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Using the single-mode approximation, we first calculate entanglement measures such as negativity (1-3 and 1-1 tangles) and von Neumann entropy for a tetrapartite W-Class system in noninertial frame and then analyze the whole entanglement measures, the residual π 4 and geometric Π 4 average of tangles. Notice that the difference between π 4 and Π 4 is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer to four accelerated observers. The results show that there still exists entanglement for the complete system even when acceleration r tends to infinity. The degree of entanglement is disappeared for the 1-1 tangle case when the acceleration r>0.472473. We reexamine the Unruh effect in noninertial frames. It is shown that the entanglement system in which only one qubit is accelerated is more robust than those entangled systems in which two or three or four qubits are accelerated. It is also found that the von Neumann entropy S of the total system always increases with the increasing accelerated observers, but the S κξ and S κζδ with two and three involved noninertial qubits first increases and then decreases with the acceleration parameter r, but they are equal to constants 1 and 0.811278 respectively for zero involved noninertial qubit.

According to the single-mode approximation applied to two different mo des, each associated with different uniformly accelerating reference frames, we present analytical expression of the Minkowski states for both the ground and first excited states. Applying such an approximation, we study the entanglement property of Bell and Greenberger–Horne–Zeilinger (GHZ) states formed by such states. The corresponding entanglement properties are described by studying negativity and von Neumann entropy. The degree of entanglement will be degraded when the acceleration parameters increase. We find that the greater the number of particles in the entangled system, the more stable the system that is studied by the von Neumann entropy. The present results will be reduced to those in the case of the uniformly accelerating reference frame.

The informational re-interpretation of the basic laws of the mechanics exploiting the Landauer principle is suggested. When a physical body is in rest or it moves rectilinearly with the constant speed, zero information is transferred; thus, the informational affinity of the rest state and the rectilinear motion with a constant speed is established. Inertial forces may be involved in the erasure/recording of information. The analysis of the minimal Szilard thermal engine as seen from the noninertial frame of references is carried out. The Szilard single-particle minimal thermal engine undergoes isobaric expansion relative to accelerated frame of references, enabling the erasure of 1 bit of information. The energy ΔQ spent by the inertial force for the erasure of 1 bit of information is estimated as Δ Q ≅ 5 3 k B T ¯ , which is larger than the Landauer bound but qualitatively is close to it. The informational interpretation of the equivalence principle is proposed: the informational content of the inertial and gravitational masses is the same.

We study both pentapartite GHZ and W-class states in the noninertial frame and explore their entanglement properties by carrying out the negativities including 1-4, 2-3, and 1-1 tangles, the whole entanglement measures such as algebraic and geometric averages π5 and Π5, and von Neumann entropy. We illustrate graphically the difference between the pentapartite GHZ and W-class states. We find that all 1-4, 2-3 tangles and the whole entanglements, which are observer dependent, degrade more quickly as the number of accelerated qubits increases. The entanglements of these quantities still exist even at the infinite acceleration limit. We also notice that all 1-1 tangles of pentapartite GHZ state Nαβ=NαIβ=NαIβI=0 where α,β∈(A,B,C,D,E), whereas all 1-1 tangles of the W-class state Nαβ,NαIβ and NαIβI are unequal to zero, e.g., Nαβ=0.12111 but NαIβ and NαIβI disappear at r>0.61548 and r>0.38671, respectively. We notice that the entanglement of the pentapartite GHZ and W-class quantum systems decays faster as the number of accelerated particles increases. Moreover, we also illustrate the difference of von Neumann entropy between them and find that the entropy in the pentapartite W-class state is greater than that of GHZ state. The von Neumann entropy in the pentapartite case is more unstable than those of tripartite and tetrapartite subsystems in the noninertial frame.

The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia using a unified Hamiltonian. For that purpose, we first re-derive, using the purely algebraic method, the energy spectrum of charged particles moving in a plane perpendicular to a constant and uniform magnetic field either (i) under the influence of a nonlinear gravitational potential or (ii) under the influence of a constant rotation. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained. The electrons mutual Coulomb interaction that gives rise to the familiar fractional quantum Hall effect is also discussed within such a combination.

Observers following special classes of finite-lifetime trajectories have been shown to experience an effective temperature, a generalisation of the Unruh temperature for uniformly accelerated observers. We consider a mirror following such a trajectory-and is hence localised to a strictly bounded causal diamond-that perfectly reflects incoming field modes. We find that inertial observers in the Minkowski vacuum detect particles along the half null-rays at the beginning and end of the mirror's lifetime. These particle distributions exhibit multi-partite entanglement, which reveals novel structure within the vacuum correlations. The interaction is modelled using a non-perturbative circuit model and does not suffer from energy divergences.

In this work we analyze the characteristics of quantum entanglement of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity N ABI ( ρ TA ABI ) increases with F but decreases with the variable y, while the variation of the negativity N BIBII ( ρ TA ABI ) is opposite to that of the negativity N ABI ( ρ TA ABI ). We also study the von Neumann entropies S( ρ ABI ) and S( ρ BIBII ). We find that the S( ρ ABI ) increases with variable y but S( ρ BIBII ) is independent of it. However, both S( ρ ABI ) and S( ρ BIBII ) first decreases with F and then increases with it. The concurrences C( ρ ABI ) and C( ρ BIBII ) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it.

In quantum mechanics, the reference frames of the observers are often not explicitly mentioned and quantization for a physical system is usually performed in inertial reference systems. Quantization in noninertial reference systems is an important topic and should be studied systematically. In the framework of nonrelativistic quantum mechanics, the quantum mechanical equations in noninertial reference frames could be derived from those in inertial reference frames using unitary transformation operators. Here, we use canonical quantization scheme to derive quantum mechanics wave equations and Hamiltonian operator in general noninertial coordinate systems in nonrelativistic and relativistic spacetime directly from the classical Hamiltonian formulation based on the basic physical principles. As a special case, the Schrödinger equation in rotating coordinate system of nonrelativistic spacetime, and the KG equation and the first-order wave equation in rotating coordinate systems of Minkowski spacetime were derived from the classical Hamiltonian using canonical quantization scheme. In curved spacetime, the matrix-valued vector field γ a in the first-order wave equation determines the spacetime metric g ab and spacetime geometry and has great gauge freedom. In the gauge defined by the gauge constraint γ b ∇ b γ a  = 0, the Dirac equation in curved spacetime is reduced to our first-order wave equation. A Hamiltonian operator in general spacetime is derived from the first-order wave equation, which is Hermitian only in a special class of spacetimes.

The macroscopic quantum states of the dilute bosonic ensemble in helical laser trap at the temperatures about 10 −6  K are considered in the framework of the Gross-Pitaevskii equation. The helical interference pattern is composed of the two counter propagating Laguerre-Gaussian optical vortices with opposite orbital angular momenta ℓħ and this pattern is driven in rotation via angular Doppler effect. Macroscopic observables including linear momentum and angular momentum of the atomic cloud are evaluated explicitly. It is shown that rotation of reference frame is transformed into translational motion of the twisted matter wave. The speed of translation equals the group velocity of twisted wavetrain V z = Ωℓ / k and alternates with a sign of the frame angular velocity Ω and helical pattern handedness  ℓ . We address detection of this effect using currently accessible laboratory equipment with emphasis on the difference between quantum and classical fluids.

We study the question of conditions for the existence of negative-energy states of particles in the absence of external fields in inertial and noninertial frames of reference. We show that in the nonrelativistic case in noninertial reference frames, there always exist domains where the energy of particles is negative. We also show that in the relativistic case, the existence of negative-energy states of point particles does not lead to violations of the energy dominance condition. We consider conditions for the appearance of negative and zero energies of particles in the Milne universe and Rindler space–time.