1,588 research outputs found
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 . 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
and the coupling constant. More importantly, we show that the model
considered here becomes essentially trivial in the limit
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
Dynamics of Sound Waves in an Interacting Bose Gas
We consider a non-relativistic quantum gas of bosonic atoms confined to a
box of volume in physical space. The atoms interact with each other
through a pair potential whose strength is inversely proportional to the
density, , of the gas. We study the time evolution of
coherent excitations above the ground state of the gas in a regime of large
volume and small ratio . 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 . 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 . 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
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 ). Our estimates allow us to interchange the thermodynamic
with the mean-field limit.Comment: 27 pages, typos corrected, a few more explanations adde
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
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 PLECSÂź(i.e., the simulation platform for power electronic systems from Plexim) environment to validate the feasibility and effectiveness of the proposed control strategy
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
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 mĂąles minor, en accord avec l'hypothese d'un plus important investissement dans le systeme reproductif soutenu par cette morphe
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