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Register a new userComment on Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches
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We point out a misleading treatment in a recent paper published in this Journal [Eur. Phys. J. C (2018)78:106] regarding solutions for the Schr{o}dinger equation with a anharmonic oscillator potential embedded in the background of a cosmic string mapped into biconfluent Heun equation. This fact jeopardizes the thermodynamical properties calculated in this system.
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We examine the non-inertial effects of a rotating frame on a Dirac oscillator in a cosmic string space-time with non-commutative geometry in phase space. We observe that the approximate bound-state solutions are related to the biconfluent Heun polynomials. The related energies cannot be obtained in a closed form for all the bound states. We find the energy of the fundamental state analytically by taking into account the hard-wall confining condition. We describe how the ground-state energy scales with the new non-commutative term as well as with the other physical parameters of the system.
In this paper we attempt to examine the possibility of construction of a traversable wormhole on the Randall-Sundrum braneworld with ordinary matter employing the Kuchowicz potential as one of the metric potentials. In this scenario, the wormhole shape function is obtained and studied, along with validity of Null Energy Condition (NEC) and the junction conditions at the surface of the wormhole are used to obtain a few of the model parameters. The investigation, besides giving an estimate for the bulk equation of state parameter, draws important constraints on the brane tension which is a novel attempt in this aspect and very interestingly the constraints imposed by a physically plausible traversable wormhole is in high confirmity with those drawn from more general space-times or space-time independent situations involved in fundamental physics. Also, we go on to claim that the possible existence of a wormhole may very well indicate that we live on a three-brane universe.
The Riemann Hypothesis states that the Riemann zeta function $zeta(z)$ admits a set of non-trivial zeros that are complex numbers supposed to have real part $1/2$. Their distribution on the complex plane is thought to be the key to determine the number of prime numbers before a given number. We analyze two approaches. In the first approach, suggested by Hilbert and Polya, one has to find a suitable Hermitian or unitary operator whose eigenvalues distribute like the zeros of $zeta(z)$. In the other approach one instead compares the distribution of the zeta zeros and the poles of the scattering matrix $S$ of a system. We apply the infinite-components Majorana equation in a Rindler spacetime to both methods and then focus on the $S$-matrix approach describing the bosonic open string for tachyonic states. In this way we can explain the still unclear point for which the poles and zeros of the $S$-matrix overlaps the zeros of $zeta(z)$ and exist always in pairs and related via complex conjugation. This occurs because of the relationship between the angular momentum and energy/mass eigenvalues of Majorana states and from the analysis of the dynamics of the poles of $S$. As shown in the literature, if this occurs, then the Riemann Hypothesis can in principle be satisfied.
The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics. Namely, by linearizing the geodesic equation and its conserved charges, we arrive at the invariant Wronskians for the Jacobi system that are linear in the `deviation momenta and thus yield a system of first-order differential equations that can be integrated. The procedure is illustrated on an example of a rotating black hole spacetime described by the Kerr geometry and its higher-dimensional generalizations. A number of related topics, including the phase space formulation of the theory and the derivation of the covariant Hamiltonian for the Jacobi system are also discussed.
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