arXiv subjects

A Calogeracos

Publications and source records attributed to A Calogeracos.

7 recordsLinked to original sources

arXiv2001

Radiation from accelerated perfect or dispersive mirrors following prescribed relativistic asymptotically inertial trajectories

We address the question of radiation emission from both perfect and dispersive mirrors following prescribed relativistic trajectories. The trajectories considered are asymptotically inertial: the mirror starts from rest and eventually reverts to motion at uniform velocity. This enables us to provide a description in terms of in and out states. We calculate exactly the Bogolubov alpha and beta coefficients for a specific form of the trajectory, and stress the analytic properties of the amplitudes and the constraints imposed by unitarity. A formalism for the description of emission of radiation from a dispersive mirror is presented.

gr-qc↗

arXiv2000

Supercriticality and Transmission Resonances in the Dirac equation

It is shown that a Dirac particle of mass $m$ and arbitrarily small momentum will tunnel without reflection through a potential barrier $V=U_c(x)$ of finite range provided that the potential well $V=-U_c(x)$ supports a bound state of energy $E=-m.$ This is called a supercritical potential well.

hep-th↗

arXiv1999

History and Physics of the Klein Paradox

The early papers by Klein, Sauter and Hund which investigate scattering off a high step potential in the context of the Dirac equation are discussed to derive the 'paradox' first obtained by Klein. The explanation of this effect in terms of electron-positron production is reassessed. It is shown that a potential well or barrier in the Dirac equation can become supercritical and emit positrons or electrons spontaneously if the potential is strong enough. If the well or barrier is wide enough, a seemingly constant current is emitted. This phenomenon is transient whereas the tunnelling first calculated by Klein is time-independent. It is shown that tunnelling without exponential suppression occurs when an electron is incident on a high barrier, even when the barrier is not high enough to radiate. Klein tunnelling is therefore a property of relativistic wave equations and is not necessarily connected to particle emission. The Coulomb potential is investigated and it is shown that a heavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly, as $Z$ increases the Coulomb barrier should become increasingly transparent to positrons. This is an example of Klein tunnelling. Phenomena akin to supercritical positron emission may be studied experimentally in superfluid $^3$He

quant-ph↗

arXiv1999

Radiation From a Sine-Gordon Soliton Propagating in an External Potential

The interaction of a fast moving sine-Gordon soliton with an external periodic potential is examined. The resulting equation of motion for the collective coordinate representing the position of the soliton is given in relativistic form. We examine the radiation emitted due to the interaction of the soliton with the potential and we calculate the potential dependent part of the time evolution equation for the creation and annihilation operators for fluctuations.

cond-mat↗

arXiv1998

The Continuum Limit and Integral Vacuum Charge

We investigate a commonly used formula which seems to give non-integral vacuum charge in the continuum limit. We show that the limit is subtle and care must be taken to get correct results.

quant-ph↗

arXiv1998

Klein Tunnelling and the Klein Paradox

The Klein paradox is reassessed by considering the properties of a finite square well or barrier in the Dirac equation. It is shown that spontaneous positron emission occurs for a well if the potential is strong enough. The vacuum charge and lifetime of the well are estimated. If the well is wide enough, a seemingly constant current is emitted. These phenomena are transient whereas the tunnelling first calculated by Klein is time-independent. Klein tunnelling is a property of relativistic wave equations, not necessarily connected to particle emission. The Coulomb potential is investigated in this context: it is shown that a heavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly, it is expected that as $Z$ increases the Coulomb barrier will become increasingly transparent to positrons. This is an example of Klein tunnelling.

quant-ph↗

arXiv1995

Spontaneous Fermion Production by a Supercritical Potential Well

A second quantised theory of electrons and positrons in a deep time-dependent potential well is discussed. It is shown that positron production from the well is a natural consequence of Dirac's hole theory when the strength of the well becomes supercritical. A formalism is developed whereby the amplitude for emission of a positron of a given momentum can be calculated. The difference between positron production and electron-positron pair production is demonstrated. Considerations of the vacuum charge and of Levinson's theorem are required for a full description of the problem.

quant-ph↗