Springer Science and Business Media LLC

Using the new equation of state density from the generalized uncertainty principle in quantum gravity, we study statistical entropy of a dielectric black hole. When λ introduced in the generalized uncertainty principle takes a specific value, we find that the leading term of the statistical entropy of the dielectric black hole takes the Bekenstein-Hawking entropy form. In addition a finite correction term is also obtained. Comparing with the original brick-wall model, in our calculation there is no divergence and the small mass approximation is also not needed.

The Majorana concept of neutrality is applied to the solutions ofj=1 Weinberg equations in the (j, 0)⊕(0,j) representation of the Poincaré group.

Hawking and Turok (HT) have recently proposedthat an open universe can be created from nothing. Theinstanton describing this process is singular, andtherefore its validity has been subject to question. In particular, Vilenkin has shown that aninstanton with the same singular structure as Hawkingand Turok's would lead to the unsuppressed decay of flatspace. However, Vilenkin's solution can be seen as the dimensional reduction of a five-dimensionalnonsingular instanton. In this context the unsuppressedinstability of flat space can be traded formetastability with a low decay rate, provided that the size of the extra dimension is large comparedwith the Planck scale. Implications for the HT model arediscussed.

Invariant path integrals on symmetric and group spaces are defined in terms of a sum over the paths formed by broken geodesic segments. Their evaluation proceeds by using the mean value properties of functions over the geodesic and complex radius spheres. It is shown that on symmetric spaces the invariant path integral gives a kernel of the Schrödinger equation in terms of the spectral resolution of the zonal functions of the space. On compact group spaces the invariant path integral reduces to a sum over powers of Gaussian-type integrals which, for a free particle, yields the standard Van Vleck-Pauli propagator. Explicit calculations are performed for the case ofSU(2) andU(N) group spaces.

Holographic dark energy (HDE), presents a dynamical view of dark energy which is consistent with the observational data and has a solid theoretical background. Its definition follows from the entropy-area relation S(A), where S and A are entropy and area respectively. In the framework of loop quantum gravity, a modified definition of HDE called “entropy-corrected holographic dark energy” (ECHDE) has been proposed recently to explain dark energy with the help of quantum corrections to the entropy-area relation. Using this new definition, we establish a correspondence between modified variable Chaplygin gas, new modified Chaplygin gas and the viscous generalized Chaplygin gas with the entropy corrected holographic dark energy and reconstruct the corresponding scalar potentials which describe the dynamics of the scalar field.

The main goal of the present work is to investigate the validity of the second law of gravitational thermodynamics in an expanding Gödel-type universe filled with generalized Chaplygin gas interacting with cold dark matter. By assuming the Universe as a thermodynamical system bounded by the apparent horizon, and calculating separately the entropy variation for generalized Chaplygin gas, cold dark matter and for the horizon itself, we obtained an expression for the time derivative of the total entropy. We conclude that the 2nd law of gravitational thermodynamics is conditionally valid in the cosmological scenario where the generalized Chaplygin gas interacts with cold dark matter.

The mechanics of an affinely-rigid body is investigated on both the classical and the quantum level. An affinely-rigid body is defined as a system of material points or a continuous medium in which all affine relations are frozen. Our treatment is based on the general theory of systems with closed teleparallelisms, presented in Section 2 of this paper.

We propose the general reduced channel matrices of multi-partite state for determining the entanglement pattern of the state. The matrix elements of reduced channel matrices are nothing but the coefficients of the state so that the rank of channel matrices can be easier determined. The entanglement pattern can be obtained from the evaluation of the rank of reduced matrices in various level of the reduced state. We apply the method on three multi-qubit states as example.

We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the leader election problem). We also provide a general method (extending an idea employed in the decidability proof in Dunn et al. (J. Symb. Log. 70:353–359, 2005)) for proving the decidability of a range of quantum logics, interpreted on finite-dimensional Hilbert spaces. We give general conditions for the applicability of this method, and in particular we apply it to prove the decidability of PLQP.