Radial Oscillations and Dynamical Instability Analysis for Linear GUP-modified White Dwarfs

A modification to the Heisenberg uncertainty principle is called thegeneralized uncertainty principle (GUP), which emerged due to the introductionof a minimum measurable length, common among phenomenological approaches toquantum gravity. An approach to GUP called linear GUP (LGUP) has recently beendeveloped that satisfies both the minimum measurable length and the maximummeasurable momentum, resulting to a phase space volume proportional to thefirst-order momentum $(1 - \alpha p)^{-4} d^3x d^3p$, where $\alpha$ is thestill-unestablished GUP parameter. In this study, we explore the mass-radiusrelations of LGUP-modified white dwarfs, and provide them with radialperturbations to investigate the dynamical instability arising from theoscillations. We find from the mass-radius relations that LGUP results to awhite dwarf with a lower maximum mass, and this effect gets more apparent withlarger the values of $\alpha$. We also observe that the mass of the white dwarfcorresponding to the vanishing of the square of the fundamental frequency$\omega_0$ is the maximum mass the white dwarf can have in the mass-radiusrelations. The dynamical instability analysis also shows that instability setsin for all values of the GUP parameters $\alpha$, and at lower centraldensities $\rho_c$ (corresponding to lower maximum masses) for increasing$\alpha$, which verifies the results obtained from the mass-radius relationsplots. Finally, we note that the mass limit is preserved for LGUP-modifiedwhite dwarfs, indicating that LGUP supports gravitational collapse of thecompact object.<br

Equation of State and Mass-Radius Relations of Quadratic Generalized Uncertainty Principle-modified White Dwarfs with Arbitrary Temperatures

We study the mass-radius relations of finite temperature white dwarfsmodified by the quadratic generalized uncertainty principle (QGUP), aprediction that arises from quantum gravity phenomenology. This QGUP approachextends the Heisenberg uncertainty principle by a quadratic term in momenta,which then modifies the phase space volume in the Chandrasekhar equation ofstate (EoS). This EoS was first calculated by treating the GUP parameter$\beta$ as perturbative. This perturbative EoS exhibits the expected thermaldeviation for low pressures, while showing conflicting behaviors in the highpressure regime dependent on the sign of the $j$th order of approximation,$(\mathcal{O}(\beta^j))$. To explore the effects of QGUP further, we proceedwith a full numerical simulation, and showed that in general, finitetemperatures cause the EoS at low pressures to soften, while QGUP stiffens theEOS at high pressures. This modified EoS was then applied to theTolman-Oppenheimer-Volkoff equations and its classical approximation to obtainthe modified mass-radius relations for general relativistic and Newtonian whitedwarfs. The relations for both cases were found to exhibit the expected thermaldeviations at small masses, where low-mass white dwarfs are shifted to thehigh-mass regime at large radii, while high-mass white dwarfs acquire largermasses, beyond the Chandrasekhar limit. Additionally, we find that forsufficiently large values of the GUP parameter and temperature, we obtainmass-radius relations that are completely removed from the ideal case, ashigh-mass deviations due to GUP and low-mass deviations due to temperature areno longer mutually exclusive.<br

Andreev States in long shallow SNS constrictions

We study Andreev bound states in a long shallow normal constriction, which is open to a superconductor at both ends. The interesting features of such setup include the absence of electron-hole symmetry and the interference of electron waves along the constriction. We compare results of a numerical approach based on the Bogoliubov equations with those of a refined semiclassical description. Three types of Andreev bound states occur in the constriction: {\it i}) one where both electron and hole wave part of the bound state propagate through the constriction, {\it ii}) one where neither electron nor hole wave part propagate, and {\it iii}) one where only the electron wave propagates. We show that in a wide energy region the spacing between the Andreev states is strongly modulated by the interference of electron waves passing the constriction

An inverter-chain link implementation of quantum teleportation and superdense coding

A new perspective in terms of inverter-chain link (ICL) diagrams of quantum entanglement faithfully captures the fundamental concept of quantum teleportation and superdense coding. The ICL may be considered a series of {\sigma}_{x} Pauli-matrix operations, where a physical/geometric representation provides the mysterious link raised by EPR. Here, we employ discrete phase space and ICL analyses of quantum entanglement as a resource for quantum teleportation and superdense coding. We underscore the quantum superposition principle and Hadamard transformation under a local single-qubit operation. On the fundamental question posed by EPR, our result seems to lend support to the geometric nature of quantum entanglement. In concluding remarks, we discuss very briefly a bold conjecture in physics aiming to unify general relativity with quantum mechanics, namely, ER=EPR.Comment: 12 pages 3 figures. arXiv admin note: text overlap with arXiv:2112.1029

Equation of State and Mass-Radius Relations of Quadratic Generalized Uncertainty Principle-modified White Dwarfs with Arbitrary Temperatures

We study the mass-radius relations of finite temperature white dwarfs modified by the quadratic generalized uncertainty principle (QGUP), a prediction that arises from quantum gravity phenomenology. This QGUP approach extends the Heisenberg uncertainty principle by a quadratic term in momenta, which then modifies the phase space volume in the Chandrasekhar equation of state (EoS). This EoS was first calculated by treating the GUP parameter $\beta$ as perturbative. This perturbative EoS exhibits the expected thermal deviation for low pressures, while showing conflicting behaviors in the high pressure regime dependent on the sign of the $j$th order of approximation, $(\mathcal{O}(\beta^j))$. To explore the effects of QGUP further, we proceed with a full numerical simulation, and showed that in general, finite temperatures cause the EoS at low pressures to soften, while QGUP stiffens the EOS at high pressures. This modified EoS was then applied to the Tolman-Oppenheimer-Volkoff equations and its classical approximation to obtain the modified mass-radius relations for general relativistic and Newtonian white dwarfs. The relations for both cases were found to exhibit the expected thermal deviations at small masses, where low-mass white dwarfs are shifted to the high-mass regime at large radii, while high-mass white dwarfs acquire larger masses, beyond the Chandrasekhar limit. Additionally, we find that for sufficiently large values of the GUP parameter and temperature, we obtain mass-radius relations that are completely removed from the ideal case, as high-mass deviations due to GUP and low-mass deviations due to temperature are no longer mutually exclusive

Radial Oscillations and Dynamical Instability Analysis for Linear GUP-modified White Dwarfs

A modification to the Heisenberg uncertainty principle is called the generalized uncertainty principle (GUP), which emerged due to the introduction of a minimum measurable length, common among phenomenological approaches to quantum gravity. An approach to GUP called linear GUP (LGUP) has recently been developed that satisfies both the minimum measurable length and the maximum measurable momentum, resulting to a phase space volume proportional to the first-order momentum $(1 - \alpha p)^{-4} d^3x d^3p$, where $\alpha$ is the still-unestablished GUP parameter. In this study, we explore the mass-radius relations of LGUP-modified white dwarfs, and provide them with radial perturbations to investigate the dynamical instability arising from the oscillations. We find from the mass-radius relations that LGUP results to a white dwarf with a lower maximum mass, and this effect gets more apparent with larger the values of $\alpha$. We also observe that the mass of the white dwarf corresponding to the vanishing of the square of the fundamental frequency $\omega_0$ is the maximum mass the white dwarf can have in the mass-radius relations. The dynamical instability analysis also shows that instability sets in for all values of the GUP parameters $\alpha$, and at lower central densities $\rho_c$ (corresponding to lower maximum masses) for increasing $\alpha$, which verifies the results obtained from the mass-radius relations plots. Finally, we note that the mass limit is preserved for LGUP-modified white dwarfs, indicating that LGUP supports gravitational collapse of the compact object