Quantum Illumination and Quantum Radar: A Brief Overview

Quantum illumination (QI) and quantum radar have emerged as potentially groundbreaking technologies, leveraging the principles of quantum mechanics to revolutionise the field of remote sensing and target detection. The protocol, particularly in the context of quantum radar, has been subject to a great deal of aspirational conjecture as well as criticism with respect to its realistic potential. In this review, we present a broad overview of the field of quantum target detection focusing on QI and its potential as an underlying scheme for a quantum radar operating at microwave frequencies. We provide context for the field by considering its historical development and fundamental principles. Our aim is to provide a balanced discussion on the state of theoretical and experimental progress towards realising a working QI-based quantum radar, and draw conclusions about its current outlook and future directions

Magnetic biosensors: modelling and simulation

In the past few years, magnetoelectronics has emerged as a promising new platform technology in various biosensors for detection, identification, localisation and manipulation of a wide spectrum of biological, physical and chemical agents. The methods are based on the exposure of the magnetic field of a magnetically labelled biomolecule interacting with a complementary biomolecule bound to a magnetic field sensor. This Review presents various schemes of magnetic biosensor techniques from both simulation and modelling as well as analytical and numerical analysis points of view, and the performance variations under magnetic fields at steady and nonstationary states. This is followed by magnetic sensors modelling and simulations using advanced Multiphysics modelling software (e.g. Finite Element Method (FEM) etc.) and home-made developed tools. Furthermore, outlook and future directions of modelling and simulations of magnetic biosensors in different technologies and materials are critically discussed

Quantum Illumination and Quantum Radar:A Brief Overview

Quantum illumination (QI) and quantum radar have emerged as potentially groundbreaking technologies, leveraging the principles of quantum mechanics to revolutionise the field of remote sensing and target detection. The protocol, particularly in the context of quantum radar, has been subject to a great deal of aspirational conjecture as well as criticism with respect to its realistic potential. In this review, we present a broad overview of the field of quantum target detection focusing on QI and its potential as an underlying scheme for a quantum radar operating at microwave frequencies. We provide context for the field by considering its historical development and fundamental principles. Our aim is to provide a balanced discussion on the state of theoretical and experimental progress towards realising a working QI-based quantum radar, and draw conclusions about its current outlook and future directions

Photon-Photon Correlations as a Probe of Vacuum Induced Coherence Effects

We present new experimental implications of the effects of vacuum induced coherence on the photon -photon correlation in the pi-polarized fluorescence in j = 1/2 to j = 1/2 transition. These effects should be thus observable in measurements of photon statistics in for example Hg and Ba ion traps.Comment: 7 pages, 6 figures, submitted to Physical Review

Stability of Geodesically Complete Cosmologies

We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator $~^{(3)}{R} \delta N~$ is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.Comment: 18 pages, 2 figures. v2: minor changes; references added; version published in JCA

State-space Geometry, Statistical Fluctuations and Black Holes in String Theory

We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a new perspective of black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic state-space geometric meaning of the statistical fluctuations, local and global stability conditions and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, \textit{viz.}, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory. Keywords: Intrinsic Geometry; String Theory; Physics of black holes; Classical black holes; Quantum aspects of black holes, evaporation, thermodynamics; Higher-dimensional black holes, black strings, and related objects; Statistical Fluctuation; Flow Instability. PACS: 02.40.Ky; 11.25.-w; 04.70.-s; 04.70.Bw; 04.70.Dy; 04.50.Gh; 5.40.-a; 47.29.KyComment: 28 pages. arXiv admin note: substantial text overlap with arXiv:1102.239

HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants

Hilbert scheme topological invariants of plane curve singularities are identified to framed threefold stable pair invariants. As a result, the conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve singularities is given a Calabi-Yau threefold interpretation. The motivic Donaldson-Thomas theory developed by M. Kontsevich and the third author then yields natural motivic invariants for algebraic knots. This construction is motivated by previous work of V. Shende, C. Vafa and the first author on the large $N$ duality derivation of the above conjecture.Comment: 59 pages; v2 references added, minor corrections; v3: exposition improved, proofs expanded, results unchanged, to appear in Comm. Num. Th. Phy

Trimmed Serendipity Finite Element Differential Forms

We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity family and the (non-trimmed) serendipity family developed by Arnold and Awanou [Math. Comp. 83(288) 2014] is analogous to the relation between the trimmed and (non-trimmed) polynomial finite element differential form families on simplicial meshes from finite element exterior calculus. We provide degrees of freedom in the general setting and prove that they are unisolvent for the trimmed serendipity spaces. The sequence of trimmed serendipity spaces with a fixed polynomial order r provides an explicit example of a system described by Christiansen and Gillette [ESAIM:M2AN 50(3) 2016], namely, a minimal compatible finite element system on squares or cubes containing order r-1 polynomial differential forms.Comment: Improved results, detailed comparison to prior and contemporary work, and further explanation of computational benefits have been added since the original version. This version has been accepted for publication in Mathematics of Computatio