4,671 research outputs found
A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term
The properties of a nonlinear oscillator with an additional term ,
characterizing the isotonic oscillator, are studied. The nonlinearity affects
to both the kinetic term and the potential and combines two nonlinearities
associated to two parameters, and , in such a way that for
all the characteristics of of the standard isotonic system are
recovered. The first part is devoted to the classical system and the second
part to the quantum system. This is a problem of quantization of a system with
position-dependent mass of the form , with a
-dependent non-polynomial rational potential and with an additional
isotonic term. The Schr\"odinger equation is exactly solved and the
-dependent wave functions and bound state energies are explicitly
obtained for both .Comment: two figure
Muon Anomalous Magnetic Moment and Lepton Flavor Violating Tau Decay in Unparticle Physics
We study effects of unparticle physics on muon g-2 and LFV tau decay
processes. LFV interactions between the Standard Model sector and unparticles
can explain the difference of experimental value of muon g-2 from the Standard
Model prediction. While the same couplings generate LFV tau decay, we found
that LFV coupling can be of O(0.1 ... 1) without conflict with experimental
bounds of LFV tau decay if the scaling dimension of unparticle operator d_{U} >
1.6.Comment: 12 pages, 7 figure
Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability
The existence of a Lagrangian description for the second-order Riccati
equation is analyzed and the results are applied to the study of two different
nonlinear systems both related with the generalized Riccati equation. The
Lagrangians are nonnatural and the forces are not derivable from a potential.
The constant value of a preserved energy function can be used as an
appropriate parameter for characterizing the behaviour of the solutions of
these two systems. In the second part the existence of two--dimensional
versions endowed with superintegrability is proved. The explicit expressions of
the additional integrals are obtained in both cases. Finally it is proved that
the orbits of the second system, that represents a nonlinear oscillator, can be
considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure
Models of Cosmic Order: Physical Expression of Sacred Space Among the Ancient Maya
The archaeological record, as well as written texts, oral traditions, and iconographic representations, express the Maya perception of cosmic order, including the concepts of quadripartite division and layered cosmos. The ritual act of portioning and layering created spatial order and was used to organize everything from the heavens to the layout of altars. These acts were also metaphors for world creation, world order, and establishing the center as a position of power and authority. This article examines the articulations of these concepts from the level of caches to the level of regions from the past and present in an attempt to understand these ancient perceptions. We emphasize that basic organizational notions of the cosmos permeate all societal levels and argue that scholars should expand their focus to include how the sacred landscape and its related ideology were reproduced in the lives of everyday people
Compound transfer matrices: Constructive and destructive interference
Scattering from a compound barrier, one composed of a number of distinct
non-overlapping sub-barriers, has a number of interesting and subtle
mathematical features. If one is scattering classical particles, where the wave
aspects of the particle can be ignored, the transmission probability of the
compound barrier is simply given by the product of the transmission
probabilities of the individual sub-barriers. In contrast if one is scattering
waves (whether we are dealing with either purely classical waves or quantum
Schrodinger wavefunctions) each sub-barrier contributes phase information (as
well as a transmission probability), and these phases can lead to either
constructive or destructive interference, with the transmission probability
oscillating between nontrivial upper and lower bounds. In this article we shall
study these upper and lower bounds in some detail, and also derive bounds on
the closely related process of quantum excitation (particle production) via
parametric resonance.Comment: V1: 28 pages. V2: 21 pages. Presentation significantly streamlined
and shortened. This version accepted for publication in the Journal of
Mathematical Physic
Synergy between HIV-1 Tat and adenovirus E1A is principally due to stabilization of transcriptional elongation
We studied the combined effects of Tat and general trans-activators, such as E1A and phorbol esters, on human immunodeficiency virus-1 (HIV-1) gene expression. Interaction between these two types of trans-activators may be involved in the transition from transcriptional quiesence during viral latency to active gene expression during productive infection. E1A cooperated with Tat to produce a fourfold greater increase in accumulation of full-length, cytoplasmic HIV-1-directed RNA than is expected if they were acting additively to increase RNA accumulation. Similarly, phorbol 12-myristate 13-acetate (PMA) also cooperated with Tat to elevate HIV RNA levels synergistically. Analysis of transcription rates across the HIV-1-directed transcription unit indicated, unexpectedly, that synergy between Tat and E1A could not be accounted for by increased promoter proximal transcription rates that were merely additive. However, Tat and E1A produced a greater than additive increase in transcription rates in the 3' end of the gene. These findings imply that synergy between Tat and E1A (or other general transcriptional activators) is due principally to stabilization of transcriptional elongation. Furthermore, the observation that Tat elicits only a small increase in promoter proximal transcription in the presence of E1A suggests that the magnitude of the effect of Tat on initiation is decreased when the basal level of transcription is increased. These findings underscore the importance of the ability of Tat to stabilize elongation, as well as to stimulate initiation, in an HIV-1-directed transcription unit
Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators
Ground state energies and wave functions of quartic and pure quartic
oscillators are calculated by first casting the Schr\"{o}dinger equation into a
nonlinear Riccati form and then solving that nonlinear equation analytically in
the first iteration of the quasilinearization method (QLM). In the QLM the
nonlinear differential equation is solved by approximating the nonlinear terms
by a sequence of linear expressions. The QLM is iterative but not perturbative
and gives stable solutions to nonlinear problems without depending on the
existence of a smallness parameter. Our explicit analytic results are then
compared with exact numerical and also with WKB solutions and it is found that
our ground state wave functions, using a range of small to large coupling
constants, yield a precision of between 0.1 and 1 percent and are more accurate
than WKB solutions by two to three orders of magnitude. In addition, our QLM
wave functions are devoid of unphysical turning point singularities and thus
allow one to make analytical estimates of how variation of the oscillator
parameters affects physical systems that can be described by the quartic and
pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl
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