Short distance modification of the quantum virial theorem

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schr\"odinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schr\"odinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schr\"odinger-Newton equation, a short distance modification of the Schr\"odinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.Comment: 16 page

Short Distance Modification of a Gravitational System and its Optical Analog

Motivated by developments in string theory, such as T-duality, it has been proposed that the geometry of spacetime should have an intrinsic minimal length associated with it. This would modify the short distance behavior of quantum systems studied on such a geometry, and an optical analog for such a short distance modification of quantum system has also been realized by using non-paraxial nonlinear optics. As general relativity can be viewed as an effective field theory obtained from string, it is expected that this would also modify the short distance behavior of general relativity. Now the Newtonian approximation is a valid short distance approximation to general relativity, and Schrodinger-Newton equation can be obtained as a non-relativistic semi-classical limit of such a theory, we will analyze the short distance modification of Schrodinger-Newton equation from an intrinsic minimal length in the geometry of spacetime. As an optical analog of the Schrodinger-Newton equation has been constructed, it is possible to optically realize this system. So, this system is important, and we will numerical analyze the solutions for this system. It will be observed that the usual Runge-Kutta method cannot be used to analyze this system. However, we will use a propose and use a new numerical method, which we will call as the two step Runge-Kutta method, for analyzing this system.Comment: 21 pages, 3 figures, 2 table

Bounds on Slow Roll at the Boundary of the Landscape

We present strong evidence that the tree level slow roll bounds of arXiv:1807.05193 and arXiv:1810.05506 are valid, even when the tachyon has overlap with the volume of the cycle wrapped by the orientifold. This extends our previous results in the volume-dilaton subspace to a semi-universal modulus. Emboldened by this and other observations, we investigate what it means to have a bound on (generalized) slow roll in a multi-field landscape. We argue that for $any$ point $\phi_0$ in an $N$-dimensional field space with $V(\phi_0) > 0$, there exists a path of monotonically decreasing potential energy to a point $\phi_1$ within a path length $\lesssim {\cal O}(1)$, such that $\sqrt{N}\ln \frac{V(\phi_1)}{V(\phi_0)} \lesssim - {\cal O} (1)$. The previous de Sitter swampland bounds are specific ways to realize this stringent non-local constraint on field space, but we show that it also incorporates (for example) the scenario where both slow roll parameters are intermediate-valued and the Universe undergoes a small number of e-folds, as in the Type IIA set up of arXiv:1310.8300. Our observations are in the context of tree level constructions, so we take the conservative viewpoint that it is a characterization of the classical "boundary" of the string landscape. To emphasize this, we argue that these bounds can be viewed as a type of Dine-Seiberg statement.Comment: v4: one more referenc

Quantum Fluctuations of a BTZ Black Hole in Massive Gravity

In this work, we shall analyze the effects of quantum fluctuations on the properties of a BTZ black hole, in a massive theory of gravity. We will analyze this for a charged BTZ black hole in asymptotically AdS and dS space-times. The quantum fluctuations would produce thermal fluctuations in the thermodynamics of this BTZ black hole. As these fluctuations would become relevant at a sufficiently small scale, we shall discuss the effects of such thermal fluctuations on the entropy of a small charged BTZ black. We shall also analyze the effects of these fluctuations on the stability of such a black hole.Comment: Accepted for publication in PL

Modelling of a compact anisotropic star as an anisotropic fluid sphere in f(T)f(T) gravity

In this paper, we have studied the new exact model of anisotropic star in $f(T)$ theory of gravity. The dynamical equations in $f(T)$ theory with the anisotropic fluid have been solved by using Krori-Barua solution. We have determined that all the obtained solutions are free from central singularity and potentially stable. The observed values of mass and radius of the different strange stars RX J 1856-37, Her X-1, and Vela X-12 have been used to calculate the values of unknown constants in Krori and Barua metric. The physical parameters like anisotropy, stability and redshift of the stars have been investigated in detail.Comment: Accepted in the Canadian Journal of Physic

Non-Local Deformation of a Supersymmetric Field Theory

In this paper, we will analyse a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling. It will be observed that this deformed supersymmetric field theory contains non-local fractional derivative terms. In order to construct such deformed N=1 supersymmetric theory, a harmonic extension of functions will be used. However, the supersymmetry will be only preserved for a free theory and will be broken by the inclusion of interaction terms.Comment: 12 pages, pulished versio

Evidence of Cooperative Effects for the Fe(phen)2(NCS)2 Spin Crossover Molecular Complex in Polyaniline Plus Iron Magnetite

The spin crossover complex Fe(phen)2(NCS)2 and its composite, Fe(phen)2(NCS)2, combined with the conducting polymer polyaniline (PANI) plus varying concentrations of iron magnetite (Fe3O4) nanoparticles were studied. A cooperative effect is evident from the hysteresis width in the plot of magnetic susceptibility multiplied by temperature versus temperature (χmT versus T) for Fe(phen)2(NCS)2 with PANI plus varying concentrations of Fe3O4 nanoparticles. The hysteresis width in the composites vary no more than 2 K with respect to the pristine Fe(phen)2(NCS)2 spin crossover crystallites despite the fact that there exists a high degree of miscibility of the Fe(phen)2(NCS)2 spin crossover complex with the PANI. The Fe3O4 nanoparticles in the Fe(phen)2(NCS)2 plus PANI composite tend to agglomerate at higher concentrations regardless of the spin state of Fe(phen)2(NCS)2. Of note is that the Fe3O4 nanoparticles are shown to be antiferromagnetically coupled with the Fe(phen)2(NCS)2 when Fe(phen)2(NCS)2 is in the high spin state

The surface termination of a Fe (III) spin crossover molecular salt

From a comparison of the known molecular stoichiometry and X-ray photoemission spectroscopy (XPS), it is evident that the Fe(III) spin crossover salt [Fe(qsal)2Ni(dmit)2], where qsal = N(8quinolyl)salicylaldimine, and dmit2- = 1,3-dithiol-2-thione-4,5-dithiolato has a preferential surface termination with the Ni(dmit)2 moiety. This preferential surface termination leads to a significant surface to bulk core level shift for the Ni 2p X-ray photoemission core level, not seen in the corresponding Fe 2p core level spectra. A similar surface to bulk core level shift is seen in Pd 3d in the related [Fe(qsal)2]2Pd(dmit)2, ], where qsal = N(8quinolyl)salicylaldimine, and dmit2- = 1,3-dithiol-2-thione-4,5-dithiolato. Inverse photoemission spectroscopy (IPES), compared with the X-ray absorption spectra at the Ni-L3,2 edge provides some indication of the density of states resulting from the dmit2- = 1,3-dithiol-2-thione-4,5-dithiolato ligand unoccupied molecular orbitals and thus supports the evidence regarding surface termination in the Ni(dmit)2 moiety

Chiral effects at the metal center in Fe(III) spin crossover coordination salts

Evidence of chirality was observed at the Fe metal center in Fe(III) spin crossover coordination salts [Fe(qsal)2][Ni(dmit)2] and [Fe(qsal)2](TCNQ)2from x-ray absorption (XAS) spectroscopy at the Fe 2p3/2core threshold. Based on the circularly polarized XAS data, the x-ray natural circular dichroism for [Fe(qsal)2][Ni(dmit)2] and [Fe(qsal)2](TCNQ)2is far stronger than seen for [Fe(qsal)2]Cl suggesting this natural circular dichroism signature is a ligand effect rather than a result of just a loss of octahedral symmetry on the Fe core. The larger the chiral effects in the Fe 2p core to bound XAS, the greater the perturbation of the Fe 2p3/2to 2p1/2spin-orbit splitting seen in the XAS spectra