholm equation of the first kind. Several different…

Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…

We study the semi-classical behavior of the spectral function of the Schr\"{o}dinger operator with short range potential. We prove that the spectral function is a semi-classical Fourier integral operator quantizing the forward and backward…

Systems exhibiting the Hilbert-space fragmentation are nonergodic, and their Hamiltonians decompose into exponentially many blocks in the computational basis. In many cases, these blocks can be labeled by eigenvalues of statistically…

We derive semiclassical expressions for spectra, weighted by matrix elements of a Gaussian observable, relevant to a range of molecular and mesoscopic systems. We apply the formalism to the particular example of the resonant tunneling diode…

In 2005 a new topological invariant defined in terms of the Brouwer degree of a determinant map, was introduced by Musso, Pejsachowicz and the first name author for counting the conjugate points along a semi-Riemannian geodesic. This…

We review the status of the semiclassical trace formula with emphasis on the particular types of singularities that occur in the Gutzwiller-Voros zeta function for bound chaotic systems. To understand the problem better we extend the…

This paper deals with recovering an unknown vector $\theta$ from the noisy data $Y=A\theta+\sigma\xi$, where $A$ is a known $(m\times n)$-matrix and $\xi$ is a white Gaussian noise. It is assumed that $n$ is large and $A$ may be severely…

A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…

We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting $N$ asymptotically stable periodic orbits. We construct a discrete-time, continuous-space Markov chain,…

We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable potentials. Direct problems in terms of spectral functions…

X-ray spectral fitting of astronomical sources requires convolving the intrinsic spectrum or model with the instrumental response. Standard forward modeling techniques have proven success in recovering the underlying physical parameters in…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

We present randomized algorithms based on block Krylov space method for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using the properties of Chebyshev polynomial and Gaussian random matrix, we…