Entanglement between two fermionic atoms inside a cylindrical harmonic trap

We investigate quantum entanglement between two (spin-1/2) fermions inside a cylindrical harmonic trap, making use of the von Neumann entropy for the reduced single particle density matrix as the pure state entanglement measure. We explore the dependence of pair entanglement on the geometry and strength of the trap and on the strength of the pairing interaction over the complete range of the effective BCS to BEC crossover. Our result elucidates an interesting connection between our model system of two fermions and that of two interacting bosons.Comment: to appear in PR

Calculation of compressible turbulent boundary layers with pressure gradients and heat transfer

Calculation of compressible turbulent boundary layers with pressure gradients and heat transfe

Dressed Qubits

Inherent gate errors can arise in quantum computation when the actual system Hamiltonian or Hilbert space deviates from the desired one. Two important examples we address are spin-coupled quantum dots in the presence of spin-orbit perturbations to the Heisenberg exchange interaction, and off-resonant transitions of a qubit embedded in a multilevel Hilbert space. We propose a ``dressed qubit'' transformation for dealing with such inherent errors. Unlike quantum error correction, the dressed qubits method does not require additional operations or encoding redundancy, is insenstitive to error magnitude, and imposes no new experimental constraints.Comment: Replaced with published versio

The Fundamental-Weak Scale Hierarchy in the Standard Model

The multiple point principle, according to which several vacuum states with the same energy density exist, is put forward as a fine-tuning mechanism predicting the ratio between the fundamental and electroweak scales in the Standard Model (SM). It is shown that this ratio is exponentially huge: $\sim e^{40}$. Using renormalisation group equations for the SM, we obtain the effective potential in the 2-loop approximation and investigate the existence of its postulated second minimum at the fundamental scale. The investigation of the evolution of the top quark Yukawa coupling constant in the 2-loop approximation shows that, with initial values of the top Yukawa coupling in the interval $h(M_t)=0.95\pm 0.03$ (here $M_t$ is the top quark pole mass), a second minimum of the SM effective potential can exist in the region $\phi_{min2}\approx 10^{16}-10^{22}$ GeV. A prediction is made of the existence of a new bound state of 6 top quarks and 6 anti-top quarks, formed due to Higgs boson exchanges between pairs of quarks/anti-quarks. This bound state is supposed to condense in a new phase of the SM vacuum. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The existence of three vacuum states (new, electroweak and fundamental) solves the hierarchy problem in the SM.Comment: 30 pages, 7 figures; to be published in Phys. Atom. Nuc

The Initial Value Problem For Maximally Non-Local Actions

We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at most discretely enlarged, and may even be restricted, with respect to that of a local theory. We show that the solutions are those of a local theory whose (spacetime constant) parameters vary with the initial value data according to algebraic equations. The various roots of these algebraic equations can be plausibly interpreted in quantum mechanics as different components of a multi-component wave function. It is also possible that the consistency of these algebraic equations imposes constraints upon the initial value data which appear miraculous from the context of a local theory.Comment: 8 pages, LaTeX 2 epsilo

F(750), We Miss You as a Bound State of 6 Top and 6 Antitop Quarks, Multiple Point Principle

We review our speculation, that in the pure Standard Model the exchange of Higgses, including also the ones "eaten by $W^{\pm}$ and Z", and of gluons together make a bound state of 6 top plus 6 anti top quarks bind so strongly that its mass gets down to about 1/3 of the mass of the collective mass 12 $m_t$ of the 12 constituent quarks. The true importance of this speculated bound state is that it makes it possible to uphold, even inside the Standard Mode, our proposal for what is really a new law of nature saying that there are several phases of empty space, vacua, all having very small energy densities (of the order of the present energy density in the universe). The reason suggested for believing in this new law called the "Multiple (Criticality) Point Principle" is, that estimating the mass of the speculated bound state using the "Multiple Point Principle" leads to two consistent mass-values; and they even agree with a crude bag-model like estimate of the mass of this bound state. Very, unfortunately, the statistical fluctuation so popular last year, when interpreted as the digamma resonance F(750), turned out not to be a real resonance, because our estimated bound state mass is just around the mass of 750 GeV.Comment: 25 pages, 11 figures, Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity", 31 August - 23 September, 2016, Corfu, Greec