Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Delta transition form factors at large momentum transfer squared Q(2). The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.

Trimer-Tetramer Interwoven States in the Scaling Limit

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Single-Particle Momentum Distributions for Bosonic Trimer States in Two and Three Dimensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Supersymmetric Isospectral Formalism for the Calculation of Near-Zero Energy States: Application to the Very Weakly Bound He-4 Trimer Excited State

We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features are generated by supersymmetric isospectral formalism. The near-zero energy Efimov state in the original potential is effectively trapped in the deep well of the isospectral family and facilitates more accurate calculation of the Efimov state. Application to the first excited state in He-4 trimer is presented.

Messung des Realteils der gebundenen 3 He-Streulänge

Streulängen beschreiben die s-Wellen-Streuung niederenergetischer Neutronen an Kernen. Solche Streuprozesse laufen nahezu ausschließlich über die starke Wechselwirkung ab. Wegen der Spinabhängigkeit der starken Wechselwirkung werden den Multiplett-Streulängen, d.h. den Streulängen der Gesamtspinzustände J, im Allgemeinen verschiedene Werte zugeordnet. Im Experiment sind die Multiplett-Streuzustände an makroskopischen Proben in der Regel nicht unmittelbar zugänglich. Messbar sind jedoch der polarisationsabhängige und -unabhängige Anteil der Streulänge, welche als inkohärente Streulänge und kohärente Streulänge bezeichnet werden und Linearkombinationen der Multiplettstreulängen sind. Durch komplexe Streulängen lässt sich der für reine Streuprozesse entwickelte Formalismus erweitern: Der Imaginärteil der Streulänge beschreibt dann die Absorption von Projektilen im Target. Sämtliche Reaktionsquerschnitte lassen sich als Funktionen der Streulänge angeben. Verbesserte Messungen der 3He-Streulängen sind für die Entwicklung theoretischer Modelle von Wenig-Nukleonen-Systemen wichtig. Für die Systeme (n,D) und (n,T) wurden in den letzten Jahren u.a. präzise theoretische Vorhersagen für die Multiplett-Streulängen gemacht. Die Übereinstimmung mit den experimentellen Ergebnissen untermauert, dass die theoretischen Unsicherheiten dieser Werte nur etwa 1 Promille betragen. Demgegenüber ist die theoretische Behandlung des n-3He-Systems aufwändiger. Bis zu Beginn der 1980er Jahre wurde eine Reihe von Vorhersagen für die Multiplett-Streulängen gemacht, die auf erfolgreichen Dreinukleon-Potentialmodellen basierten, untereinander aber vollkommen inkompatibel waren. Daneben waren zwei disjunkte Wertepaare für die Multiplett-Streulängen mit den experimentellen Ergebnissen verträglich. Obwohl es begründete Argumente zugunsten eines der Wertepaare gab, bestand die Hoffnung auf eine experimentelle Verifikation durch direkte Messung der inkohärenten Streulänge bereits 1980. Die Bestimmung des Realteils der inkohärenten Streulänge liefert in der Multiplettstreulängenebene eine Gerade, die fast orthogonal zum Band des Realteils der kohärenten Streulänge verläuft. Vermutlich aufgrund der unzureichenden Kenntnis der Realteile hat in den letzten Jahren keine nennenswerte Weiterentwicklung der Modelle für das System n–3He stattgefunden. Diese Arbeit entstand in der Absicht, durch polarisierte und unpolarisierte Experimente an 3He quantitative Fakten zur Beurteilung konkurrierender Vier-Nukleonen-Modelle zu schaffen und somit der theoretischen Arbeit auf diesem Feld einen neuen Impuls zu geben. Eine jüngst veröffentlichte theoretische Arbeit [H. M. Hofmann und G. M. Hale. Phys. Rev. C, 68(021002(R)): 1–4, Apr. 2003] zur spinabhängigen Streulänge des 3He belegt, dass die im Rahmen dieser Arbeit unternommenen Anstrengungen auf reges Interesse stoßen. Durch die Anwendung zweier sehr unterschiedlicher experimenteller Konzepte wurden Präzisionsmessungen der Realteile der kohärenten und inkohärenten Neutronenstreulänge des 3He durchgeführt. Während sich die Methode der Neutroneninterferometrie seit Ende der 1970er Jahre als Standardverfahren zur Messung von spinunabhängigen Streulängen etabliert hat, handelt es sich bei der Messung des pseudomagnetischen Präzessionswinkels am Spinecho-Spektrometer um ein neues experimentelles Verfahren. Wir erhalten aus den Experimenten für die gebundenen kohärenten und inkohärenten Streulängen neue Werte, welche die Unsicherheiten im Falle der kohärenten Streulänge um eine Größenordnung, im Falle der inkohärenten Streulänge sogar um den Faktor 30 reduzieren. Die Kombination dieser Resultate liefert verbesserte Werte der, für die nukleare Wenigkörper-Theorie wichtigen, Singulett- und Triplett-Streulängen. Wir erhalten neue Werte für die kohärenten und inkohärenten Anteile des gebundenen Streuquerschnitts, das für die Neutronenstreuung an der 3He-Quantenflüssigkeit wichtige Verhältnis von inkohärentem und kohärentem Streuquerschnitt und für den freien totalen Streuquerschnitt.

Interacting bosons and fermions in three-dimensional optical lattice potentials

This thesis reports on the realization, characterization and analysis of ultracold bosonic and fermionic atoms in three-dimensional optical lattice potentials. Ultracold quantum gases in optical lattices can be regarded as ideal model systems to investigate quantum many-body physics. In this work interacting ensembles of bosonic 87Rb and fermionic 40K atoms are employed to study equilibrium phases and nonequilibrium dynamics. The investigations are enabled by a versatile experimental setup, whose core feature is a blue-detuned optical lattice that is combined with Feshbach resonances and a red-detuned dipole trap to allow for independent control of tunneling, interactions and external confinement. The Fermi-Hubbard model, which plays a central role in the theoretical description of strongly correlated electrons, is experimentally realized by loading interacting fermionic spin mixtures into the optical lattice. Using phase-contrast imaging the in-situ size of the atomic density distribution is measured, which allows to extract the global compressibility of the many-body state as a function of interaction and external confinement. Thereby, metallic and insulating phases are clearly identified. At strongly repulsive interaction, a vanishing compressibility and suppression of doubly occupied lattice sites signal the emergence of a fermionic Mott insulator. In a second series of experiments interaction effects in bosonic lattice quantum gases are analyzed. Typically, interactions between microscopic particles are described as two-body interactions. As such they are also contained in the single-band Bose-Hubbard model. However, our measurements demonstrate the presence of multi-body interactions that effectively emerge via virtual transitions of atoms to higher lattice bands. These findings are enabled by the development of a novel atom optical measurement technique: In quantum phase revival spectroscopy periodic collapse and revival dynamics of the bosonic matter wave field are induced. The frequencies of the dynamics are directly related to the on-site interaction energies of atomic Fock states and can be read out with high precision. The third part of this work deals with mixtures of bosons and fermions in optical lattices, in which the interspecies interactions are accurately controlled by means of a Feshbach resonance. Studies of the equilibrium phases show that the bosonic superfluid to Mott insulator transition is shifted towards lower lattice depths when bosons and fermions interact attractively. This observation is further analyzed by applying quantum phase revival spectroscopy to few-body systems consisting of a single fermion and a coherent bosonic field on individual lattice sites. In addition to the direct measurement of Bose-Fermi interaction energies, Bose-Bose interactions are proven to be modified by the presence of a fermion. This renormalization of bosonic interaction energies can explain the shift of the Mott insulator transition. The experiments of this thesis lay important foundations for future studies of quantum magnetism with fermionic spin mixtures as well as for the realization of complex quantum phases with Bose-Fermi mixtures. They furthermore point towards physics that reaches beyond the single-band Hubbard model.

Relativistic description of 3He(e,e'p)2H

The relativistic distorted-wave impulse approximation is used to describe the 3He(e, e′ p)2H process. We describe the 3He nucleus within the adiabatic hyperspherical expansion method with realistic nucleon-nucleon interactions. The overlap between the 3He and the deuteron wave functions can be accurately computed from a three-body calculation. The nucleons are described by solutions of the Dirac equation with scalar and vector (S–V) potentials. The wave function of the outgoing proton is obtained by solving the Dirac equation with a S–V optical potential fitted to elastic proton scattering data on the residual nucleus. Within this theoretical framework, we compute the cross section of the reaction and other observables like the transverse-longitudinal asymmetry, and compare them with the available experimental data measured at JLab.

Universality of weakly bound dimers and Efimov trimers close to Li-Cs Feshbach resonances

We study the interspecies scattering properties of ultracold Li-Cs mixtures in their two energetically lowest spin channels in the magnetic field range between 800 and 1000 G. Close to two broad Feshbach resonances (FR) we create weakly bound LiCs dimers by radio-frequency association and measure the dependence of their binding energy on the external magnetic field strength. Based on the binding energies and complementary atom loss spectroscopy of three other Li-Cs s-wave FRs we construct precise molecular singlet and triplet electronic ground state potentials using a coupled-channels calculation. We extract the Li-Cs interspecies scattering length as a function of the external field and obtain almost a ten-fold improvement in the precision of the values for the pole positions and widths of the s-wave FRs as compared to our previous work (Pires et al 2014 Phys. Rev. Lett. 112 250404). We discuss implications on the Efimov scenario and the universal geometric scaling for LiCsCs trimers.

Distillable entanglement and area laws in spin and harmonic-oscillator systems

We address the presence of nondistillable (bound) entanglement in natural many-body systems. In particular, we consider standard harmonic and spin-1/2 chains, at thermal equilibrium and characterized by few interaction parameters. The existence of bound entanglement is addressed by calculating explicitly the negativity of entanglement for different partitions. This allows us to individuate a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We discuss how the appearance of bound entanglement can be linked to entanglement-area laws, typical of these systems. Various types of interactions are explored, showing that the presence of bound entanglement is an intrinsic feature of these systems. In the harmonic case, we analytically prove that thermal bound entanglement persists for systems composed by an arbitrary number of particles. Our results strongly suggest the existence of bound entangled states in the macroscopic limit also for spin-1/2 systems.

Many-body theory for systems of composite hadrons

Many-body systems of composite hadrons are characterized by processes that involve the simultaneous presence of hadrons and their constituents. We briefly review several methods that have been devised to study such systems and present a novel method that is based on the ideas of mapping between physical and ideal Fock spaces. The method, known as the Fock-Tani representation, was invented years ago in the context of atomic physics problems and was recently extended to hadronic physics. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, Hermitian Hamiltonians with a clear physical interpretation are obtained. The use of the method in connection with the linked-cluster formalism to describe short-range correlations and quark deconfinement effects in nuclear matter is discussed. As an application of the method, an effective nucleon-nucleon interaction is derived from a constituent quark model and used to obtain the equation of state of nuclear matter in the Hartree-Fock approximation.

EXOTIC CARBON SYSTEMS IN TWO-NEUTRON HALO THREE-BODY MODELS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Exotic neutron-rich nuclei in a three-body model

We present results for spatial distributions of weakly-bound three-body systems, derived from a universal scaling function that depends on the mass ratio of the particles, as well as on the nature of the subsystems. © 2007 American Institute of Physics.

Strong Local Passivity in Finite Quantum Systems

Passive states of quantum systems are states from which no system energy can be extracted by any cyclic (unitary) process. Gibbs states of all temperatures are passive. Strong local (SL) passive states are defined to allow any general quantum operation, but the operation is required to be local, being applied only to a specific subsystem. Any mixture of eigenstates in a system-dependent neighborhood of a nondegenerate entangled ground state is found to be SL passive. In particular, Gibbs states are SL passive with respect to a subsystem only at or below a critical system-dependent temperature. SL passivity is associated in many-body systems with the presence of ground state entanglement in a way suggestive of collective quantum phenomena such as quantum phase transitions, superconductivity, and the quantum Hall effect. The presence of SL passivity is detailed for some simple spin systems where it is found that SL passivity is neither confined to systems of only a few particles nor limited to the near vicinity of the ground state.

Optimum Evaluation of Reactive Power Requirements in Power Distribution-Systems

This paper presents three methodologies for determining optimum locations and magnitudes of reactive power compensation in power distribution systems. Method I and Method II are suitable for complex distribution systems with a combination of both radial and ring-main feeders and having different voltage levels. Method III is suitable for low-tension single voltage level radial feeders. Method I is based on an iterative scheme with successive powerflow analyses, with formulation and solution of the optimization problem using linear programming. Method II and Method III are essentially based on the steady state performance of distribution systems. These methods are simple to implement and yield satisfactory results comparable with the results of Method I. The proposed methods have been applied to a few distribution systems, and results obtained for two typical systems are presented for illustration purposes.

Multistep Methods for Integrating the Solar System

High order multistep methods, run at constant stepsize, are very effective for integrating the Newtonian solar system for extended periods of time. I have studied the stability and error growth of these methods when applied to harmonic oscillators and two-body systems like the Sun-Jupiter pair. I have also tried to design better multistep integrators than the traditional Stormer and Cowell methods, and I have found a few interesting ones.