M-body Pure State Entanglement

The simple entanglement of N-body N-particle pure states is extended to the more general M-body or M-body N-particle states where $N\neq M$. Some new features of the M-body N-particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose-Einstien condensate model is demonstrated.Comment: 9 pages, 2 figure

Cat state, sub-Planck structure and weak measurement

Heisenberg-limited and weak measurements are the two intriguing notions, used in recent times for enhancing the sensitivity of measurements in quantum metrology. Using a quantum cat state, endowed with sub-Planck structure, we connect these two novel concepts. It is demonstrated that these two phenomena manifest in complementary regimes, depending upon the degree of overlap between the mesoscopic states constituting the cat state under consideration. In particular, we find that when sub-Planck structure manifests, the imaginary weak value is obscured and vice-versa.Comment: 7 pages, 7 figure

A nucleon-pair and boson coexistent description of nuclei

We study a mixture of s-bosons and like-nucleon pairs with the standard pairing interaction outside a inert core. Competition between the nucleon-pairs and s-bosons is investigated in this scenario. The robustness of the BCS-BEC coexistence and crossover phenomena is examined through an analysis of pf-shell nuclei with realistic single-particle energies in which two configurations with Pauli blocking of nucleon-pair orbits due to the formation of the s-bosons is taken into account. When the nucleon-pair orbits are considered to be independent of the s-bosons, the BCS-BEC crossover becomes smooth with the number of the s-bosons noticeably more than that of the nucleonpairs near the half-shell point, a feature that is demonstrated in the pf-shell for several values of the standard pairing interaction strength. As a further test of the robustness of the BCS-BEC coexistence and crossover phenomena in nuclei, results are given for B(E2; 0^{+}_{g}->2^{+}_1) values of even-even 102-130Sn with 100Sn taken as a core and valence neutron pairs confined within the 1d5/2, 0g7/2, 1d3/2, 2s1/2, 1h11/2 orbits in the nucleon-pair orbit and the s-boson independent approximation. The results indicate that the B(E2) values are well reproduced.Comment: 5.1 pages, 3 figures, LaTe

Simple and Nearly Optimal Polynomial Root-finding by Means of Root Radii Approximation

We propose a new simple but nearly optimal algorithm for the approximation of all sufficiently well isolated complex roots and root clusters of a univariate polynomial. Quite typically the known root-finders at first compute some crude but reasonably good approximations to well-conditioned roots (that is, those isolated from the other roots) and then refine the approximations very fast, by using Boolean time which is nearly optimal, up to a polylogarithmic factor. By combining and extending some old root-finding techniques, the geometry of the complex plane, and randomized parametrization, we accelerate the initial stage of obtaining crude to all well-conditioned simple and multiple roots as well as isolated root clusters. Our algorithm performs this stage at a Boolean cost dominated by the nearly optimal cost of subsequent refinement of these approximations, which we can perform concurrently, with minimum processor communication and synchronization. Our techniques are quite simple and elementary; their power and application range may increase in their combination with the known efficient root-finding methods.Comment: 12 pages, 1 figur

A broadband microwave Corbino spectrometer at 3^3He temperatures and high magnetic fields

We present the technical details of a broadband microwave spectrometer for measuring the complex conductance of thin films covering the range from 50 MHz up to 16 GHz in the temperature range 300 mK to 6 K and at applied magnetic fields up to 8 Tesla. We measure the complex reflection from a sample terminating a coaxial transmission line and calibrate the signals with three standards with known reflection coefficients. Thermal isolation of the heat load from the inner conductor is accomplished by including a section of NbTi superconducting cable (transition temperature around 8 $-$ 9 K) and hermetic seal glass bead adapters. This enables us to stabilize the base temperature of the sample stage at 300 mK. However, the inclusion of this superconducting cable complicates the calibration procedure. We document the effects of the superconducting cable on our calibration procedure and the effects of applied magnetic fields and how we control the temperature with great repeatability for each measurement. We have successfully extracted reliable data in this frequency, temperature and field range for thin superconducting films and highly resistive graphene samples