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The multiconfiguration Dirac-Fock (MCDF) model uses a linear combination of Slater determinants to approximate the electronic $N$-body wave function of a relativistic molecular system, resulting in a coupled system of nonlinear eigenvalue…
In a multiband Hubbard model the self-consistency relations for the two-body bound-state bands are in the form of a nonlinear eigenvalue problem. Assuming that the resultant eigenvectors form an orthonormal set, e.g., in the strong-binding…
Using shortcuts to adiabaticity, we solve the time-dependent Schroedinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent…
We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac's gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space.…
The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space…
Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…
The Dirac-Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting…
We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing…
Effects of two-body dipolar interactions on the effective permittivity/conductivity of a binary, symmetric, random dielectric composite are investigated in a self-consistent framework. By arbitrarily splitting the singularity of the Green…
The correlated two-particle problem is solved analytically in the presence of a finite cavity. The method is demonstrated here in terms of exactly solvable models for both the cavity as well as the two-particle correlation where the…
The solution of the Breit equation with an instantaneous potential for the case of two spin-1/2 particles in a pseudoscalar bound state is considered. This is then applied to charmonium using a potential of the Cornell type. The masses of…
A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with various forms of including the interaction for the system of the spin-1/2 and spin-0 particles is…
Following Dirac's brane variation prescription, the brane must not be deformed during the variation process, or else the linearity of the variation may be lost. Alternatively, the variation of the brane is done, in a special Dirac frame, by…
In the present work we establish a simple relation between the Dirac equation with a scalar and an electromagnetic potentials in a two-dimensional case and a pair of decoupled Vekua equations. In general these Vekua equations are bicomplex.…
A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the…
We consider two-dimensional (2D) Dirac quantum ring systems formed by the infinite mass constraint. When an Aharonov-Bohm magnetic flux is present, e.g., through the center of the ring domain, persistent currents, i.e., permanent currents…
A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a $\delta$-function potential, which appear naturally in the model.…
A two-particle self-consistency is rarely part of mean-field theories. It is, however, essential for avoiding spurious critical transitions and unphysical behavior. We present a general scheme for constructing analytically controllable…
Some observational constraints on the brane-world based on predictions from specific models in five dimensions, have been recently reported, both on local and cosmological scales. In order to identify the origins of these constraints, the…
Two numerical methods are used to evaluate the relativistic spectrum of the two-centre Coulomb problem (for the $H_{2}^{+}$ and $Th_{2}^{179+}$ diatomic molecules) in the fixed nuclei approximation by solving the single particle…