Related papers: Higher order constraints for the ($\beta$-deformed…
Systematic discovery of reduced-order closure models for multi-scale processes remains an important open problem in complex dynamical systems. Even when an effective lower-dimensional representation exists, reduced models are difficult to…
Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…
Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealers has centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these…
We present a family of modified Hermite integrators of arbitrary order possessing superior behaviour for the integration of Keplerian and near-Keplerian orbits. After recounting the derivation of Hermite N-body integrators of arbitrary…
We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…
We introduce $t$-Hermitian forms of arbitrary degree $k$, a natural extension of classical degree $k$ Hermitian forms obtained through a synthesis of the tensor transformation law and the $t$-product of third-order tensors. We show that…
As the Yangian double with center,which is deformed from affine algebra by the additive loop parameter $\hbar$ ,we get the commuting relation and the bosonization of quantum $\hbar$-deformed Virasoro algebra. The corresponding Miura…
We study the beta-deformed matrix models using the method of refined topological string theory. The refined holomorphic anomaly equation and boundary conditions near the singular divisors of the underlying geometry fix the refined…
In this paper we prove that certain matrix elements of vertex operators of deformed W-algebra satisfy Macdonald difference equations and form n! -dimensional space of solutions. These solutions are the analogues of Harish Chandra solutions…
We investigate the preservation of unitarity in a Lorentz and CPT-violating QED model containing higher-order operators. In particular, we consider modifications in the fermion sector with dimension-five operators. The higher-order…
Hurwitz numbers count branched covers of the sphere and have been of interest in various fields of mathematics. Motivated by the Matching-Jack conjecture of Goulden and Jackson, Chapuy and Do\l\k{e}ga recently introduced a notion of…
A direct relation between the conformal formalism for 2d-quantum gravity and the W-constrained KP hierarchy is found, without the need to invoke intermediate matrix model technology. The Kontsevich-Miwa transform of the KP hierarchy is used…
We develop a classification of composite operators without gradients at Anderson-transition critical points in disordered systems. These operators represent correlation functions of the local density of states (or of wave-function…
We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space,…
In this paper, we investigate a class of fractional Hardy type operators $\mathscr{H}_{\beta_{1},\cdots,\beta_{m}}$ defined on higher-dimensional product spaces…
The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irreducible representations of the Spin group. In this paper, we…
This work prolongs recent investigations by Bergeron et al [see 2012 J. Phys. A: Math. Theo. 45 244028] on new SUSYQM coherent states for P\"oschl-Teller potentials. It mainly addresses explicit computations of eigenfunctions and spectrum…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…