Related papers: Comment on "Simplified LCAO Method for the Periodi…
In this paper we present a historical and scientific account of the development of the theory of the L\"owner-Kufarev classical and stochastic equations spanning the 90-year period from the seminal paper by K.L\"owner in 1923 to recent…
Ellipsoids possess several beautiful properties associated with classical potential theory. Some of them are well known, and some have been forgotten. In this article we hope to bring a few of the "lost" pieces of classical mathematics back…
Periodic orbit theory for classical hyperbolic system is very significant matter of how we can interpret spectral statistics in terms of semiclassical theory. Although pruning is significant and generic property for almost all hyperbolic…
We have reviewed the comment in [3], posted on arXiv.org concerning our recent work in [1]. We reply to the comment in this paper.
We discuss the semiclassical approaches for describing systems with spin-orbit interactions by Littlejohn and Flynn (1991, 1992), Frisk and Guhr (1993), and by Bolte and Keppeler (1998, 1999). We use these methods to derive trace formulae…
Recently Bosc et al. (J Cheminform 11(1): 4, 2019), published an article describing a case study that directly compares conformal predictions with traditional QSAR methods for large-scale predictions of target-ligand binding. We consider…
Recently, the paper B. Georgeot and D.L. Shepelyansky, Phys. Rev. Lett._86_, 5393 (2001) has been criticized [C. Zalka, quant-ph/0110019; L. Di'osi, quant-ph/0110026]. The Letter claims an exponential speedup and reduction in error…
The idea of writing a table of probabilistic data for a quantum or classical system, and of decomposing this table in a compact way, leads to a shortcut for Hardy's formalism, and gives new perspectives on foundational issues.
We consider two dimensional real-valued analytic potentials for the Schr\"odinger equation which are periodic over a lattice $L$. Under certain assumptions on the form of the potential and the lattice $L$, we can show there is a large class…
A comment on a misleading statement contained in [Phys. Rev. A 97, 062115 (2018)]. v2: a typo corrected
The celebrated Kronig-Penney model traditionally has been formulated with square well potentials representing atomic centres. Here, we use a slightly more realistic potential, the truncated harmonic oscillator, in lieu of square well…
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…
In this Letter we extend the proof, by Faraco and Lindberg, of Taylor's conjecture in multiply connected domains to cover arbitrary vector potentials and remove the need to impose conditions on the magnetic field due to gauge invariance.…
We update our paper: The collapse of Bell determinism (Physics Letters A, 359 (2006): 122-125; available online 16 June 2006). First, we point out that Olivier Brunet, using lattice theoretic methods, has recently, and quite independently,…
It is demonstrated that the recently proposed pseudoclassical model for Weyl particles [1] (D.M. Gitman, A.E. Goncalves and I.V. Tyutin, Phys. Rev. D 50 (1994) 5439) is classically inconsistent. A possible way of removing the classical…
We propose a simplification of the full "2 sets" Time dependent Self Interaction Correction (TD-SIC) method, applying the Optimized Effective Potential (OEP) method. The new resulting scheme is called time-dependent "Generalized SIC-OEP". A…
We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole periodic table and we present a complete table of pseudopotential…
Littlewood--Paley theory is a fundamental tool for frequency localization, square-function control, and multiplier analysis, yet a systematic counterpart in the fractional Fourier transform (FrFT) setting has remained incomplete. We develop…
We present pseudo-potential coefficients for the first two rows of the periodic table. The pseudo potential is of a novel analytic form, that gives optimal efficiency in numerical calculations using plane waves as basis set. At most 7…