Modern Physics Letters A

Theories of quantum control have, until recently, made the assumption that the Hilbert space of a quantum system can be truncated to finite dimensions. Such truncations, which can be achieved for most quantum systems via bandwidth restrictions, have enabled the development of a rich variety of quantum control and optimal control schemes. Recent studies in quantum information processing have addressed the control of infinite-dimensional quantum systems such as the quantum states of a trapped-ion. Controllability in an infinite-dimensional quantum system is hard to prove with conventional methods, and infinite-dimensional systems provide unique challenges in designing control fields.

In this paper, we will discuss the control of a popular system for quantum computing the trapped-ion qubit. This system, modeled by a spin-half particle coupled to a quantized harmonic oscillator, is an example for a surprisingly rich variety of control problems. We will show how this infinite-dimensional quantum system can be examined via the lens of the Finite Controllability Theorem, two-color STIRAP, the generalized Heisenberg system, etc.

These results are important from the viewpoint of developing more efficient quantum control protocols, particularly in quantum computing systems. This work shows how one can expand the scope of quantum control research to beyond that of finite-dimensional quantum systems.

This paper concerns random sprinklings of points into Minkowski spacetime (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to "Lorentz breaking" effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.

In this paper we show that the canonical seesaw mechanism can naturally be implemented in a particular class of electroweak SU(4)_L ⊗ U(1)_Y gauge models. The resulting neutrino mass spectrum is determined by just tuning a unique free parameter a within the algebraical method of treating gauge models with high symmetries proposed several years ago by Cotăescu. All the Standard Model phenomenology is preserved, being unaffected by the new physics occurring at a high breaking scale m ~ 10¹¹GeV.

There has been much debate about the form of the quantum area spectrum for a black hole horizon, with the evenly spaced conception of Bekenstein having featured prominently in the discourse. Here, we refine a very recently proposed method for calibrating the Bekenstein form of the spectrum. Our refined treatment predicts, as did its predecessor, a uniform spacing between adjacent spectral levels of 8π in Planck units — notably, an outcome that already has a pedigree as a proposed "universal" value for this intrinsically quantum-gravitational measure. Although the two approaches are somewhat similar in logic and quite agreeable in outcome, we argue that our version is conceptually more elegant and formally simpler than its precursor. Moreover, our rendition is able to circumvent a previously unnoticed technical issue and, as an added bonus, translates to generic theories of gravity in a very direct manner.

An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.

We show that the two-mode photon-subtracted squeezed state (TPSSS) is a squeezed two-variable Hermite polynomial excitation state, and we can therefore determine its normalization as a Jacobi polynomial of the squeezing parameter. Some new relations about the Jacobi polynomials are obtained by this analysis. We also show that the TPSSS can be treated as a two-variable Hermite-polynomial excitation on squeezed vacuum state. The technique of integration within an ordered product of operators brings convenience in our derivation.

The static properties of protons are useful for understanding the quark structure of the proton. In his work we have introduced the hypercentral constituent quark model and isospin dependent potentials. Here constituent quarks interact with each other via a potential in which we have taken into account the three-body force effect and the standard two-body potential contributions. According to our model the static properties of protons containing u and d quarks are better than the other models and closer to experimental results. The two key ingredients of this improvement are the effective quark–gluon hypercentral potentials, and hyperfine interaction and isospin dependence potential. Recently, Schrödinger equation has been solved by Giannini but we have solved the Dirac equation exact analytically and we have shown that a considerable improvement in the description of the static properties of proton is obtained with an isospin dependent potential and the complete interaction including spin and isospin terms reproduces the position of the quark.

In the present work we have derived the gravitational anomaly from a fundamentally different perspective: it emerges due to the tunneling of particles (in the present case fermions) across the black hole horizon. The latter effect is in fact the Hawking radiation. We have used the analogy of an early idea^17,18 of visualizing chiral gauge anomaly as an effect of spectral flow of the energy levels, from the negative energy Dirac sea, across zero energy level in the presence of gauge interactions. This was extended to conformal anomaly in Ref. 23. In the present work, we exploit the latter formalism in black hole physics where we interpret crossing the horizon of black hole (the zero energy level) as a spectral flow since it is also accompanied by a change of sign in the energy of the particle. Furthermore, Hawking radiation induces a shrinking of the radius of the horizon^15,16 which reminds us of a similar rearrangement in the Fermi level generated by the spectral flow.^17,18,21 Hence in our formulation the negative energy states below horizon play a similar role as the Dirac sea. We successfully recover the gravitational anomaly.