Quantum decay rates in chaotic scattering

This paper presents a novel theoretical framework that reinterprets the cosmological constant problem through a quantum decay perspective. I propose a time-dependent quantum vacuum decay model wherein vacuum energy density gradually decreases through probabilistic processes, naturally explaining the vast 10120 discrepancy between Quantum Field Theory predictions and observed dark energy values. Beyond addressing this longstanding problem, this model reveals a profound connection between quantum decay and time itself, suggesting time is an emergent phenomenon fundamentally linked to quantum decay rates. This perspective offers elegant interpretations of gravitational time dilation, relativistic time dilation, and the cosmic speed limit without modifying general relativity or quantum mechanics, but by unifying their underlying mechanisms. I demonstrate mathematical correspondence between quantum decay rates and relativistic time dilation formulas, providing a microscopic foundation for macroscopic spacetime phenomena. The theory generates specific, testable predictions for precision atomic clock experiments, black hole observations, and cosmological measurements, potentially resolving tensions in current Lambda Cold Dark Matter model data. This framework bridges quantum mechanics and relativity by establishing a common mechanism governing both the cosmological constant and the nature of time, offering a pathway toward reconciling two pillars of modern physics.

We predict and numerically observe strong periodic orbit effects in the properties of weakly open quantum systems with a chaotic classical limit. Antiscars lead to a large number of exponentially narrow isolated resonances when the single-channel (or tunneling) opening is located on a short unstable orbit of the closed system; the probability to remain in the system at long times is thus exponentially enhanced over the random matrix theory prediction. The distribution of resonance widths and the probability to remain are quantitatively given in terms of only the stability matrix of the orbit on which the opening is placed. The long-time remaining probability density is nontrivially distributed over the available phase space; it can be enhanced or suppressed near orbits other than the one on which the lead is located, depending on the periods and classical actions of these other orbits. These effects of the short periodic orbits on quantum decay rates have no classical counterpart, and first appear on times scales much larger than the Heisenberg time of the system. All the predictions are quantitatively compared with numerical data.

The spectroscopy of solid anthracene is examined both experimentally and theoretically. To avoid experimental complications such as self-absorption and polariton effects, ultrathin polycrystalline films deposited on transparent substrates are studied. To separate the contributions from different emitting species, the emission is resolved in both time and wavelength. The spectroscopic data are interpreted in terms of a three-state kinetic model, where two excited states, a high energy state 1 and a low energy state 2, both contribute to the luminescence and are kinetically coupled. Using this model, we analyze the spectral lineshape, relative quantum yield, and relaxation rates as a function of temperature. For state 1, we find that the ratio of the 0-0 vibronic peak to the 0-1 peak is enhanced by roughly a factor of 3.5 at low temperature, while the quantum yield and decay rates also increase by a similar factor. These observations are explained using a theoretical model previously developed for herringbone polyacene crystals. The early-time emission lineshape is consistent with that expected for a linear aggregate corresponding to an edge-dislocation defect. The results of experiment and theory are quantitatively compared at different temperatures in order to estimate that the singlet exciton in our polycrystalline films is delocalized over about ten molecules. Within these domains, the exciton's coherence length steadily increases as the temperature drops, until it reaches the limits of the domain, whereupon it saturates and remains constant as the temperature is lowered further. While the theoretical modeling correctly reproduces the temperature dependence of the fluorescence spectral lineshape, the decay of the singlet exciton appears to be determined by a trapping process that becomes more rapid as the temperature is lowered. This more rapid decay is consistent with accelerated trapping due to increased delocalization of the exciton at lower temperatures. These observations suggest that exciton coherence can play an important role in both radiative and nonradiative decay channels in these materials. Our results show that the spectroscopy of polyacene solids can be analyzed in a self-consistent fashion to obtain information about electronic delocalization and domain sizes.

The notion of a centerpoint of a finite set of points in two and higher dimensions is a generalisation of the concept of the median of a (finite) set of points on the real line. In this paper, we present an algorithm for computing a centerpoint of a set of n points in the plane. The algorithm has complexity O(n) which significantly improves the O(n log3 n) complexity of the previously best known algorithm. We use suitable modifications of the ham-sandwich-cut algorithm and the prune-and-search technique to achieve this improvement.

The study deals with plastic and non-plastic sub-spaces A of the real-line ℝ with the usual Euclidean metric d. It investigates non-expansive bijections, proves properties of such maps, and demonstrates their relevance by hands of examples. Finally, it is shown that the plasticity property of a sub-space A contains at least two complementary questions, a purely geometric and a topological one. Both contribute essential aspects to the plasticity property and get more critical in higher dimensions and more abstract metric spaces.

Core flooding experiments to determine multiphase flow in properties of rock such as relative permeability can show significant fluctuations in terms of pressure, saturation, and electrical conductivity. That is typically not considered in the Darcy scale interpretation but treated as noise. However, in recent years, flow regimes that exhibit spatio-temporal variations in pore scale occupancy related to fluid phase pressure changes have been identified. They are associated with topological changes in the fluid configurations caused by pore-scale instabilities such as snap-off. The common understanding of Darcy-scale flow regimes is that pore-scale phenomena and their signature should have averaged out at the scale of representative elementary volumes (REV) and above. In this work, it is demonstrated that pressure fluctuations observed in centimeter-scale experiments commonly considered Darcy-scale at fractional flow conditions, where wetting and non-wetting phases are co-injected into porous rock at small (<10−6) capillary numbers are ultimately caused by pore-scale processes, but there is also a Darcy-scale fractional flow theory aspect. We compare fluctuations in fractional flow experiments conducted on samples of few centimeters size with respective experiments andin-situmicro-CT imaging at pore-scale resolution using synchrotron-based X-ray computed micro-tomography. On that basis we can establish a systematic causality from pore to Darcy scale. At the pore scale, dynamic imaging allows to directly observe the associated breakup and coalescence processes of non-wetting phase clusters, which follow “trajectories” in a “phase diagram” defined by fractional flow and capillary number and can be used to categorize flow regimes. Connected pathway flow would be represented by a fixed point, whereas processes such as ganglion dynamics follow trajectories but are still overall capillary-dominated. That suggests that the origin of the pressure fluctuations observed in centimeter-sized fractional flow experiments are capillary effects. The energy scale of the pressure fluctuations corresponds to 105-106times the thermal energy scale. This means the fluctuations are non-thermal. At the centimeter scale, there are non-monotonic and even oscillatory solutions permissible by the fractional flow theory, which allow the fluctuations to be visible and—depending on exact conditions—significant at centimeter scale, within the viscous limit of classical (Darcy scale) fractional flow theory. That also means that the phenomenon involves both capillary aspects from the pore or cluster scale and viscous aspects of fractional flow and occurs right at the transition, where the physical description concept changes from pore to Darcy scale.

We prove resolvent estimates for semiclassical operators such as − <it>h</it>2 Δ + <it>V</it>(<it>x</it>) in scattering situations. Provided the set of trapped classical trajectories supports a chaotic flow and is sufficiently filamentary, the analytic continuation of the resolvent is bounded by <it>h</it>− <it>M</it> in a strip whose width is determined by a certain topological pressure associated with the classical flow. This polynomial estimate has applications to local smoothing in Schrödinger propagation and to energy decay of solutions to wave equations.

Using fixed point theorems we discuss continuous solutions of Γ-equivariance for a polynomial-like iterative equation on the real line, where Γ is a closed subgroup of the general linear group GL(R). Our main results guarantee the existence of solutions with certain kinds of symmetry. We show that, under restrictive hypotheses, similar results can be proved in a higher-dimensional case, where the symmetry group is a topologically finitely generated subgroup of the group generated by rotations and dilations in N-dimensional Euclidean space.

31 Nonparametric methods in directional data analysis

The continuum and discrete quasirelativistic one-electron Sturmian basis sets associated with the second-order Dirac–Coulomb equation are constructed by solving appropriate Sturm–Liouville problems. The potential-weighted orthogonality and closure relations obeyed by the members of such sets are discussed. The special case where both quasirelativistic Coulomb Sturmian basis sets are used to obtain solutions to the Gell-Mann–Feynman equation is presented. It is proved that for the continuum quasirelativistic Sturm–Liouville problem, the spectrum of potential strengths is continuous and covers the whole real axis. We have also introduced the complete outgoing continuum quasirelativistic Coulomb wavefunctions and presented the discretization of its radial components. The compact representation of the fully relativistic and quasirelativistic Coulomb Green’s functions is outlined. By making use of the Sturmian expansion of the Coulomb Green’s functions, closed-form expressions of two-photon spontaneous decay rates are derived for arbitrary multipole channels. For the sake of assessing the domain of applicability of quasirelativistic basis sets, an illustrative application is then carried out for two-photon decay rates for hydrogen-like ions. A comparison of present results with reference values previously obtained within a fully relativistic scheme (Bona et al 2014) is undertaken.

We propose a method for designing accurate interpolation formulas on the real axis for the purpose of function approximation in weighted Hardy spaces. In particular, we consider the Hardy space of functions that are analytic in a strip region around the real axis, being characterized by a weight function $w$ that determines the decay rate of its elements in the neighborhood of infinity. Such a space is considered as a set of functions that are transformed by variable transformations that realize a certain decay rate at infinity. Popular examples of such transformations are given by the single exponential (SE) and double exponential (DE) transformations for the SE-Sinc and DE-Sinc formulas, which are very accurate owing to the accuracy of sinc interpolation in the weighted Hardy spaces with single and double exponential weights $w$, respectively. However, it is not guaranteed that the sinc formulas are optimal in weighted Hardy spaces, although Sugihara has demonstrated that they are near optimal. An explicit form for an optimal approximation formula has only been given in weighted Hardy spaces with SE weights of a certain type. In general cases, explicit forms for optimal formulas have not been provided so far. We adopt a potential theoretic approach to obtain almost optimal formulas in weighted Hardy spaces in the case of general weight functions $w$. We formulate the problem of designing an optimal formula in each space as an optimization problem written in terms of a Green potential with an external field. By solving the optimization problem numerically, we obtain an almost optimal formula in each space. Furthermore, some numerical results demonstrate the validity of this method. In particular, for the case of a DE weight, the formula designed by our method outperforms the DE-Sinc formula.

Haemoglobinopathies and the Protection Against Severe Malaria: Probing Cytoadhesion and
\nMechanics of Plasmodium falciparum Infected Erythrocytes
\nAim of this thesis was the probing of the cytoadhesion and the mechanical properties of
\nPlasmodium falciparum infected human wildtype and haemoglobinopathic erythrocytes, to shed
\nlight on the protection mechanism against severe malaria associated with haemoglobin
\npolymorphisms.
\nIn Chapter 3, the cytoadhesion of infected wildtype and haemoglobinopathic erythrocytes was
\nprobed using solid-supported lipid bilayers functionalized with CD36 or ICAM-1, acting as in vitro
\nendothelial cell membrane models. Under static conditions, the binding strength was quantified
\nin terms of the critical pressure of detachment based on cell detachment by laser induced pressure
\nwaves. Additionally, the number of binding events and the critical shear stress of detachment
\nwere determined based on classical parallel plate flow experiments at physiological relevant
\nshear stresses. Furthermore, the shear stress dependent changes in tight adhesion area were
\ninvestigated based on label-free reflection interference contrast microscopy.
\nIn Chapter 4, the parasite induced changes to the erythrocyte mechanics were probed at different
\nparasite stages using label and contact-free flicker spectroscopy, yielding the membrane bending
\nmodulus, the membrane tension, the harmonic membrane confinement by the cytoskeleton and
\nthe apparent cytosolic viscosity.
\nMoreover, a comprehensive image of the intraerythrocytic parasite metabolism was generated
\nusing quantitative scanning X-ray fluorescence microscopy.

Linear modulational and subharmonic dynamics of spectrally stable Lugiato-Lefever periodic waves

A complex number is formed by a real part and an imaginary part, the latter being composed of a real number multiplied by the imaginary unit “i,” defined as the square root of . For this reason, imaginary numbers cannot be placed on the real number line. The geometric representation of complex numbers is done in the so-called complex plane, composed of a real axis and an imaginary axis, orthogonal to the real line. However, from a philosophical point of view, the fact that the imaginary axis is not identified with any axis in three-dimensional Euclidean space raises ontological questions that transcend the well-established mathematical formalism of the set of complex numbers: are imaginary numbers just a sophism, an arbitrary invention, or a true mathematical discovery? Are imaginary numbers a glimpse of a parallel reality that is beyond our perception? In this article, I seek to demonstrate that the imaginary unit can be interpreted as an algebraic ambiguity that arises when representing certain vectors in the real plane as one-dimensional variables. Consequently, we will see how it is possible to express complex numbers in terms of real numbers.

cording to the same law. The engineer can readily produce other examples-some exquisitely pretty, others fair but mundane-from his bag of tricks and handy formulas. With the observation that there exists identity of form in such diverse phenomena, one man might be led into deep philosophical speculations upon the nature of order in the universe, while his more practical brother might shrug it off as interesting but who needs it? An extremist of the former persuasion might pursue the philosophical vision at all costs while his opposite can be imagined campaigning vigorously against such impractical boondoggles. Depending upon ones system of values, speculations such as these will rate a position somewhere along the real number axis from minus to plus infinity. The amazing collection of mathematical topics which we call thetheory of numbers and the British know as the Higher Arithmetic, in similar vein, qualifies to be rated somewhere on the closed interval from the ridiculous to the sublime, its exact position again depending upon the individual system of values. There is no doubt, however, that the subject has intrigued the amateur and challenged the keenest resources of the greatest professionals since Thales. The source of difficulty in this subject lies in the restriction to whole numbers in the problems it considers. But this appears exotic to us who work with the results of the physical sciences and adopt, or inherit, the assumption that physical phenomena are continuous and their measure capable of occupying any point at all along the real line or in manifolds of higher dimensionality. Once in a great while, a genuine number theory problem finds physical application and more rarely,