Non-inertial Frame Research Articles

Quantum speed limit time for the damped Jaynes-Cummings and Ohmic-like dephasing models in Schwarzschild space-time

Quantum theory sets the bound on the minimal evolution time between initial and final states of the quantum system. This minimal evolution time can be used to specify the maximal speed of the evolution in open and closed quantum systems. Quantum speed limit is one of the interesting issue in the theory of open quantum systems. One may investigate the influence of the relativistic effect on the quantum speed limit time. When several observers are placed in different inertial or non-inertial frames, or in Schwarzschild space-time, the relativistic effect should be taken into account. In this work, the quantum speed limit time in Schwarzschild space-time will be studied for two various model consist of damped Jaynes-Cummings and Ohmic-like dephasing. First, it will be observed that how quantum coherence is affected by Hawking radiation. According to the dependence of quantum speed limit time on quantum coherence and the dependence of quantum coherence on relative distance of quantum system to event horizon R_{0}, it will be represented that the quantum speed limit time in Schwarzschild space-time is decreased by increasing R_{0} for damped Jaynes-Cummings model and conversely. It is increased by increasing R_{0} for Ohmic-like dephasing model.

A Level Set Approach for Dynamics of Flow in Accelerating Rectangular Container

The level set approach is a numerical technique to capture the interface for a system of two immiscible fluids separated by a sharp interface. Since the interface is captured by an implicit function using this approach, this is a Eulerian formulation of the evolution of interface. The different fluids must be identified by using a marker function, called the level set function that takes different values in the various fluids. The present work uses a level set approach for modeling the dynamics of flow and the shape of the liquid free surface in a partly filled rectangular tank which is subjected to an impulsive motion from rest. The governing equations are written about a non-inertial frame attached to the container in motion. Extremely high viscosity and density ratios of the two immiscible fluids make the problem more challenging. The surface tension forces are ignored in this study. The signed distance property of the level set function is retained by using the reinitialization algorithm. In the present study, we have compared the computed shapes of equilibrium free surface with theoretically predicted shapes at equilibrium.

Stability and ground experiments of a spinning triangular tethered satellite formation on a low earth orbit

This paper studies the spinning stability of a triangular tethered satellite formation that flies on a low earth orbit. The spinning around the center of mass at a constant angular rate gives rise to a periodic motion in the non-inertial orbital frame. Floquet theory is used to analyze the stability of the periodic motion. A dynamic similarity between the on-orbit dynamics and ground experimental models is built to construct an equivalent ground experiment to verify the stability analysis. The analytical and experimental results show that a stable periodic motion can be guaranteed if the spinning angular rate of the system exceeds a critical value.

Active particles in noninertial frames: How to self-propel on a carousel.

Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion, and fluctuations occur relative to a noninertial frame and thereby the active Brownian motion model is generalized to noninertial frames. First, analytical solutions are presented for the overdamped case, both for linear swimmers and for circle swimmers. For a frame rotating with constant angular velocity ("carousel"), the resulting noise-free trajectories in the static laboratory frame are trochoids if these are circles in the rotating frame. For systems governed by inertia, such as vibrated granulates or active complex plasmas, centrifugal and Coriolis forces become relevant. For both linear and circling self-propulsion, these forces lead to out-spiraling trajectories which for long times approach a spira mirabilis. This implies that a self-propelled particle will typically leave a rotating carousel. A navigation strategy is proposed to avoid this expulsion, by adjusting the self-propulsion direction at will. For a particle, initially quiescent in the rotating frame, it is shown that this strategy only works if the initial distance to the rotation center is smaller than a critical radius R_{c} which scales with the self-propulsion velocity. Possible experiments to verify the theoretical predictions are discussed.

Hybrid vibration control of a Two-Link Flexible manipulator

This research work deals with tip vibration control of a Two-Link Flexible manipulator using hybrid control technique. This technique involves the implementation of unconstrained viscoelastic damping layer on the links in conjunction with active damping using piezoelectric sensors and actuators. Mathematical modelling of the complete system is done using the finite element approach in the inertial frame. Viscoelastic damping is modelled using Kelvin–Voigt elements for which a damping matrix is derived. Active damping is modelled as time-dependent uniformly distributed load applied by the piezoelectric actuator on the flexible link working under feedback control. The angular and linear velocities of the tips of flexible links are used for direct feedback. The unconstrained viscoelastic damping layer effectively reduces the vibrations of the system. The effectiveness of the active control depends upon the relative position of sensors and actuators on the links. The novelty of the work lies in control of torsional and flexural vibrations through the application of passive and active damping methods to the non-inertial frames represented by the manipulator links.

Universal transformation of displacement operators and its application to homodyne tomography in differing relativistic reference frames

In this paper, we study how a displacement of a quantum system appears under a change of relativistic reference frame. We introduce a generic method in which a displacement operator in one reference frame can be transformed into another reference frame. It is found that, when moving between non-inertial reference frames there can be distortions of phase information, modal structure and amplitude. We analyse how these effects affect traditional homodyne detection techniques. We then develop an in principle homodyne detection scheme which is robust to these effect, called the ideal homodyne detection scheme. We then numerically compare traditional homodyne detection with this in principle method and illustrate regimes when the traditional homodyne detection schemes fail to extract full quantum information.

On the added-mass force and moment and the vortex projection method. Application to thin airfoils

The force and moment on a solid body in non-uniform motion in an incompressible fluid are derived following the projection technique of Quartapelle and Napolitano (1983 AIAA J. 21, 911–913) and Chang (1992 Proc. R. Soc. A-Math. Phys. Engng Sci. 437, 517–525) in a compact vector form, identifying added-mass terms equivalent to those resulting from potential-flow theory. The expressions are formally much simpler in a non-inertial frame fixed relative to the body, though general relations for an inertial frame are also given. Approximate analytical expressions are obtained for the force and moment on two-dimensional elliptic bodies at high Reynolds numbers, each one consisting of just two terms: an added-mass component and a vortex term (integration of a projection of Lamb’s vector). The formulation is applied to a flat plate in steady motion and in non-uniform oscillatory motion, recovering classical results in both cases, but adding new physical insight about the origin of the different elements of the force and moment. It is shown that, in the non-steady motion, the added-mass components of the force and moment cancel out with part of their respective vortex terms, so that all the force and moment come from appropriate projections of Lamb’s vector, including the supposedly added-mass force and moment. This result indicates that one has to be cautious about simplified aerodynamic models for flapping foils based on a simple separation of the added-mass and vortical components of the force and moment. The present results can be used to obtain analytically the force and moment on an ellipse with arbitrary motion through an incompressible fluid at high Reynolds numbers.

Tetrapartite entanglement measures of W-class in noninertial frames**Project partially supported by the CONACYT, Mexico under the Grant No. 288856-CB-2016, partially by 20190234-SIP-IPN, Mexico, and partially by the program XXVIII Verano de la Investigación Científica 2018 supported by the Academia Mexicana de Ciencias.

We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The 1–1 tangle, 1–3 tangle, and whole entanglement measurements and , are studied and illustrated with graphics through their dependence on the acceleration parameter rd for the first case and rc and rd for the second case. It is found that the negativities (1–1 tangle and 1–3 tangle) and π-tangle decrease when the acceleration parameter rd or in the second case rc and rd increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the 1–1 tangle for the first case vanishes at infinite accelerations, but for the second case the 1–1 tangle disappears completely when . An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.

Quantum simulation of Unruh radiation

Exploring quantum phenomena in a curved spacetime is an emerging interdisciplinary area relating many fields in physics such as general relativity, thermodynamics, and quantum information. One famous prediction is the Hawking-Unruh thermal radiation, the manifestation of Minkowski vacuum in an accelerating reference frame. We simulate the radiation by evolving a parametrically driven Bose-Einstein condensate of $\approx 10^5$ atoms, which radiates coherent pairs of atoms with opposite momenta. We observe a matterwave field which follows a Boltzmann distribution for a local observer. The extracted temperature and entropy from the atomic distribution are in agreement with Unruh's predictions. We further observe the long-distance phase coherence and temporal reversibility of emitted matter-waves, hallmarks that distinguish Unruh radiations from classical counterparts. Our results may lead to further insights regarding the nature of the Hawking and Unruh effects and behaviors of quantum physics in a curved spacetime.

Two-fluid equations for two-phase flows in moving systems

Abstract Recently, ocean nuclear reactors have received attention due to enhanced safety features. The movable and transportable characteristics distinguish ocean nuclear reactors from land-based nuclear reactors. Therefore, for safety/design analysis of the ocean reactor, the thermos-hydraulics must be investigated in the moving system. However, there are no studies reporting the general two-fluid equations that can be used for multi-dimensional simulations of two-phase flows in moving systems. This study is to systematically formulate the multi-dimensional two-fluid equations in the non-inertial frame of reference. To demonstrate the applicability of the formulated equations, we perform a total of six different simulations in 2D tanks with translational and/or rotational motions.

Optimal oscillation parameters of vibrating screens

Optimal oscillation parameters of vibrating screens are determined using analytical methods by investigating movement of a single spherical grain particle in the vibrating sieve’s non-inertial reference frame. Dimensionless parameters determining the efficiency of screening process are defined. Effect of interactions between multiple numbers of particles moving on the screen is analyzed using discrete element method. By comparing the analytical and numerical results, it can be seen, that the analytical evaluation of screening efficiency can be used until a given contaminant size unlimitedly in the examined range of screen angle. Additionally in case of this minimal contaminant size there is a maximal screening angle value. Above this angle it seems, that the use of our discrete element based evaluation of screening efficiency is unavoidable.

Giant Unruh effect in hyperbolic metamaterial waveguides.

The Unruh effect is the prediction that an accelerating object perceives its surroundings as a bath of thermal radiation, even if it accelerates in vacuum. The Unruh effect is believed to be very difficult to observe in an experiment, since an observer accelerating at g=9.8 m/s2 should see a vacuum temperature of only 4×10-20 K. Here we demonstrate that photons in metamaterial waveguides may behave as massive quasi-particles accelerating at up to 1024 g, which is about 12 orders of magnitude larger than the surface acceleration near a stellar black hole. These record high accelerations may enable experimental studies of the Unruh effect and the loss of quantum entanglement in strongly accelerated reference frames.

Завершенная форма для численного анализа постоянной распространения электромагнитных волн в неинерциальной системе отсчета.

Завершенная форма для численного анализа постоянной распространения электромагнитных волн в неинерциальной системе отсчета.

A geometrically-exact momentum-based non-linear theory applicable to beams in non-inertial frames

A geometrically-exact non-linear beam model is developed based on conservation of momentum for application to arbitrarily-shaped beams having large deformations and large overall motions. Coordinate transformations are used to derive the non-linear inertial forces and moments and the non-linear relationships between displacements and strains, enabling rigorous consideration of kinematic and geometric nonlinearities. General non-linear equations of motion are first derived in a differential form, and then are simplified using practical engineering assumptions, including developments of a linearized model for small angles and small strains and a discretized model using finite volumes. A separation of displacements technique is proposed, which enables non-linear beam dynamics to be rigorously reduced to a series of piecewise-linear models. The proposed model is unique amongst existing geometrically-exact beam formulations in that it is formulated using dynamic quantities relative to intermediate non-inertial coordinates, allowing general Lagrangian formulations to be established in floating frames with inertial coupling effects, which is compatible with multibody models. The practical value of these theoretical developments is demonstrated through numerical implementation and convergence analyses. The piecewise-linear dynamic solver in which displacements are computed from an evolving configuration is shown to capture non-linear dynamic behaviors using linear solutions without iteration at each time-step.

How robust is the indistinguishability between quantum fluctuation seen from noninertial frame and real thermal bath

We re-advocated the conjecture of indistinguishability between the quantum fluctuation observed from a Rindler frame and a real thermal bath, for the case of a free massless scalar field. To clarify the robustness and how far such is admissible, in this paper, we investigate the issue from two different non-inertial observers' perspective. A detailed analysis is being done to find the observable quantities as measured by two non-inertial observers (one is Rindler and another is uniformly rotating) on the real thermal bath and Rindler frame in Minkowski spacetime. More precisely, we compare Thermal-Rindler with Rindler-Rindler and Thermal-rotating with Rindler-rotating situations. In the first model it is observed that although some of the observables are equivalent, all the components of renormalised stress-tensor are not the same. In the later model, we again find that this equivalence is not totally guaranteed. Therefore we argue that the indistinguishability between the real thermal bath and the Rindler frame may not be totally true.

Quantum teleportation of Dirac fields in noninertial frames with amplitude damping

We investigate quantum teleportation between users located in noninertial frames and analyze how the acceleration can improve the fidelity of quantum teleportation between two relatively accelerating partners. We see that the fidelity increases with respect to the acceleration as a consequence of the Unruh effect. In our scheme, Alice and Rob initially share a special $\mathsf{X}$-type state, Alice stays stationary, while Rob is uniformly accelerated with respect to Alice. We additionally study the system-environment dynamics in the noninertial frames, i.e., the $\mathsf{X}$-type state shared between Alice and Rob interacts with the environment via amplitude damping channel. Our results demonstrate a monogamy relation of the fidelity with acceleration and amplitude damping channel, these result suggest that the fidelity of quantum teleportation cannot be enhanced simultaneously by both the acceleration and amplitude damping channel. Such a property may have potential applications in protecting the fidelity of quantum teleportation performed by observers in relative motion.

Effect of partial-collapse measurement on quantum Stackelberg duopoly game in noninertial frame

An efficient method is proposed to improve the payoffs of the firms in quantum Stackelberg duopoly game under noninertial frame using partial-collapse measurement. It is shown that the payoffs of firms can be enhanced to a great extent. We obtain the maximally retrievable payoffs of firms for maximally entangled initial state and unentangled initial state respectively. In particular, the payoffs of firms approach to certain constants and Nash equilibrium exists for the whole range values of the acceleration parameter by changing partial-collapse measurement strength. Our work provides a novel method to recover payoffs in quantum game under Unruh decoherence and exhibits the ability of partial-collapse measurement as an important technique in relativistic quantum game.

Precession Intuitively Explained

Formal explanations of the dynamics of free and heavy tops are considered to be known for centuries. However, intuitive understanding of their unexpected behavior is still a challenge. In this paper, we present elementary force based explanations of several phenomena related the dynamics of heavy symmetric tops, derived in inertial and non-inertial reference frames. Simple calculations are enabled by a model equivalent to a spinning top, namely a square-formed tube carrying a streaming ideal fluid or a frictionless chain. Precession in a combined, gravitational and magnetic field is also discussed.

Cosmic Matter Creation from Viscous Energy Dissipation: A Resurrection of Fred Hoyle’s Dream

Fred Hoyle is known as creator of the so-called “steady state universe” which latter, although permanently expanding, does not change its state of matter, especially keeping its density constant. To achieve this virtue Hoyle introduced into the energy-momentum tensor of the GRT field equations a term derived from a so-called ad-hoc creation field astonishingly leading to field equations very similar to the ones already developed by Tolman when introducing energy sources connected with viscous dissipation forces acting upon dust-like cosmic matter [1]. In this article here we shall again study the action of viscous forces in cosmic baryonic matter and shall boil it down to volume viscosity contributions to the viscous stress tensor in a universe with a compressible Hubble flow. Assuming that by collisions of any kind the energy of the differential Hubble drift between two collision points of cosmic matter particles, seen in the non-inertial rest frames of moving particles, is randomized and converted into thermal energy, one can then show with the help of a kinetic transport equation that during the cosmic expansion permanently thermal energy is generated leading to the result that the matter temperature, instead of falling-off, is linearly increasing with the scale of the universe. This not only questions the standard use of the model of pressure-free, dust-like matter in the universe, but furthermore indicates the possibility of an asymptotic cosmic-ray-like matter state including the possibility of matter creation by pair production.

An investigation of some quantum correlations of Dirac fields in noninertial frames

In this paper, some concepts of quantum correlations, such as one-way quantum deficit, purity, and entanglement of formation are investigated between the modes of Dirac fields in noninertial frames. We consider two bipartite divisions of a tripartite system constructed by initial Werner states, which is shared between two relatively accelerated observers. The degradation of these quantum correlations is shown when the acceleration parameter increases. However, a nonzero amount of correlations survives even at infinite acceleration limit. Furthermore, we study the inevitable influence of mixedness factor of initial state on the quantum correlations behaviour. Finally, we review our calculation beyond single-mode approximation and point out some differences and similarities between the two regimes.