Fabrication and First Full Characterisation of Timing Properties of 3D Diamond Detectors

Tracking detectors at future high luminosity hadron colliders are expected to be able to stand unprecedented levels of radiation as well as to efficiently reconstruct a huge number of tracks and primary vertices. To face the challenges posed by the radiation damage, new extremely radiation hard materials and sensor designs will be needed, while the track and vertex reconstruction problem can be significantly mitigated by the introduction of detectors with excellent timing capabilities. Indeed, the time coordinate provides extremely powerful information to disentangle overlapping tracks and hits in the harsh hadronic collision environment. Diamond 3D pixel sensors optimised for timing applications provide an appealing solution to the above problems as the 3D geometry enhances the already outstanding radiation hardness and allows to exploit the excellent timing properties of diamond. We report here the first full timing characterisation of 3D diamond sensors fabricated by electrode laser graphitisation in Florence. Results from a 270MeV pion beam test of a first prototype and from tests with a β source on a recently fabricated 55×55μm2 pitch sensor are discussed. First results on sensor simulation are also presented.

Another Proof of Born’s Rule on Arbitrary Cauchy Surfaces

In 2017, Lienert and Tumulka proved Born’s rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born’s rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born’s rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $$\Sigma $$ Σ , then the observed particle configuration on $$\Sigma $$ Σ is a random variable with distribution density $$|\Psi _\Sigma |^2$$ | Ψ Σ | 2 , suitably understood. The main different assumption is that the Born and collapse rules hold on any spacelike hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically, this follows if the dynamics of the detectors is Lorentz invariant.

A separated representation involving multiple time scales within the Proper Generalized Decomposition framework

Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.

On the angular momentum and spin of generalized electromagnetic field for r-vectors in (k, n) space-time dimensions

This paper studies the relativistic angular momentum for the generalized electromagnetic field, described by r-vectors in (k, n) space-time dimensions, with exterior-algebraic methods. First, the angular-momentum tensor is derived from the invariance of the Lagrangian to space-time rotations (Lorentz transformations), avoiding the explicit need of the canonical tensor in Noether’s theorem. The derivation proves the conservation law of angular momentum for generic values of r, k, and n. Second, an integral expression for the flux of the tensor across a $$(k+n-1)$$ ( k + n - 1 ) -dimensional surface of constant $$\ell $$ ℓ -th space-time coordinate is provided in terms of the normal modes of the field; this analysis is a natural generalization of the standard analysis of electromagnetism, i. e. a three-dimensional space integral at constant time. Third, a brief discussion on the orbital angular momentum and the spin of the generalized electromagnetic field, including their expression in complex-valued circular polarizations, is provided for generic values of r, k, and n.

Experimental verification of the field theory of specific heat with the scaling in crystalline matter

The field (geometrical) theory of specific heat is based on the universal thermal sum, a new mathematical tool derived from the evolution equation in the Euclidean four-dimensional spacetime, with the closed time coordinate. This theory made it possible to explain the phenomena of scaling in the heat capacity of condensed matter. The scaling of specific heat of the carbon group elements with a diamond lattice is revisited. The predictions of the scaling characteristics for natural diamond and grey tin are verified with published experimental data. The fourth power in temperature in the quasi-low temperature behaviour of the specific heat of both materials is confirmed. The phenomenon of scaling in the specific heat, previously known only in glassy matter, is demonstrated for some zincblend lattice compounds and diamond lattice elements, with their characteristic temperatures. The nearly identical elastic properties of grey tin and indium antimonide is the cause for similarity of their thermal properties, which makes it possible to make conjectures about thermal properties of grey tin.

On the coupling of relativistic particle to gravity and Wheeler–DeWitt quantization

A system consisting of a point particle coupled to gravity is investigated. The set of constraints is derived. It was found that a suitable superposition of those constraints is the generator of the infinitesimal transformations of the time coordinate [Formula: see text] and serves as the Hamiltonian which gives the correct equations of motion. Besides that, the system satisfies the mass shell constraint, [Formula: see text], which is the generator of the worldline reparametrizations, where the momenta [Formula: see text], [Formula: see text], generate infinitesimal changes of the particle’s position [Formula: see text] in spacetime. Consequently, the Hamiltonian contains [Formula: see text], which upon quantization becomes the operator [Formula: see text], occurring on the right-hand side of the Wheeler–DeWitt equation. Here, the role of time has the particle coordinate [Formula: see text], which is a distinct concept than the spacetime coordinate [Formula: see text]. It is also shown how the ordering ambiguities can be avoided if a quadratic form of the momenta is cast into the form that instead of the metric contains the basis vectors.

Exact solutions of (deformed) Jackiw–Teitelboim gravity

It is well known that Jackiw–Teitelboim (JT) gravity posses the simplest theory on 2-dimensional gravity. The model has been fruitfully studied in recent years. In the present work, we investigate exact solutions for both JT and deformed JT gravity recently proposed in the literature. We revisit exact Euclidean solutions for Jackiw-Teitelboim gravity using all the non-zero components of the dilatonic equations of motion using proper integral transformation over Euclidean time coordinate. More precisely, we study exact solutions for hyperbolic coverage, cusp geometry and another compact sector of the AdS$$_2$$ 2 spacetime manifold.

On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric

The paper discusses possible consequences of A. D. Sakharov’s hypothesis of cosmological transitions with changes in the signature of the metric, based on the path integral approach. This hypothesis raises a number of mathematical and philosophical questions. Mathematical questions concern the definition of the path integral to include integration over spacetime regions with different signatures of the metric. One possible way to describe the changes in the signature is to admit time and space coordinates to be purely imaginary. It may look like a generalization of what we have in the case of pseudo-Riemannian manifolds with a non-trivial topology. The signature in these regions can be fixed by special gauge conditions on components of the metric tensor. The problem is what boundary conditions should be imposed on the boundaries of these regions and how they should be taken into account in the definition of the path integral. The philosophical question is what distinguishes the time coordinate among other coordinates but the sign of the corresponding principal value of the metric tensor. In particular, there is an attempt in speculating how the existence of the regions with different signature can affect the evolution of the Universe.

Experiments on the symmetry of length and time

The F - t curve obtained from the process of applying and releasing force to the piezoelectric sensor shows that in the atomic scale, the time coordinate is equivalent to the position coordinate. The time-position coordinate relationship calculated by the experimental data is consistent with the geometric unit obtained in the general theory of relativity, thus the experiment verifies the symmetry of length and time,and connection between the microscopic - quantum mechanics and the macroscopic - general theory of relativity, and a new method for calculating the speed of light is obtained.

Experimental Verification of the Field Theory of Specific Heat With the Scaling in Crystalline Matter

The field (geometrical) theory of specific heat is based on the universal thermal sum, a new mathematical tool derived from the evolution equation in the Euclidean four-dimensional spacetime, with the closed time coordinate. This theory made it possible to explain the phenomena of scaling in the heat capacity of condensed matter. The scaling of specific heat of the carbon group elements with a diamond lattice is revisited. The predictions of the scaling characteristics for natural diamond and grey tin are verified with published experimental data. The fourth power in temperature in the quasi-low temperature behaviour of the specific heat of both materials is confirmed. The phenomenon of scaling in the specific heat, previously known only in glassy matter, is demonstrated for some zincblend lattice compounds and diamond lattice elements, with their characteristic temperatures. The nearly identical elastic properties of grey tin and indium antimonide is the cause for similarity of their thermal properties, which makes it possible to make conjectures about thermal properties of grey tin.