Symmetry Sectors Research Articles

Anomalous decay of pion and eta at finite density

We study the anomalous decays π0, η→γγ in the framework of the three-flavor Nambu–Jona-Lasinio [NJL] model, in the vacuum and in quark matter in β-equilibrium. It is found that the behavior of the relevant observables essentially reflects a manifestation of the partial restoration of chiral symmetry, in nonstrange and strange sectors. The probability of such decays decreases with density, showing that anomalous mesonic interactions are significantly affected by the medium.

Flavor Violation in Supersymmetric Theories with Gauged Flavor Symmetries

In this paper we study flavor violation in supersymmetric models with gauged flavor symmetries. There are several sources of flavor violation in these theories. The dominant flavor violation is the tree-level $D$-term contribution to scalar masses generated by flavor symmetry breaking. We present a new approach for suppressing this phenomenologically dangerous effects by separating the flavor-breaking sector from supersymmetry-breaking one. The separation can be achieved in geometrical setups or in a dynamical way. We also point out that radiative corrections from the gauginos of gauged flavor symmetries give sizable generation-dependent masses of scalars. The gaugino mass effects are generic and not suppressed even if the dominant $D$-term contribution is suppressed. We also analyze the constraints on the flavor symmetry sector from these flavor-violating corrections.

Darwinian Aspects of Molecular Evolution at Sublinear Propagation Rates

Mean fitness is non-decreasing in the symmetry sector of the frequency trajectory followed in competitive replication at sublinear propagation rates (parabolic time course). This sector contains the pairwise symmetric distribution of species frequencies and its neighboring states, and represents at least half the possible states of an evolving sublinear system. States in the non-symmetry sector produce a negative rate of change in mean fitness. The heterogeneous steady state attained in a finite sublinear system is destabilized by formation of a variant with above-threshold fitness. Evolution in the post-steady-state interval elevates the fitness threshold for coexistence. Contrary to the proposition that ‘parabolic growth invariably results in the survival of all competing species’, only species with sufficient fitness to avoid subthreshold fitness survive.

Identification of excitons in conjugated polymers: A density-matrix renormalization-group study

This work addresses the question of whether low-lying excitations in conjugated polymers are comprised of free charge-carriers or excitons. States are characterised as bound or unbound according to the scaling of the average particle-hole separation with system size. We critically examine other criteria commonly used to characterise states. The polymer is described by an extended Hubbard model with alternating transfer integrals. The model is solved by exact diagonalisation and the density matrix renormalisation group (DMRG) method. We demonstrate that the DMRG accurately determines excitation energies, transition dipole moments and particle-hole separations of a number of dipole forbidden (Ag) and dipole allowed (Bu) states. Within a parameter regime considered reasonable for polymers such as polyacetylene, it is found that the charge gap, often used to define the exciton binding energy, is not a good criterion by which to decide whether a state is bound or unbound. The essential non-linear optical state mAg is found to mark the onset of unbound excitations in the Ag symmetry sector. In the Bu symmetry sector, on the other hand, it is found that all low lying states are unbound and that there is no well defined nBu state. That is, the 1Bu state marks the onset of unbound excitations in this sector.

Theory on the lattice - an effective potential study

We study the behaviour, on a lattice, of a scalar bidimensional theory with quartic and sextic interactions, the theory. We investigate its phase diagram identifying the sectors where first- and second-order phase transitions occur. We build the effective potential for this theory for different sectors of the phase diagram and verify that the effective potential can be undefined for certain values of the fields, both in the symmetric and broken symmetry sectors, when these sectors are separated by first order phase transitions. We also discuss the existence or not of objects like solitonic kinks and polarons and their dependence with the phase transition order.

Dissipative dynamics in a quantum register

A model for a quantum register dissipatively coupled with a bosonic thermal bath is studied. The register consists of $N$ qubits (i.e. spin ${1/2}$ degrees of freedom), the bath is described by $N_b$ bosonic modes. The register-bath coupling is chosen in such a way that the total number of excitations is conserved. The Hilbert space splits allowing the study of the dynamics separately in each sector. Assuming that the coupling with the bath is the same for all qubits, the excitation sectors have a further decomposition according the irreducible representations of the $su(2)$ spin algebra. The stability against environment-generated noise of the information encoded in a quantum state of the register depends on its $su(2)$ symmetry content. At zero temperature we find that states belonging to the vacuum symmetry sector have for long time vanishing fidelity, whereas each lowest spin vector is decoupled from the bath and therefore is decoherence free. Numerical results are shown in the one-excitation space in the case qubit-dependent bath-system coupling.

Superradiant amplification in an optically dense gas

We solve numerically the coupled integro-differential Maxwell-Bloch equations describing the amplification of a pulse in an inverted pressure broadened resonant medium, without assuming the Slowly Varying Envelope Approximation in space. Our algorithm incorporates the effects of the backward wave and that of the Local Field Corrections. We show that the superradiant regime sets on for much smaller values of αL than that predicted by the Forward Wave Approximation, and that it is possible to convert most of the energy stored in the atomic system into transmitted and reflected bursts whose duration are substantially shorter than either the dephasing or relaxation times of the atomic system, for sample lengths that are only few wavelengths long. Furthermore, we show that in the superradiant regime, except for sample lengths that are in the neighborhood of an integer multiple of the half-wavelength, the atomic polarizability possesses definite spatial symmetry with respect to the midpoint of the sample, resulting there in equal energy release for the transmitted and reflected signals. The transition domain between two consecutive opposite spatial symmetry sectors is manifested through unequal intensity for the transmitted and reflected bursts and in different frequency shifts in the spectral distributions of the two output signals.

Monotonicity of Born-Oppenheimer electronic energies for excited molecular states

The authors consider adiabatic molecular systems consisting of one electron and N>or=2 nuclei with arbitrary positive charges. If all the nuclei are arranged on a line, the angular momentum around the internuclear axis is conserved; using the corresponding separability in cylindrical coordinates it is shown that the lowest electronic energies in each symmetry sector of fixed angular momentum increase if the internuclear distances become larger. This extends previous monotonicity results for the ground state by Lieb and Simon (1978). For the physically most important case N=2 (or N=3) they give a separate proof that emphasizes the basic role of reflection positivity in this context.

Adiabatic calculations and properties of the He 2+ molecular ion

The MRDCI procedure and large Gaussian basis sets are employed to calculate the lowest two potential energy curves in each of the 2Σ u,g and 2Π u,g symmetry sectors of He 2 +. Using the obtained adiabatic curves, for both systems 3He 4He + and 4He 2 + vibrational rotational energy levels and various transition frequencies are computed. Comparison of the results and the dissociation energy D e with other recent theoretical and experimental data indicates that the achieved accuracy is of the same order as eventual nonadiabatic corrections.

CP ASYMMETRIES IN B0DECAYS BEYOND THE STANDARD MODEL

Of the many ingredients of the Standard Model that are relevant to the analysis of CP asymmetries in B0 decays, some are likely to hold even beyond the Standard Model while others are sensitive to new physics. Consequently, certain predictions are maintained while others may show dramatic deviations from the Standard Model. Many classes of models may show clear signatures when the asymmetries are measured: four quark generations, Z-mediated flavor-changing neutral currents, supersymmetry and “real superweak” models. On the other hand, models of left-right symmetry and multi-Higgs sectors with natural flavor conservation are unlikely to modify the Standard Model predictions.

Rigorous bounds on eigenvalues of two-electron atomic Hamiltonians

Upper and lower bounds on the first two energy levels of atomic two-electron systems within various symmetry sectors are calculated. These bounds are mathematically completely rigorous because no uncontrolled numerical approximations are involved. The explicit and simple form of these bounds allows their application as input for further analytical manipulations. Examples of such applications are given for the problem of level ordering and the absorption of bound states into the continuum.

Measurement of secondary flow vortices in a rod bundle

Secondary flow vortices in infinite rod bundles have been predicted by a number of theoretical analyses. Nevertheless experimental verification was difficult, since the magnitude of the secondary velocities appeared to be less than the accuracy of the experimental techniques used. Only indications of the maximum velocity magnitude have been available but no report on successful direct measurement is known to the author. At ECN, laser Doppler velocimetry is successfully used for measurement of secondary flow vortices in two regular subchannels of a triangularly arranged bare rod bundle with pitch-to-diameter ratio P D = 1.3 under the Reynolds number conditions 60 000 and 175 000. One single secondary vortex, having the average tangential velocity slightly less than 0.1% of the mean bulk velocity, is resolved per minimum symmetry sector of the bundle geometry. Ensemble averages are made to obtain quantitative description of the vortex and to form a data base for comparison with calculations.

Laminar convection in wall sub-channels and transport rates for finite rod-bundle assemblies by superposition

Finite rod-clusters in circular, square and hexagonal shells have been divided along the symmetry lines into a number of interior, wall and corner subchannels. Laminar fluid flow and heat transfer results have been generated for these subchannels with varying pitch-to-diameter and wall distance-to-diameter ratios. Wall shear stress and temperature variations for typical wall subchannels are presented. Friction factor values for finite bundles are then obtained by superposing the results of the subchannels that constitute the bundles. The values so generated are in excellent agreement with previous work in the literature obtained by the method of symmetry sectors. Considerable disagreements were, however, observed in the superposed values of Nusselt number, apparently due to conduction effects.

Status of the Nevis Synchrocyclotron Modification

After 20 years of operation as a conventional synchrocyclotron producing 0.4 μA time average internal beam current of protons (increased to 1.6 μA in 1967) of ~ 385 MeV, we stopped operation in September 1970 for the major modification for which we have been planning since 1965. The major study program and the conversion project are supported by a $ 3.9 M grant from the NSF. The conversion retains the basic cyclotron magnet (2000 tons of Fe and ~ 300 tons of Cu coils), but adds a 10-in. thick Fe band around the outside magnet perimeter to lower the return path reluctance. A new larger vacuum chamber is used, with auxilliary excitation coils. Pole iron within 30 in. of the median plane is replaced by a new configuration which includes N=3 symmetry sector iron with a small median plane gap. <B xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> = 18 kG near the center and 20 kG near 80 in. radius. Strong azimuthal magnetic field flutter begins at &lt; 2 in. radius to give strong focusing νz, and νr∦1. We expect to obtain ~ 550 MeV proton energy, with high extraction efficiency for a 10 to 40 μA time average external beam (~ 50% duty factor), when operation starts later this year. Additional details are given in companion papers in these Proceedings. The system will still be a synchrocyclotron and will have a 300 Hz FM repetition rate, with a new RF system, etc.</B>