ILC Operating Scenarios

The ILC Technical Design Report documents the design for the construction of a linear collider which can be operated at energies up to 500 GeV. This report summarizes the outcome of a study of possible running scenarios, including a realistic estimate of the real time accumulation of integrated luminosity based on ramp-up and upgrade processes. The evolution of the physics outcomes is emphasized, including running initially at 500 GeV, then at 350 GeV and 250 GeV. The running scenarios have been chosen to optimize the Higgs precision measurements and top physics while searching for evidence for signals beyond the standard model, including dark matter. In addition to the certain precision physics on the Higgs and top that is the main focus of this study, there are scientific motivations that indicate the possibility for discoveries of new particles in the upcoming operations of the LHC or the early operation of the ILC. Follow-up studies of such discoveries could alter the plan for the centre-of-mass collision energy of the ILC and expand the scientific impact of the ILC physics program. It is envisioned that a decision on a possible energy upgrade would be taken near the end of the twenty year period considered in this report

Critical strength of attractive central potentials

We obtain several sequences of necessary and sufficient conditions for the existence of bound states applicable to attractive (purely negative) central potentials. These conditions yields several sequences of upper and lower limits on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant (strength), $g$, of the potential, $V(r)=-g v(r)$, for which a first $\ell$-wave bound state appears, which converges to the exact critical value.Comment: 18 page

A revision of the Generalized Uncertainty Principle

The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant $G_N = L_{Pl}^2$. On the other hand, the emerging picture suggests a set of departures from the standard theory which demand a revision of all the arguments used to deduce heuristically the new rule. In particular, one can now argue that the leading order correction to the Heisenberg Uncertainty Principle is proportional to the first power of the Planck length $L_{Pl}$. If so, the departures from ordinary quantum mechanics would be much less suppressed than what is commonly thought.Comment: 6 pages, 1 figur

Minimal Length and the Quantum Bouncer: A Nonperturbative Study

We present the energy eigenvalues of a quantum bouncer in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP) via quantum mechanical and semiclassical schemes. In this paper, we use two equivalent nonperturbative representations of a deformed commutation relation in the form [X,P]=i\hbar(1+\beta P^2) where \beta is the GUP parameter. The new representation is formally self-adjoint and preserves the ordinary nature of the position operator. We show that both representations result in the same modified semiclassical energy spectrum and agrees well with the quantum mechanical description.Comment: 14 pages, 2 figures, to appear in Int. J. Theor. Phy

Deformed Heisenberg algebra and minimal length

A one-dimensional deformed Heisenberg algebra $[X,P]=if(P)$ is studied. We answer the question: For what function of deformation $f(P)$ there exists a nonzero minimal uncertainty in position (minimal length). We also find an explicit expression for the minimal length in the case of arbitrary function of deformation.Comment: to be published in JP

Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition

Successful applications of the Kruskal-Segur approach to interfacial pattern formation have remained limited due to the necessity of an integral formulation of the problem. This excludes nonlinear bulk equations, rendering convection intractable. Combining the method with Zauderer's asymptotic decomposition scheme, we are able to strongly extend its scope of applicability and solve selection problems based on free boundary formulations in terms of partial differential equations alone. To demonstrate the technique, we give the first analytic solution of the problem of velocity selection for dendritic growth in a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page