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Novel analytic solutions are derived for integrals that involve the generalized Marcum Q-function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for the specific cases of the generic integrals.…
We introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in finite lattice. We introduce the $L$-operator related with the $U_q(sl_2)$ $R$-matrix, and…
Semi-local density functionals for the exchange-correlation energy of electrons are extensively used as it produce realistic and accurate results for finite and extended systems. The choice of techniques play crucial role in constructing…
A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schr\"odinger equation. The local symmetries of the potential are encoded into…
The multiplicative (or geometric) calculus is a non-Newtonian calculus derived from an arithmetic in which the operations of addition/subtraction/multiplication are replaced by multiplication/division/exponentiation. A major difference…
In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the…
Over the past two decades, many studies in the Density Functional Theory context revealed new aspects and properties of strongly correlated superfluid quantum systems in numerous configurations that can be simulated in experiments. This was…
By the quenched lattice QCD simulation for two nucleons with finite scattering energy, validity of the delivative expansion of the general nucleon-nucleon potential U(r,r') = V(r, {\nabla}_r) \delta^3(r-r') is studied. The relative kinetic…
We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and $\mathcal{PT}$-symmetric QFTs. Finite-density QCD is symmetric under the…
Inspired by general relativity, we suggest an approach for long-range potential scattering. In scattering theory, there is a general theory for short-range potential scattering, but there is no general theory for long-range potential…
We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation $\,n\,$ and a wave number $\,\vec K\,$ restricted to the Brillouin zone. A noncompact formulation of…
A nontrivial conformally invariant model is obtained via generalization the method of obtaining conformally invariant models in $2D$ Euclidean space to the Euclidean space with dimension $D>2$. This method was previously developed by E.S.…
I discuss several theoretical tools which are useful for analyzing perturbative and non-perturbative problems in quantum chromodynamics, including (a) the light-cone Fock expansion, (b) the effective charge $\alpha_V$, (c) conformal…
We derive the exchange-correlation potential corresponding to the nonlocal van der Waals density functional [M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)]. We use this potential…
New approach to computation of canonical partition functions in $N_f=2$ lattice QCD is presented. We compare results obtained by new method with results obtained by known method of hopping parameter expansion. We observe agreement between…
In this paper, we introduce a novel first-order derivative for functions on a lattice graph, and establish its weak (1, 1) estimate as well as strong (p, p) estimate for p > 1 in weighted spaces. This derivative is designed to reconstruct…
We present improved wave functions for the ground state, Laughlin quasihole and quasiparticle excitations of the fractional quantum Hall effect. These depend explicitly on the effective strength of Coulomb interaction and reproduce…
A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the…
We formulate a method for calculating the hadron-hadron scattering amplitudes at nonzero chemical potential ($\mu$) in the hadronic phase at zero temperature, where the baryon number symmetry remains to be violated. Although it is widely…
We describe recent three-flavor QCD lattice data for the pressure, speed of soun d and interaction measure at nonzero temperature and vanishing chemical potentia l within a virial expansion. For the deconfined phase we use a…