Related papers: Rigorous bounds on Transmission, Reflection, and B…
While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little…
Motivated by the fact that the null-shell of a collapsing black hole can be described by a perfectly reflecting accelerating mirror, we investigate an extension of this model to mirror semi-transparency and derive a general implicit…
Transmission through and reflection from a potential barrier, and the very closely related issue of particle production from a parametric resonance, are topics of considerable general interest in quantum physics. We have developed a rather…
Transmission through a potential barrier, and the related issue of particle production from a parametric resonance, are topics of considerable general interest in quantum physics. The authors have developed a rather general bound on quantum…
One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this article I establish some very general bounds for reflection and transmission coefficients for one-dimensional…
Particle production in cosmology is often efficiently computed in terms of Bogoliubov transforms. Restricting to a particular class of dispersion relationships, we identify a map between the number of particles produced in a special…
Exactly solvable models are interesting for science and education, since they help in scientific search and in understanding of phenomena. Some exact solutions for simple quantum-mechanical models are considered. The models include two…
Our boundary-value approach to quantum processes in the gravitational collapse to a black hole leads to quantum amplitudes (not just probabilities) for transitions between data posed on initial and final hypersurfaces $\Sigma_{I,F}$,…
We study the reflection coefficient, the transmission coefficient and the greybody factors for black holes with topologically non trivial transverse sections in 4 and d-dimensions, in the limit of low energy. Considering a massive scalar…
In this paper we revisit the one-dimensional tunnelling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the…
We investigate Hawking-like particle production in analogue gravity systems with superluminal modified dispersion relations. For a broad class of even, convex, and polynomially bounded dispersion relations, we show that the relevant…
We show the exact solution of Bogoliubov equations at zero-energy in the critical supercurrent state for arbitrary shape of potential barrier. With use of this solution, we prove the absence of perfect transmission of excitations in the…
The familiar approach to quantum radiation following collapse to a black hole proceeds via Bogoliubov transformations, and yields probabilities for final outcomes. In our (complex) approach, we find quantum amplitudes, not just…
We study transmission and reflection properties of a perfectly amplifying as well as absorbing medium analytically by using the tight binding equation. Different expressions for transmittance and reflectance are obtained for even and odd…
Bogoliubov's 1947 approximation, originally developed in the microscopic theory of superfluidity, laid the foundation for solving previously intractable quantum models and later became part of "quantum mathematics". Regarding mathematically…
A brief survey of the author's works on the fundamental conceptual ideas of quantum statistical physics developed by N. N. Bogoliubov and his school was given. The development and applications of the method of quasiaverages to quantum…
We discuss the method of calculating the reflection coefficient using complex trajectory WKB (CWKB) approximation. This enables us to give an interpretation of non-reflecting nature of the potential under certain conditions and clarify some…
The calculation of the Bogoliubov coefficients is a key piece to obtain the reheating temperature of the Universe. In all cases this calculation is performed either in toy models where some derivative of the potential is discontinuous at…
Extending a computation which appeared recently in hep-th/0301173, we compute the transmission and reflection coefficients for massless uncharged scalars and gravitational waves scattered by d>=4 Schwarzschild or d=4 Reissner-Nordstrom…
We exactly calculate the thermal distribution and temperature of Hawking radiation for a two-dimensional charged dilatonic black hole after it has settled down to an "equilibrium" state. The calculation is carried out using the Bogoliubov…