相关论文: Spinless Salpeter Equation: Analytic Results
In this paper we investigate a family of models for a qubit interacting with a bosonic field. More precisely, we find asymptotic limits of the Hamiltonian as the strength of the interaction tends to infinity. The main result has two…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…
The Dirac equation for the Coulomb problem is restated by incorporating a nonlinear effective interaction into the Dirac Hamiltonian: one keeps the $1/r$ dependence for the Coulomb field, but the coupling constant is modified by a factor…
Dirac Hamiltonian is scaled in the atomic units $\hbar =m=1$, which allows us to take the non-relativistic limit by setting the Compton wavelength $% \lambda \rightarrow 0 $. The evolutions of the spin and pseudospin symmetries towards the…
Coulomb repulsion between two moving electrons loses its spherical symmetry due to relativistic effects. In presence of a uniform positive ion background this asymmetry uncovers an angular dependent attraction potential in the direction of…
We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one…
Nonlocal terms in the Einstein Hilbert(EH) action appears as IR corrections in effective theory of quantum gravity. Here we have considered such an action keeping the terms which are quadratic in Ricci Scalar. We obtain the solution for a…
A spin $\frac 12$ relativistic particle described by a general potential in terms of the sum of the Coulomb potential with a Lorentz scalar potential is investigated via supersymmetry in quantum mechanics.
A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
There is currently much interest in the two-axis countertwisting spin squeezing Hamiltonian suggested originally by Kitagawa and Ueda, since it is useful for interferometry and metrology. No analytical solution valid for arbitrary spin…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We integrate the corresponding Hamiltonian equations in…
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually…
In this work, we consider the relativistic Duffin-Kemmer-Petiau equation for spin-one particles with a nonminimal vector interaction in the presence of minimal uncertainty in momentum. By using the position space representation we exactly…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
The energy relaxation in the spin-polarized disordered electron systems is studied in the diffusive regime. We derived the quantum kinetic equation in which the kernel of electron-electron collision integral explicitly depends on the…
The possibility that leptons, quarks or both might be highly relativistic bound states of a spin-0 and spin-1/2 constituent bound by minimal electrodynamics is discussed. Typically, strongly bound solutions of the Bethe-Salpeter equation…
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin^c-complex under consideration is allowed to be further twisted by certain exterior power…
A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal…