Related papers: Improved variational approach for the Cornell pote…
Cornell potential is known to represent the quark-antiquark confinement interaction. In addition to the Cornell potential, there have been other interactions in the literature that demonstrate confining structure in the quark-antiquark…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
In the framework of chiral perturbation theory virtual photons are included. We calculate the divergences of the generating functional to one loop and determine the structure of the local action that incorporates the counterterms which…
The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the…
Within the framework of the quark model and the variational method, the bound states of four heavy quarks (tetraquarks) are investigated. The basis variational wave functions are chosen in the Gaussian form. The matrix elements of the…
The heavy quark potential and particularly the one proposed by Richardson to incorporate both asymptotic freedom and linear confinement is analyzed in terms of a generalized Borel Transform recently proposed. We were able to obtain, in the…
We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated…
In the variational approach to quantum statistics, a smearing formula describes efficiently the consequences of quantum fluctuations upon an interaction potential. The result is an effective classical potential from which the partition…
The construction of trial wave functions based on neural networks combined with the variational Monte Carlo method is discussed. The mathematical formulation for representing quantum states as artificial neural networks is introduced. The…
Based on the Dirac approach we have developed the relativistic vision of the WKB method for centrally symmetrical potential with mixed Lorenz structure. We have obtained relativistic wavefunctions of light quark and the new rule of…
Spontaneous breaking of chiral symmetry is investigated in the Hamiltonian approach to QCD in Coulomb gauge. The quark wave functional is determined by the variational principle using an ansatz which goes beyond the commonly used BCS-type…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
The quark-antiquark potential is constructed by making use of a new analytic running coupling in QCD. This running coupling arises under ``analytization'' of the renormalization group equation. The rising behavior of the quark-antiquark…
We study the two-pion exchange potential at next-to-next-to-leading order in chiral effective field theory. We propose a new cut-off scheme for the pion loop integrals based on spectral function regularization. We show that this method…
The chiral symmetry is applied to an extended constituent quark potential model. With random phase approximation (RPA), the model comprises sea quark excitations. To obtain the pseudoscalar $\pi$ meson as a Goldstone boson, the quark…
We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear and perturbative methods. In the Newton method, the parameter variations are calculated from the…
Radial wave functions for power-law potentials are approximated with the help of power-law substitution and explicit summation of the leading constituent WKB series. Our approach reproduces the correct behavior of the wave functions at the…
The electromagnetic tensor for inclusive electron scattering off the pion, ($W^{\mu\nu}$), for momentum transfers such that $q^+=0$, ($q^+=q^0+q^3$) is shown to obey a sum-rule for the component $W^{++}$. From this sum-rule, one can define…
Many body trial wave functions are the key ingredient for accurate Quantum Monte Carlo estimates of total electronic energies in many electron systems. In the Coupled Electron-Ion Monte Carlo method, the accuracy of the trial function must…
This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The…