arXiv subjects
Publications and source records attributed to H. C. Rosu.
Aristotle was the first to declare himself in the class of natural philosophers ({\em physiologoi}) and he was the first physicist because he spelled out the first definitions of some basic physical concepts. Moreover, he was the first encyclopedist of the world and perhaps the greatest
We use the Milne phase function in the continuum part of the spectrum of the particular Coulomb problem that has been employed by Bhaduri, Khare, and Law as an equivalent physical way for calculating the density of zeros of the Riemann's function on the critical line. The Milne function seems to be a promising approximate method to calculate the density of prime numbers
An aperiodic (low frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low frequency regime. In place we introduce a new signal processing tool based on the Ramanujan sums c_q(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasi-periodic versus the time n of the resonance and aperiodic versus the order q of the resonance. New results arise from the use of this Ramanujan-Fourier transform (RFT) in the context of arithmetical and experimental signals
The quantum oscillator thermodynamic actions are the conjugate intensive parameters for the frequency in any frequency changing process. These oscillator actions fulfill simple Riccati equations. Interesting Darboux transformations of the fundamental Planck and pure vacuum actions are discussed here in some detail. It is shown that the one-parameter "Darboux-Transformed-Thermodynamics" refers to superpositions of boson and fermion excitations of positive and negative absolute temperature, respectively. A Darboux generalization of the fluctuation-dissipation theorem is also briefly sketched
Micron-sized black holes do not necessarily have a constant horizon temperature distribution. The black hole remote-sensing problem means to find out the `surface' temperature distribution of a small black hole from the spectral measurement of its (Hawking) grey pulse. This problem has been previously considered by Rosu, who used Chen's modified Moebius inverse transform. Here, we hint on a Ramanujan generalization of Chen's modified Moebius inverse transform that may be considered as a special wavelet processing of the remote-sensed grey signal coming from a black hole or any other distant grey source
We present the statistics of the significant nouns and adjectives of social impact figuring in the nominations of the Nobel prizes in Physics and Chemistry over the period of the awards from 1901 to 2001
We use nonrelativistic supersymmetry, mainly Darboux transformations of the general (one-parameter) type, for the quantum oscillator thermodynamic actions. Interesting Darboux generalizations of the fundamental Planck and pure vacuum cases are discussed in some detail with relevant plots. It is shown that the one-parameter Darboux-transformed Thermodynamics refers to superpositions of boson and fermion excitations of positive and negative absolute temperature, respectively. Recent results of Arnaud, Chusseau, and Philippe physics/0105048 regarding a single mode oscillator Carnot cycle are extended in the same Darboux perspective. We also conjecture a Darboux generalization of the fluctuation-dissipation theorem
We present a simple SUSY N=2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get selfconsistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution
We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^ε$. For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems
The Riccati equation for the Hubble parameter H of barotropic FRW cosmologies in conformal time for κ\neq 0 spatial geometries and in comoving time for the κ=0 geometry, respectively, is generalized to odd Grassmannian time parameters. We obtain a system of simple differential equations for the four supercomponents (two of even type and two of odd type) of the Hubble superfield function {\cal H} that is explicitly solved. The second even Hubble component does not have an evolution governed by general relativity although there are effects of the latter upon it
Zero point quantum fluctuations as seen from non-inertial reference frames are of interest for several reasons. In particular, because phenomena such as Unruh radiation (acceleration radiation) and Hawking radiation (quantum leakage from a black hole) depend intrinsically on both quantum zero-point fluctuations and some appropriate notion of an accelerating vacuum state, any experimental test of zero-point fluctuations in non-inertial frames is implicitly a test of the foundations of quantum field theory, and the Unruh and Hawking effects
Applying standard mathematical methods, it is explicitly shown how the Riccati equation for the Hubble parameter H(η) of barotropic open FRW cosmologies is connected with a Korteweg-de Vries equation for adiabatic index solitons. It is also shown how one can embed a discrete sequence of adiabatic indices of the type n^2({3/2}γ-1)^2 (γ\neq 2/3) in the sech FRW adiabatic index soliton
I apply (i) a classical version of the Ermakov-Lewis procedure and (ii) the strictly isospectral supersymmetric approach to the Schroedinger free fall of the bouncing ball type. In both cases, the Airy function Bi, which in general is eliminated as being unphysical, plays a well-defined role. Relevant plots are displayed
A Darboux-transformed surface gravitational acceleration of the constant gravitational acceleration for a body endowed with an atmospheric layer is shown to turn the atmospheric free fall with quadratic resistance in the opposite motion, i.e., a free rising. Although the atmosphere of such a body may look completely normal, it is the time dependence of its gravitational field that produces this type of motion. The result is a consequence of general, one-parameter-dependent Darboux transformations in mathematical physics
Using the concept of spectral engineering we explore the possibilities of building potentials with prescribed spectra offered by a modified intertwining technique involving operators which are the product of a standard first-order intertwiner and a unitary scaling. In the same context we study the iterations of such transformations finding that the scaling intertwining provides a different and richer mechanism in designing quantum spectra with respect to that given by the standard intertwining
A one-parameter family of time dependent adiabatic indices is introduced for any given type of cosmological fluid of constant adiabatic index by a mathematical method belonging to the class of Darboux transformations. The procedure works for zero cosmological constant at the price of introducing a new constant parameter related to the time dependence of the adiabatic index. These fluids can be the real cosmological fluids that are encountered at cosmological scales and they could be used as a simple and efficient explanation for the recent experimental findings regarding the present day accelerating universe. In addition, new types of cosmological scale factors, corresponding to these fluids, are presented
The Hawking effect and the Unruh effect are two of the most important predictions in the theoretical physics of the last quarter of the 20th century. In parallel to the theoretical investigations there is great interest in the possibility of revealing effects of this type in some sort of experiments. I present a general discussion of the proposals to measure the Hawking and Unruh effects and/or their `analogues' in the laboratory, and I make brief comments on each of them. The reader may also find the various physical pictures corresponding to the two effects which were applied to more common phenomena, and vice versa
This is the first Internet course on elementary quantum mechanics written in Spanish ("castellano") for the benefit of Spanish speaking students. I thank my eight Mexican students at the Institute of Physics, University of Guanajuato, Leon, (IFUG), for the collaboration that made this possible. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves