Related papers: The Hagedorn--Hermite Correspondence
We formulate a new quasi-Hermitian delta-shell pseudopotential for higher partial wave scattering, and show that any such potential must have an energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads to a complete…
Single-Hessian Gaussian wavepacket dynamics (GWD) significantly reduces the computational burden of Heller's local harmonic GWD, while maintaining comparable accuracy in approximating vibronic spectra. Here, we provide a new, symplectic…
In this letter, we experimentally investigate the directional characteristics of propagating, finite-amplitude wave packets in lattice materials, with an emphasis on the functionality enhancement due to the nonlinearly-generated higher…
Daubechies-type theorems for localization operators are established in the multi-variate setting, where Hagedorn wavepackets are identified as the proper substitute of the Hermite functions. The class of Reinhardt domains is shown to be the…
A remarkable mathematical property -- somehow hidden and recently rediscovered -- allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. That opens the possibility to get the wavefunctions from the…
Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…
We analyze conditions under which a projection from the vector-valued Jack or Macdonald polynomials to scalar polynomials has useful properties, especially commuting with the actions of the symmetric group or Hecke algebra, respectively,…
In this paper, we report results for the wave packet dynamics in a class of quasiperiodic chains consisting of two types of weakly coupled clusters. The dynamics are studied by means of the return probability and the mean square…
For matrix model and QFT, we discuss how dual gravitational geometry emerges from matrix degrees of freedom (specifically, adjoint scalars in super Yang-Mills theory) and how operator algebra that describes an arbitrary region of the bulk…
We extend and generalize the construction of Sturm-Liouville problems for a family of Hamiltonians constrained to fulfill a third-order shape-invariance condition and focusing on the "$-2x/3$" hierarchy of solutions to the fourth Painlev\'e…
Regular semisimple Hessenberg varieties are subvarieties of the flag variety $\mathrm{Flag}(\mathbb{C}^n)$ arising naturally in the intersection of geometry, representation theory, and combinatorics. Recent results of…
Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract…
This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…
For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The…
We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an…
An extended multi-hadron operator is developed to extract the spectra of irreducible representations in the finite volume. The irreducible representations of the cubic group are projected using a coordinate-space operator. The correlation…
We study Toeplitz-type operators with respect to specific wavelets whose Fourier transforms are related to Laguerre polynomials. On the one hand, this choice of wavelets underlines the fact that these operators acting on wavelet subspaces…
A $\mathbb{D}$-semi-classical weight is one which satisfies a particular linear, first order homogeneous equation in a divided-difference operator $\mathbb{D}$. It is known that the system of polynomials, orthogonal with respect to this…
We study generalized Hermite polynomials with rectangular matrix arguments arising in multivariate statistical analysis and the theory of zonal polynomials. We show that these are well-suited for expressing the Wiener-Ito chaos expansion of…
In this note we discuss the relationship between the generating functions of some Hermite polynomials $H$, $ \sum\limits_{j=0}^\infty H_{j\cdot n}(u) z^n/n!$, generalized Airy-Heat equations…