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

Variability of the Conductance Changes Associated with the Change in the Spin State in Molecular Spin Crossover Complexes

Here, we examine the conductance changes associated with the change in spin state in a variety of different structures, using the example of the spin crossover complex [Fe(H2B(pz)2)2(bipy)] (pz = (pyrazol-1-yl)-borate and bipy = 2,2′-bipyridine) and [Fe(Htrz)2(trz)](BF4)] (Htrz = 1H-1,2,4-triazole) thin films. This conductance change is highly variable depending on the mechanism driving the change in spin state, the substrate, and the device geometry. Simply stated, the choice of spin crossover complex used to build a device is not the only factor in determining the change in conductance with the change in spin state

The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle

In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space

Boundary effects in super-Yang–Mills theory

Abstract In this paper, we shall analyze a three dimensional supersymmetry theory with $$\mathcal {N} = 2$$ N = 2 supersymmetry. We will analyze the quantization of this theory, in the presence of a boundary. The effective Lagrangian used in the path integral quantization of this theory, will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. Even though the supersymmetry of this effective Lagrangian will also be broken due to the presence of a boundary, it will be demonstrated that half of the supersymmetry of this theory can be preserved by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will analyze the Slavnov–Taylor identity for this $$\mathcal {N} = 2$$ N = 2 Yang–Mills theory with a boundary