相关论文: A semiclassical approach to the Dirac equation

Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…

We give a formulation of quantum ergodicity for Pauli Hamiltonians with arbitrary spin in terms of a Wigner-Weyl calculus. The corresponding classical phase space is the direct product of the phase space of the translational degrees of…

We show how to relate the full quantum dynamics of a spin-1/2 particle on R^d to a classical Hamiltonian dynamics on the enlarged phase space R^d x S^2 up to errors of second order in the semiclassical parameter. This is done via an…

The Gutzwiller trace formula provides a semiclassical approximation for the density of states of a quantum system in terms of classical periodic orbits. In its original form Gutzwiller derived the trace formula for quantum systems without…

We find out classical particles, starting from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. We recover the results by Mathisson-Papapetrou, hence establishing a…

We study the stroboscopic dynamics of a spin-$S$ object subjected to $\delta$-function kicking in the transverse magnetic field which is generated following the Fibonacci sequence. The corresponding classical Hamiltonian map is constructed…

We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a…

Starting from a continuum constituted by charged tops, we formulate the classical counterpart of a previously obtained covariant continuity-like equation for the spin current. Such a formulism provides an intuitive picture to elucidate the…

We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The…

We study the dynamics of a one-dimensional classical particle in a space and time dependent potential with randomly chosen parameters. The focus of this work is a quasi-periodic potential, which only includes a finite number of Fourier…

We study a class of theories in which space-time is treated classically, while interacting with quantum fields. These circumvent various no-go theorems and the pathologies of semi-classical gravity, by being linear in the density matrix and…

We first review the application of Dirac's method to the dynamics of a classical particle constrained to a circle and its subsequent quantization. Then, we extend the analysis to a particle constrained to move on an ellipse. Particularly,…

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. Gravitational fields can be incorporated as background spacetime if the…

We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…

We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…

Dirac's leaping insight that the normalized anti-commutator of the {\gamma}^{\mu} matrices must equal the timespace signature {\eta}^{\mu}{\nu} was decisive for the success of his equation. The {\gamma}^{\mu}-s are the same in all Lorentz…

We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual…

We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield…

We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We…