Ultraviolet Properties of the Spinless, One-Particle Yukawa Model

We consider the one-particle sector of the spinless Yukawa model, which describes the interaction of a nucleon with a real field of scalar massive bosons (neutral mesons). The nucleon as well as the mesons have relativistic dispersion relations. In this model we study the dependence of the nucleon mass shell on the ultraviolet cut-off $\Lambda$. For any finite ultraviolet cut-off the nucleon one-particle states are constructed in a bounded region of the energy-momentum space. We identify the dependence of the ground state energy on $\Lambda$ and the coupling constant. More importantly, we show that the model considered here becomes essentially trivial in the limit $\Lambda\to\infty$ regardless of any (nucleon) mass and self-energy renormalization. Our results hold in the small coupling regime.Comment: 30 pages, typos corrected, references extende

The Mass Shell of the Nelson Model without Cut-Offs

The massless Nelson model describes non-relativistic, spinless quantum particles interacting with a relativistic, massless, scalar quantum field. The interaction is linear in the field. We analyze the one particle sector. First, we construct the renormalized mass shell of the non-relativistic particle for an arbitrarily small infrared cut-off that turns off the interaction with the low energy modes of the field. No ultraviolet cut-off is imposed. Second, we implement a suitable Bogolyubov transformation of the Hamiltonian in the infrared regime. This transformation depends on the total momentum of the system and is non-unitary as the infrared cut-off is removed. For the transformed Hamiltonian we construct the mass shell in the limit where both the ultraviolet and the infrared cut-off are removed. Our approach is constructive and leads to explicit expansion formulae which are amenable to rigorously control the S-matrix elements.Comment: explanations added, typos correcte

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density $\to\infty$). Our estimates allow us to interchange the thermodynamic with the mean-field limit.Comment: 27 pages, typos corrected, a few more explanations adde

Dynamics of Sound Waves in an Interacting Bose Gas

We consider a non-relativistic quantum gas of $N$ bosonic atoms confined to a box of volume $\Lambda$ in physical space. The atoms interact with each other through a pair potential whose strength is inversely proportional to the density, $\rho=\frac{N}{\Lambda}$, of the gas. We study the time evolution of coherent excitations above the ground state of the gas in a regime of large volume $\Lambda$ and small ratio $\frac{\Lambda}{\rho}$. The initial state of the gas is assumed to be close to a \textit{product state} of one-particle wave functions that are approximately constant throughout the box. The initial one-particle wave function of an excitation is assumed to have a compact support independent of $\Lambda$. We derive an effective non-linear equation for the time evolution of the one-particle wave function of an excitation and establish an explicit error bound tracking the accuracy of the effective non-linear dynamics in terms of the ratio $\frac{\Lambda}{\rho}$. We conclude with a discussion of the dispersion law of low-energy excitations, recovering Bogolyubov's well-known formula for the speed of sound in the gas, and a dynamical instability for attractive two-body potentials.Comment: 42 page

Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

We show that, in a model where a non-relativistic particle is coupled to a quantized relativistic scalar Bose field, the embedded mass shell of the particle dissolves in the continuum when the interaction is turned on, provided the coupling constant is sufficiently small. More precisely, under the assumption that the fiber eigenvectors corresponding to the putative mass shell are differentiable as functions of the total momentum of the system, we show that a mass shell could exist only at a strictly positive distance from the unperturbed embedded mass shell near the boundary of the energy-momentum spectrum.Comment: Revised version: a remark added at the end of Section

Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED

We consider a class of translation invariant models of non-relativistic QED with net charge. Under certain natural assumptions we prove that ground states do not exist in the Fock space

Power Scheduling Method for Grid Integration of a PV-BESS CHB Inverter With SOC Balancing Capability

The paper deals with a single-phase photovoltaic (PV) inverter based on the Cascaded H-Bridge (CHB) topology for Low Voltage (LV) grid. A distributed architecture of PV sources integrated with battery energy storage systems (BESS) is proposed with the particularity of avoiding the use of dc-dc converters. A method of compensating for the short-term daily variability of PV energy is also presented. The control implements power scheduling to ensure that constant active power is fed into the grid at every predetermined time interval (e.g., every quarter of an hour). Furthermore, a dedicated hybrid modulation scheme based on a sorting algorithm for balancing the state of charge (SOC) of the single cells is proposed. Numerical investigations are carried out on a 19-level CHB inverter implemented in a PLECS®(i.e., the simulation platform for power electronic systems from Plexim) environment to validate the feasibility and effectiveness of the proposed control strategy

Towards a construction of inclusive collision cross-sections in the massless Nelson model

The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field theory. Relying on these insights, we take first steps towards a non-perturbative construction of inclusive collision cross-sections in the massless Nelson model. We show that our proposal is consistent with the standard scattering theory in the absence of the infrared problem and discuss its status in the infrared-singular case.Comment: 23 pages, LaTeX. As appeared in Ann. Henri Poincar\'

Male differentiation patterns in two polyphenic sister species of the genus Onthophagus Latreille, 1802 (Coleoptera: Scarabaeidae): a geometric morphometric approach

This paper focuses on morphological (both shape and size) differences that quite similar polyphenic sister species evolve during divergence processes. Traits were analysed using a geometrical morphometric approach, which has the ability to evidence also very subtle differences in shape. As a case study, we considered males of the dung beetle sister species pair Onthophagus taurus and Onthophagus illyricus (Coleoptera, Scarabaeidae); these species represent a typical example of polyphenic trait expression concerning the facultative development of horns and considerable body size differences. External shape morphology failed to discriminate O. taurus from O. illyricus, whereas the reproductive system shape showed significant interspecific discrimination power. However, the head of O. taurus was significantly larger than that of O. illyricus and the reverse was true for the elytra. The two species also showed different allometric values of the head with respect to body size. This complex pattern of interspecific morphological divergence is discussed in the light of the differential trait divergence rate hypothesis. In both species, differences between major and minor forms concern the overall shape of head and pronotum: we suggest that such different forms, which likely reflect morphological readjustment to accommodate horns of considerable bulk and disproportionate length, may be nevertheless advantageously used by the two male morphs in their alternative reproductive tactics. Male genitalia sizes were virtually constant with respect to body size; however, the ratio between phallotheca and body size was significantly higher in minor males, in keeping with the hypothesis of a higher investment in genitalia borne by this morph. Resume Cet article porte sur les differences morphologiques (au niveau de la forme et de la taille) que deux especes voisines polypheniques ont evolue au cours des processus de divergence. L'etude utilise les methodes de la morphometrie geometrique, ayant la capacite de mettre en evidence des differences subtiles entre les formes. Comme modele d'etude nous avons considere les males de deux especes voisines de coleopteres, Onthophagus taurus et Onthophagus illyricus (Coleoptera, Scarabaeidae), qui representent un exemple typique d'expression polyphenique des traits morphologiques concernant des differences importantes de la taille du corps et le developpement facultatif des cornes. L'analyse a mis en evidence que la forme des traits de la morphologie externe ne permette pas de distinguer O. taurus par rapport aO. illyricus, alors que la forme des structures genitales masculines montre un signifiant pouvoir de discrimination interspecifique. Cependant, la tete de O. taurus a une taille plus grande par rapport aO. illyricus, et l'inverse est vrai pour la taille des elytres. Les deux especes montrent aussi une difference au niveau des valeurs allometriques de la taille de la tete respect a la taille du corps. Ce complexe pattern de differences morphologiques interspecifiques est discute sous l'hypothese d'un taux de divergence et d'evolution differentiele entre traits morphologiques differentes. Dans chaque espece, les differences entre les males minor et major concernent la forme generale de la tete et du pronotum: on suggere que ces differences de forme, qui refletent probablement des changements morphologiques necessaires a accommoder des cornes d'un poids considerable et d'une longueur disproportionnee, sont, peut-etre, cependant avantageuses dans les differentes strategies reproductives utilisees par le deux morphes. La taille de la phallotheca est resultee virtuellement constant respect a la taille du corps; cependant, les resultats de la standardisation entre la taille de la phallotheca et la taille du corps sont significativement plus hauts dans les mâles minor, en accord avec l'hypothese d'un plus important investissement dans le systeme reproductif soutenu par cette morphe