1,721,024 research outputs found
Modular Hamiltonians for the massless Dirac field in the presence of a boundary
Full text linkWe study the modular Hamiltonians of an interval for the massless Dirac fermion on the half-line. The most general boundary conditions ensuring the global energy conservation lead to consider two phases, where either the vector or the axial symmetry is preserved. In these two phases we derive the corresponding modular Hamiltonian in explicit form. Its density involves a bi-local term localised in two points of the interval, one conjugate to the other. The associated modular flows are also established. Depending on the phase, they mix fields with different chirality or charge that follow different modular trajectories. Accordingly, the modular flow preserves either the vector or the axial symmetry. We compute the two-point correlation functions along the modular flow and show that they satisfy the Kubo-Martin-Schwinger condition in both phases. The entanglement entropies are also derived
Comparative Metrics in Procedure-Oriented and Object-Oriented Software Implementation of a Simple Single-Input-Single-Output Digital Process Control Problem in Educational Environment
No full textDespite the growing popularity of object oriented programming in the last decade,
quantification of the effects of this new programming technique is still lacking. This paper
studies the impact of the introduction object-oriented programming in a formerly procedural
oriented environment within the application domain of single-input, single-output digital
process controllers.
Eighty-three senior students worked on same engineering problem first with a traditional
procedure-oriented programming (POP) approach, and later using object-oriented
programming (OOP) approach. The resulting products were analyzed and compared
quantitatively using both product quality metrics and property-based metrics.
The products developed using traditional procedure-oriented programming showed
lower failure rate, higher quality, smaller size and lower complexity in the specific
application domain. The outcome of this experiment does not mean that POP is generally
better than OOP. Rather, we suggest that the introduction of OOP in an existing POP
environment should be performed carefully, depending on the specific problem that is to be
solved, the application domain, and the working environmen
Chiral anomalies and supersymmetry
No full textThe structure of the chiral anomalies in supersymmetric gauge theories is studied. We discuss in detail the relationship between the two pictures: the manifestly SUSY-covariant approach and the Wess-Zumino gauge. A prescription for the computation of the anomalies in higher dimensions is presented and the resulting expression in six dimensions is reported
Beta functions and central charge of supersymmetric sigma models with torsion
No full textWe present a method for the computation of the renormalized group beta-functions and the central charge in two-dimensional supersymmetric sigma models in a gravitational background. The two-loops results are exhibited. We use the Pauli-Villars regularization which preserves supersymmetry and permits an unambiguous treatment of the model with torsion. The central charge we derive for a general manifold is in agreement with expression found on group manifolds
Modular Hamiltonians for the massless Dirac field in the presence of a defect
Full text linkWe study the massless Dirac field on the line in the presence of a point-like defect characterised by a unitary scattering matrix, that allows both reflection and transmission. Considering this system in its ground state, we derive the modular Hamiltonians of the subregion given by the union of two disjoint equal intervals at the same distance from the defect. The absence of energy dissipation at the defect implies the existence of two phases, where either the vector or the axial symmetry is preserved. Besides a local term, the densities of the modular Hamiltonians contain also a sum of scattering dependent bi-local terms, which involve two conjugate points generated by the reflection and the transmission. The modular flows of each component of the Dirac field mix the trajectory passing through a given initial point with the ones passing through its reflected and transmitted conjugate points. We derive the two-point correlation functions along the modular flows in both phases and show that they satisfy the Kubo-Martin-Schwinger condition. The entanglement entropies are also computed, finding that they do not depend on the scattering matrix
Correlation functions of one-dimensional anyonic fluids
No full textA universal description of correlation functions of one-dimensional anyonic gapless systems in the low-momentum regime is presented. We point out a number of interesting features, including universal oscillating terms with frequency proportional to the statistical parameter and beating effects close to the fermion points. The results are applied to the one-dimensional anyonic Lieb-Liniger model and checked against the exact results in the impenetrable limit
How effective massless fermions modify the anomalous decays of the Goldstone bosons
No full textWe consider the consequences of the anomalous Ward identities when both Goldstone bosons and massless fermions appear as low-energy degrees of freedom in confining theories. A general procedure for evaluating the anomalous vertices of the Goldstone bosons is given. We show that these vertices can be described in a compact way. The emerging structures have an intrinsic geometrical meaning. Some particular features occurring when the massless fermions are superpartners of the Goldstone bosons are illustrated on the example of supersymmetric QCD
Comparative Metrics in Procedure-Oriented and Object-Oriented Software Implementations of a Simple Single-Input-Single-Output Digital Process Control Problem in Educational Environment
No full textJunctions of anyonic Luttinger wires
No full textWe present an extended study of anyonic Luttinger liquids wires jointing at a single point. The model on the full line is solved with bosonization and the junction of an arbitrary number of wires is treated imposing boundary conditions that preserve exact solvability in the bosonic language. This allows us to reach, in the low-momentum regime, some of the critical fixed points found with the electronic boundary conditions. The stability of all the fixed points is discussed
- …
