Conformal Vacuum Research Articles

Vertical serpentine interconnect-enabled stretchable and curved electronics

Stretchable and curved electronic devices are a promising technology trend due to their remarkable advantages. Many approaches have been developed to manufacture stretchable and curved electronics. Here, to allow such electronics to better serve practical applications, ranging from wearable devices to soft robotics, we propose a novel vertical serpentine conductor (VSC) with superior electrical stability to interconnect functional devices through a silicon-based microfabrication process. Conformal vacuum transfer printing (CVTP) technology was developed to transfer the networked platform onto complex curved surfaces to demonstrate feasibility. The mechanical and electrical performance were investigated numerically and experimentally. The VSC interconnected network provides a new approach for stretchable and curved electronics with high stretchability and reliability.

Wave correlations and quantum noise in cosmology

Wave noise is correlated. While it may look random in space, correlations appear in space–time, because the noise is carried by wave propagation. These correlations of wave noise give rise to fluctuation forces such as the Casimir force, they are responsible for the particle creation in the dynamical Casimir effect and in the expanding Universe. This paper considers the noise correlations for light waves in non-exponentially expanding flat space. The paper determines the high-frequency asymptotics of the correlation spectrum in the conformal vacuum. These noise correlations give rise to a nontrivial vacuum energy that may appear as the cosmological constant.

Polarization of the Conformal Vacuum in the Milne Universe

The vacuum expectation values of the field squared and energy-momentum tensor for a massless scalar field are investigated in the Milne universe with general number of spatial dimensions. The vacuum state depends on the choice of the mode functions in the canonical quantization procedure and we assume that the field is prepared in the conformal vacuum. As the first step an integral representation for the difference of the Wightman functions corresponding to the conformal and Minkowski vacua is derived. The mean field squared and energy-momentum tensor are obtained in the coincidence limit. It is shown that the Minkowski vacuum state is interpreted as a thermal one with respect to the conformal vacuum. The thermal factor is of the Bose-Einstein type in odd dimensional space and of the Fermi-Dirac type in even number of spatial dimensions.

Extended duality condition for conformal vacuum nonlinear electrodynamics

This paper discusses the possibility of expanding the interpretation of the dual invariance condition to create a special type of nonlinear vacuum electrodynamics models that are invariant with respect to transformations of the conformal group.

Mean field squared and energy–momentum tensor for the hyperbolic vacuum in dS spacetime

We evaluate the Hadamard function and the vacuum expectation values (VEVs) of the field squared and energy–momentum tensor for a massless conformally coupled scalar field in (D+1)-dimensional de Sitter (dS) spacetime foliated by spatial sections of negative constant curvature. It is assumed that the field is prepared in the hyperbolic vacuum state. An integral representation for the difference of the Hadamard functions corresponding to the hyperbolic and Bunch–Davies vacua is provided that is well adapted for the evaluation of the expectation values in the coincidence limit. It is shown that the Bunch–Davies state is interpreted as thermal with respect to the hyperbolic vacuum. An expression for the corresponding density of states is provided. The relations obtained for the difference in the VEVs for the Bunch–Davies and hyperbolic vacua are compared with the corresponding relations for the Fulling–Rindler and Minkowski vacua in flat spacetime. The similarity between those relations is explained by the conformal connection of dS spacetime with hyperbolic foliation and Rindler spacetime. As a limiting case, the VEVs for the conformal vacuum in the Milne universe are discussed.

Casimir densities induced by a sphere in the hyperbolic vacuum of de Sitter spacetime

Complete set of modes and the Hadamard function are constructed for a scalar field inside and outside a sphere in (D+1)-dimensional de Sitter spacetime foliated by negative constant curvature spaces. We assume that the field obeys Robin boundary condition on the sphere. The contributions in the Hadamard function induced by the sphere are explicitly separated and the vacuum expectation values (VEVs) of the field squared and energy-momentum tensor are investigated for the hyperbolic vacuum. In the flat spacetime limit the latter is reduced to the conformal vacuum in the Milne universe and is different from the maximally symmetric Bunch-Davies vacuum state. The vacuum energy-momentum tensor has a nonzero off-diagonal component that describes the energy flux in the radial direction. The latter is a purely sphere-induced effect and is absent in the boundary-free geometry. Depending on the constant in Robin boundary condition and also on the radial coordinate, the energy flux can be directed either from the sphere or towards the sphere. At early stages of the cosmological expansion the effects of the spacetime curvature on the sphere-induced VEVs are weak and the leading terms in the corresponding expansions coincide with those for a sphere in the Milne universe. The influence of the gravitational field is essential at late stages of the expansion. Depending on the field mass and the curvature coupling parameter, the decay of the sphere-induced VEVs, as functions of the time coordinate, is monotonic or damping oscillatory. At large distances from the sphere the fall-off of the sphere-induced VEVs, as functions of the geodesic distance, is exponential for both massless and massive fields.

Ricci Linear Weyl/Maxwell Mutual Sourcing

We elevate the field theoretical similarities between Maxwell and Weyl vector fields into a full local scale/gauge invariant Weyl/Maxwell mutual sourcing theory. In its preliminary form, and exclusively in four dimensions, the associated Lagrangian is dynamical scalar field free, hosts no fermion matter fields, and Holdom kinetic mixing is switched off. The mutual sourcing term is then necessarily spacetime curvature (not just metric) dependent, and inevitably Ricci linear, suggesting that a non-vanishing spacetime curvature can in principle induce an electromagnetic current. In its mature form, however, the Weyl/Maxwell mutual sourcing idea serendipitously constitutes a novel variant of the gravitational Weyl-Dirac (incorporating Brans-Dicke) theory. Counter intuitively, and again exclusively in four dimensions, the optional quartic scalar potential gets consistently replaced by a Higgs-like potential, such that the co-divergence of the Maxwell vector field resembles a conformal vacuum expectation value.

The Casimir Densities for a Sphere in the Milne Universe

The influence of a spherical boundary on the vacuum fluctuations of a massive scalar field is investigated in the background of a ( D + 1 ) -dimensional Milne universe, assuming that the field obeys Robin boundary conditions on the sphere. The normalized mode functions are derived for the regions inside and outside the sphere and different vacuum states are discussed. For the conformal vacuum, the Hadamard function is decomposed into boundary-free and sphere-induced contributions and an integral representation is obtained for the latter in both the interior and exterior regions. As important local characteristics of the vacuum state, the vacuum expectation values (VEVs) of the field squared and of the energy-momentum tensor are investigated. It is shown that the vacuum energy-momentum tensor has an off-diagonal component that corresponds to the energy flux along the radial direction. Depending on the coefficient in Robin boundary conditions, the sphere-induced contribution to the vacuum energy and the energy flux can be either positive or negative. At late stages of the expansion and for a massive field the decay of the sphere-induced VEVs, as functions of time, is damping oscillatory. The geometry under consideration is conformally related to that for a static spacetime with negative constant curvature space and the sphere-induced contributions in the corresponding VEVs are compared.

Conformal vacuum and the fluctuation-dissipation theorem in a de Sitter universe and black hole spacetimes

In the studies of quantum field theory in curved spacetime, the ambiguous concept of vacuum state and the particle content is a long-standing debatable aspect. So far it is well known to us that in the background of the curved spacetime, some privileged class of observers detect particle production in the suitably chosen vacuum states of the quantum matter fields. In this work we aim to study the characteristics behaviour of these produced particles in the background of the de-Sitter (dS) Friedmann-Lama\^{i}tre-Robertson-Walker (FLRW) Universe (both for $(1+1)$ and $(3+1)$ dimensions) and $(1+1)$-dimensional Schwarzschild black hole (BH) spacetime, from the point of view of the respective privileged class of observers. Here the analysis is confined to the observers who perceive particle excitations in the conformal vacuum. We consider some test particles in the thermal bath of the produced particles and calculate the correlation function of the fluctuation of the random force as exerted by the produced quanta on the test particles. We obtain that the correlation function abides by the fluctuation-dissipation theorem, which in turn signifies that the test particles execute Brownian-like motion in the thermal bath of the produced quanta.

Detector response along null geodesics in black hole spacetimes and in a Friedmann-Lemaitre-Robertson-Walker universe

We study the detector's response when moving along an ingoing null geodesic. The backgrounds are chosen to be black hole spacetimes [($1+1$)-dimensional Schwarzschild metric and near-horizon effective metric for any stationary black hole in arbitrary dimensions] as well as a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. For black holes, the trajectories are defined in Schwarzschild coordinates, and the field modes correspond to a Boulware vacuum, whereas for the FLRW case, the detector is moving along the path defined in original cosmic time and the field modes are related to a conformal vacuum. The analysis is done for three stages (de Sitter, radiation dominated, and matter dominated) of the universe. We find that, although the detector is freely falling, it registered particles in the above-mentioned respective vacuums. We confirm this by different approaches. The detection probability distributions, in all situations, are thermal in nature.

Compact objects in conformal nonlinear electrodynamics

In this paper we consider a special case of vacuum nonlinear electrodynamics with a stress–energy tensor conformal to the Maxwell theory. Distinctive features of this model are the absence of a dimensional parameter for the nonlinearity description and a very simple form of the dominant energy condition, which can easily be verified in an arbitrary pseudo-Riemannian space-time with the consequent constraints on the model parameters. In this paper we analyze some properties of astrophysical compact objects coupled to conformal vacuum nonlinear electrodynamics.

Cosmological Solutions and Quantum Measurements in Conformal Vacuum Analogue

In a quantum measurement with post selection condition for transient short range observations with weak values as statistical ensembles in a time reversed scenario, vacuum energy fluctuations with entangled entropy and with its qubits of information can show transitions to action potentials for energy flows of an anomalous nature, so that superfluid state of vacuum as a quantum condensate system is relativistically transformed as an idealized cosmological fluid system with ultra high temperatures and vorticity, like in Blackhole analogous non singular metric of Einstein vacuum solutions of field equations. This can also explain quark gluon plasmic fluids in such metrics corresponding to quantum fluid vortex systems in a highly thermalised state. For short range and short lived observers, vacuum is measured as a quantum entangled system, with energy fluctuations in a strongly correlated state. This can have analogies with a spin coupled many body system of quantum particles corresponding to a fermionic superfluid as a scalar field with boson excitation and higher amplitude phonon modes. There is conformance with a system of strongly correlated quantum harmonic oscillators where the motion can be approximated to a Fourier Transform of KG equation as a generalised Klein Gordon one describing a quantized complex scalar field dynamics with a self interaction potential. The de Sitter vacuum invariant can be shown to correspond to a Black hole like metric in a non singular solution of field equations, with negative energy domains due to torsion tensor and Dirac Spinor minimal coupling. The geometrical vorticity with space time fluid state angular momentum of a large order can correspond to 2D quantum vortex flows in superfluids. The initial conditions of the hydrodynamic reveal negative energy and negative temperature domains prior to onset of quantum turbulence as the idealized fluid system expands and decays due to entropic effects, naturally. This can show time reversal behaviour with short lived local violations of the second law of thermodynamics, given an entropic lowering effect. However there is entanglement entropy with high mutual information due to strongly correlated state that might even imply negative conditional information. A situation thus locally exists for a time interval of a transient nature when quantum weak measurements by a nearby short range observer can manipulate quantum fluctuations like a supersystem in nature, having analogies to a quantum Maxwell demon translating high mutual information of strongly correlated quantum entangled states of conformal vacuum to action potentials for energy dissipation and work. Quantum mechanical indeterminism permits imposing post selection condition in such time reversed, scenario, so that fast thermalization can take place in a transition from negative temperature state to ultrahigh positive absolute hot conditions, as if a thermodynamic engine with higher than Carnot efficiencies is operating, locally and transiently.

Scalar Casimir effect in a linearly expanding universe

We investigate quantum vacuum effects for a massive scalar field, induced by two planar boundaries in background of a linearly expanding spatially flat Friedmann–Robertson–Walker spacetime for an arbitrary number of spatial dimensions. For the Robin boundary conditions and for general curvature coupling parameter, a complete set of mode functions is presented and the related Hadamard function is evaluated. The results are specified for the most important special cases of the adiabatic and conformal vacuum states. The vacuum expectation values of the field squared and of the energy–momentum tensor are investigated for a massive conformally coupled field. The vacuum energy–momentum tensor, in addition to the diagonal components, has nonzero off-diagonal component describing energy flux along the direction perpendicular to the plates. The influence of the gravitational field on the local characteristics of the vacuum state is essential at distances from the boundaries larger than the curvature radius of the background spacetime. In contrast to the Minkowskian bulk, at large distances the boundary-induced expectation values follow as power law for both massless and massive fields. Another difference is that the Casimir forces acting on the separate plates do not coincide if the corresponding Robin coefficients are different. At large separations between the plates the decay of the forces is power law. We show that during the cosmological expansion the forces may change the sign.

Entanglement dynamics in de Sitter spacetime

We apply a master equation approximation with dynamical coarse graining to a pair of detectors interacting with a scalar field. By solving the master equation numerically, we investigate the evolution of negativity between comoving detectors in de Sitter space. For a massless conformal scalar field with conformal vacuum, it is found that a pair of detectors can perceive entanglement beyond the Hubble horizon scale if the initial separation of detectors is sufficiently small. At the same time, violation of the Bell–Clauser–Horne–Shimony–Holt inequality on the super-horizon scale is also detected. For a massless minimal scalar field with Bunch–Davies vacuum, on the other hand, the entanglement decays within Hubble time scale, owing to the quantum noise caused by particle creations in de Sitter space, and the entanglement on the super-horizon scale cannot be detected.

Conformal invariant vacuum nonlinear electrodynamics

In this paper, a general case of conformal invariant vacuum nonlinear electrodynamics is studied. We analyze the consistency of this electrodynamics model with fundamental principles such as causality, unitarity, and the Ellis-Hawking dominant energy condition. Certain features of the electromagnetic waves in this model are investigated.

Spinorial wave equations and stability of the Milne spacetime

The spinorial versions of the conformal vacuum Einstein field equations are used to construct a system of quasilinear wave equations for the various conformal fields. As a part of the analysis we also show how to construct a subsidiary system of wave equations for the zero quantities associated to the various conformal field equations. This subsidiary system is used, in turn, to show that under suitable assumptions on the initial data a solution to the wave equations for the conformal fields implies a solution to the actual conformal Einstein field equations. The use of spinors allows for a more unified deduction of the required wave equations and the analysis of the subsidiary equations than similar approaches based on the metric conformal field equations. As an application of our construction we study the nonlinear stability of the Milne Universe. It is shown that sufficiently small perturbations of initial hyperboloidal data for the Milne Universe gives rise to a solution to the Einstein field equations which exists towards the future and has an asymptotic structure similar to that of the Milne Universe.

Signatures of energy flux in particle production: a black hole birth cry and death gasp

It is recently argued that if the Hawking radiation process is unitary, then a black hole's mass cannot be monotonically decreasing. We examine the time dependent particle count and negative energy flux in the non-trivial conformal vacuum via the moving mirror approach. A new, exactly unitary solution is presented which emits a characteristic above-thermal positive energy burst, a thermal plateau, and negative energy flux. It is found that the characteristic positive energy flare and thermal plateau is observed in the particle outflow. However, the results of time dependent particle production show no overt indication of negative energy flux. Therefore, a black hole's birth cry is detectable by asymptotic observers via particle count, whereas its death gasp is not.

Local thermal observables in spatially open FRW spaces

Certain local thermal observables are considered in well-known examples of spatially open FRW spaces: Milne, open de Sitter and anti--de Sitter as well as Einstein static universes. Another value for fixing the ambiguity in defining the Wick square and, hence, the local temperature is motivated in the last example. Physical consequences of that choice are discussed for static and conformal vacua in those spaces.

Coupling the Sorkin-Johnston state to gravity

We consider the dynamics of the Sorkin-Johnston (SJ) state for a massless scalar field in two dimensions. We conduct a study of the renormalized stress-tensor by a subtraction procedure, and compare the results with those of the conformal vacuum, with an important contribution from correction term. We find a large trace anomaly and compute backreaction effects to two dimensional (Liouville) gravity. We find a natural interpretation for the mirror behavior of the SJ state described in previous works.

Entanglement entropy and negative energy in two dimensions

It is well known that quantum effects can produce negative energy densities, though for limited times. Here we show in the context of two-dimensional CFT that such negative energy densities are present in any non-trivial conformal vacuum and can be interpreted in terms of the entanglement structure of such states. We derive an exact identity relating the outgoing energy flux and the entanglement entropy in the in-vacuum. When applied to two-dimensional models of black hole evaporation, this identity implies that unitarity is incompatible with monotonic mass loss.