Related papers: Auxiliary field method for the square root potenti…
We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field $V(x)=g_{1}x^{-1}+g_{2}x^{-2}$. For $g_{2}>0$ and $g_{1}<0$, the potential is known as the…
We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…
Heavy quark bound state systems, mesons and hybrids, are discussed in the framework of the QCD effective field theory called potential Non-Relativistic QCD.
We show that a non-relativistic particle in a combined field of a magnetic monopole and 1/r^2 potential reveals a hidden, partially free dynamics when the strength of the central potential and the charge-monopole coupling constant are…
The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
The Pair Approximation method is applied to the antiferromagnetic Heisenberg-Ising spin-1/2 bilayer with a simple cubic crystalline structure. The method allows for self-consistent calculations of thermodynamic quantities, based on the…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
We obtain eigenvalues and eigenfunctions of the Schr\"{o}dinger equation with a hyperbolic double-well potential. We consider exact polynomial solutions for some particular values of the potential-strength parameter and also numerical…
We derive an analytic form for the Heisenberg-Euler Lagrangian in the limit where the component of the electric field parallel to the magnetic field is small. We expand these analytic functions to all orders in the field strength…
The 'square root' of the interacting Dirac equation is constructed. The obtained equations lead to the Yang-Mills superfield with the appropriate equations of motion for the component fields.
We develop a theory describing the superfield extension of the 2-form field coupled to usual chiral and real scalar superfield and find the one-loop K\"{a}hlerian effective potential in this theory.
Electron-positron pair production by the superposition of two laser pulses with different frequencies and amplitudes is analyzed as a particular realization of the assisted dynamic Schwinger effect. It is demonstrated that, within a…
We extend our discussion of effective actions for stochastic partial differential equations to systems that give rise to a Martin-Siggia-Rose (MSR) type of action. This type of action naturally arises when one uses the many-body formalism…
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to…
We suggest an extension of the Yang-Mills theory which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large…
The Auxiliary-Field Quantum Monte Carlo (AFQMC) algorithm is a powerful quantum many-body method that can be used successfully as an alternative to standard quantum chemistry approaches to compute the ground state of many body systems, such…
By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a…
Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality.…
An analytical expression for the current through a single level quantum dot for arbitrary strength of the on-site electron-electron interaction is derived beyond standard mean-field theory. By describing the localised states in terms of…