Person:

Wu, Tai

With an interest in finding wires and distinguishing them from other electrically conducting objects, we have looked for an electromagnetic “fingerprint” in terms of resonances of a straight wire of length 2h and radius a. The resonances of the wire are formulated using the theory of the linear antenna, leading to an integral equation for the current on the wire. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current on the wire has non-zero solutions. By applying a variational technique we obtain approximate numerical solutions for the resonant frequencies and their widths. A table of the first five resonances is given for several ratios of wire half-length h to wire radius a. In a subsequent paper we propose to extend the method described here to deal with wires on an earth-air interface, for example as used to command the detonation of improvised explosive devices.

Using a variational method, we recently determined an electromagnetic “signature” for characterizing a straight wire in free space. The signature consists of the first five resonant frequencies and their widths, more compactly expressed as the first five complex-valued resonant frequencies. Here we apply the variational method to the much more complicated case of determining the same signature for a straight wire or wire pair on a flat interface between a homogeneous earth and air. To calculate the resonances we obtain an integral equation for the current on a wire on the interface between two dielectric media. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current in an equivalent thin strip on the interface has non-zero solutions. The variational method extracts good approximations to these complex-valued resonant frequencies, without having to solve the integral equation. A table of resonances is given for the case of a relative dielectric constant of the earth equal to 4 and for three values of the ratio of wire radius to wire half-length.

Using the results from relativistic gauge field theory, a phenomenological model is developed for the production of an isolated Higgs particle H. The specific process is p+p → A+H +B, where the group of particles A (B) mostly goes down one (the other) beam pipe. The theory and the phenomenology apply when the center-of-mass energy √s ≫ M ≫ m, with M and m the masses of the Higgs particle and the proton respectively. Thus, there are two large parameters, namely √s/M and M/m. That M ≫ m plays a central role. This phenomenological model is applied to the Large Hadron Collider (LHC) to predict the differential production cross sections. With high probability, this isolated Higgs particle is produced with a small transverse momentum of the order of 1 GeV/c. Because of this fact and the relatively small number of observed particles in such events, the method of data analysis is different from those developed so far for Higgs detection. These events can be described as due to Pomeron-Pomeron annihilation, and are ‘clean’ in the sense that those from TeV linear colliders are called ‘clean’. The LHC, with its center-of-mass design energy of 14 TeV and its design luminosity of 1034 cm−2s−1, can function exceptionally well as a Pomeron collider.

Theoretical predictions are presented for the process p+p→A+H+B, where H is the Higgs particle and A (B ) is a group of particles that mostly goes down one (the other) beam pipe. These predictions are obtained using results from relativistic quantum gauge field theory and the fact that, for the Large Hadron Collider (LHC), the center-of-mass energy ≫ Higgs mass ≫ proton mass. The average transverse momentum of the produced Higgs particle is of the order of 1 GeV/c. This process leads naturally to the concept of considering the LHC as a Pomeron Collider.

Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a function of the momentum is also derived for longer-range power-law potentials which do not fulfill these conditions.

In spite of a long history, the quantification of entanglement still calls for exploration. What matters about entanglement depends on the situation, and so presumably do the numbers suitable for its quantification. Regardless of situational complications, a necessary first step is to make available for calculation some quantitative measure of entanglement. Here we define a geometric degree of entanglement, distinct from earlier definitions, but in the case of bipartite pure states related to that proposed by Shimony (Ann N Y Acad Sci 755:675---679, 1995). The definition offered here applies also to multipartite mixed states, and a variational method simplifies the calculation. We analyze especially states that are invariant under permutation of particles, states that we call bosonic. Of interest to quantum sensing, for bosonic states, we show that no partial trace can increase a degree of entanglement. For some sample cases we quantify the degree of entanglement surviving a partial trace. As a function of the degree of entanglement of a bosonic 3-qubit pure state, we show the range of degree of entanglement for the 2-qubit reduced density matrix obtained from it by a partial trace. Then we calculate an upper bound on the degree of entanglement of the mixed state obtained as a partial trace over one qubit of a 4-qubit bosonic state. As a reminder of the situational dependence of the advantage of entanglement, we review the way in which entanglement combines with scattering theory in the example of light-based radar.

From the recent theoretical result on the production of the Higgs boson at the Large Hadron Collider, it follows that other particles will also be produced with small transverse momentum, of the order of 1 GeV/c. The leptonic decay mode of the Z is especially suited for a first observation of this phenomenon. Other related effects, such as paired jets, are also discussed.