Search results for "Mathematical physics"
showing 10 items of 2687 documents
Gravity waves from non-minimal quadratic inflation
2015
We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter cR, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adju…
Precision luminosity measurements at LHCb
2014
Measuring cross-sections at the LHC requires the luminosity to be determined accurately at each centre-of-mass energy $\sqrt{s}$. In this paper results are reported from the luminosity calibrations carried out at the LHC interaction point 8 with the LHCb detector for $\sqrt{s}$ = 2.76, 7 and 8 TeV (proton-proton collisions) and for $\sqrt{s_{NN}}$ = 5 TeV (proton-lead collisions). Both the "van der Meer scan" and "beam-gas imaging" luminosity calibration methods were employed. It is observed that the beam density profile cannot always be described by a function that is factorizable in the two transverse coordinates. The introduction of a two-dimensional description of the beams improves sig…
A family of complex potentials with real spectrum
1999
We consider a two-parameter non-Hermitian quantum mechanical Hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations. Numerical investigation shows that for some values of the potential parameters the Hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.
On the integrability of the extended nonlinear Schrödinger equation and the coupled extended nonlinear Schrödinger equations
2000
We consider the extended nonlinear Schr¨ (ENLS) equation which governs the propagation of nonlinear optical fields in a fibre with higher-order effects such as higher-order dispersion and self-steepening. We show that the ENLS equation does not pass the Painlev´ test. Similarly, we claim that the coupled ENLS equations and N -coupled ENLS equations which govern the simultaneous propagation of two and more nonlinear fields in optical fibres are also not integrable from the Painlev´ e analysis point of view.
Spatially chaotic configurations and functional equations with rescaling
1996
The functional equation is associated with the appearance of spatially chaotic structures in amorphous (glassy) materials. Continuous compactly supported solutions of the above equation are of special interest. We shall show that there are no such solutions for , whereas such a solution exists for almost all . The words `for almost all q' in the previous sentence cannot be omitted. There are exceptional values of q in the interval for which there are no integrable solutions. For example, , which is the reciprocal of the `golden ratio' is such an exceptional value. More generally, if is any Pisot - Vijayaraghavan number, or any Salem number, then is an exceptional value.
Radon transform as a set of probability distributions
2009
It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.
Hysteresis Model of Unconscious-Conscious Interconnection: Exploring Dynamics on m-Adic Trees
2015
The theoretical model outlined in this paper, has been experimentally validated by: H. Kim ,J-Y. Moon ,G.A. Mashour & U. Lee, ''Mechanisms of hysteresis in human brain networks during transitions of consciousness and unconsciousness: Theoretical principles and empirical evidence'', PLOS-Computational Biology, August 30, 2018, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1006424; International audience; In this brief note, we focus attention on a possible implementation of a basic hysteretic pattern (the Preisach one), suitably generalized, into a formal model of unconscious-conscious interconnection and based on representation of mental entities by m-adic numbers. …
Transcranial magnetic resonance imaging-guided focused ultrasound treatment at 1.5 T: a retrospective study on treatment and patient-related paramete…
2020
Objective: To present a retrospective analysis of patient- and sonication-related parameters of a group of patients treated with a transcranial magnetic resonance imaging (MRI)-guided focused ultrasound (tcMRgFUS) system integrated with a 1.5-T MRI unit. Methods: The data obtained from 59 patients, who underwent the tcMRgFUS procedure from January 2015 to April 2019, were retrospectively reviewed for this study. The following data, among others, were mainly collected: skull density ratio (SDR), skull area (SA), number of available transducer elements (Tx), and estimated focal power at target (FP). For each of the four different treatment stages, we calculated the number of sonication proces…
Three-dimensional singletons
1990
The three-dimensional analog of singleton gauge theory turns out to be related to the topological gauge theory of Schwartz and Witten. It is a fully-fledged gauge theory, though it involves only a single scalar field. Real, physical degrees of freedom propagate in 3-space, but they are ‘confined’ in the sense that they cannot be detected locally. The physical Hamiltonian density is not zero, but it is concentrated on the boundary at spatial infinity. This boundary surface, a torus, supports a two-dimensional conformal field theory.
Some topological invariants for three-dimensional flows
2001
We deal here with vector fields on three manifolds. For a system with a homoclinic orbit to a saddle-focus point, we show that the imaginary part of the complex eigenvalues is a conjugacy invariant. We show also that the ratio of the real part of the complex eigenvalue over the real one is invariant under topological equivalence. For a system with two saddle-focus points and an orbit connecting the one-dimensional invariant manifold of those points, we compute a conjugacy invariant related to the eigenvalues of the vector field at the singularities. (c) 2001 American Institute of Physics.