Related papers: Instant-Form Approach to Two-Body Systems
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…
We present a new approach to calculate real-time quantum dynamics in complex systems. The formalism is based on the partitioning of a system's environment into "core" and "reservoir" modes, with the former to be treated quantum mechanically…
In a realistic scenario, the evolution of the rotational dynamics of a celestial or artificial body is subject to dissipative effects. Time-varying non-conservative forces can be due to, for example, a variation of the moments of inertia or…
The concept of the Wigner function is used to construct a semi-classical kinetic theory describing the evolution of the axial-current phase-space density of spin-1/2 particles in the relaxation time approximation. The resulting approach can…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
A new technique for constructing the relativistic wave equation for the two-body system composed of the spin-1/2 and spin-0 particles is proposed. The method is based on the extension of the SL(2,C) group to the Sp(4,C) one. The obtained…
We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence…
Dixon's multipoles for a system of N relativistic positive-energy scalar particles are evaluated in the rest-frame instant form of dynamics. The Wigner hyperplanes (intrinsic rest frame of the isolated system) turn out to be the natural…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
The Lagrangian relativistic direct interaction theory in the various forms of dynamics is formulated and its connections with the Fokker-type action theory and with the constrained Hamiltonian mechanics are established. The motion of…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic…
Spectroscopic techniques based on core-level excitations provide powerful tools for probing molecular and electronic structures with high spatial resolution. However, accurately calculating spectral features at the L or M edges is…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…
The three well-known forms of relativistic dynamics are unitarily equivalent and the problem of constructing the current operators can be solved in any form. However the notion of the impulse approximation is reasonable only in the point…
Schrodinger equation with two-component wave function which describes a relativistic spin 1/2 particle in a weak electromagnetic field is obtained. In the same approximation Schrodinger equation with traditional norm condition and…
The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic…
We describe the formalism to compute gravitational-wave observables for compact binaries via the effective field theory framework in combination with modern tools from collider physics. We put particular emphasis on solving the "multi-loop"…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…