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Saurya Das

Publications and source records attributed to Saurya Das.

At least 109 records · Page 6Linked to original sources
arXiv2013

Entanglement entropy in all dimensions

It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann entropy. Here we show that the Renyi entropy provides a convergent alternative, yielding a quantitative measure of entanglement between quantum field theoretic degrees of freedom inside and outside hypersurfaces. For the first time, we show that the entanglement entropy in higher dimensions is proportional to the higher dimensional area. We also show that the Renyi entropy diverges at specific values of the Renyi parameter (q) in each dimension, but this divergence can be tamed by introducing a mass of the quantum field.

hep-th↗
arXiv2013

Can MOND type hypotheses be tested in a free fall laboratory environment?

The extremely small accelerations of objects required for the the onset of modified Newtonian dynamics, or MOND, makes testing the hypothesis in conventional terrestrial laboratories virtually impossible. This is due to the large background acceleration of Earth, which is transmitted to the acceleration of test objects within an apparatus. We show however, that it may be possible to test MOND-type hypotheses with experiments using a conventional apparatus capable of tracking very small accelerations of its components, but performed in locally inertial frames such as artificial satellites and other freely falling laboratories. For example, experiments involving an optical interferometer or a torsion balance in these laboratories would show nonlinear dynamics, and displacement amplitudes larger than expected. These experiments may also be able to test potential violations of the strong equivalence principle by MOND and to distinguish between its two possible interpretations (modified inertia and modified gravity).

gr-qc↗
arXiv2011

Effect of the Generalized Uncertainty Principle on Post-Inflation Preheating

We examine effects of the Generalized Uncertainty Principle, predicted by various theories of quantum gravity to replace the Heisenberg's uncertainty principle near the Planck scale, on post inflation preheating in cosmology, and show that it can predict either an increase or a decrease in parametric resonance and a corresponding change in particle production. Possible implications are considered.

hep-th↗
arXiv2011

Quantum aether and an invariant Planck scale

We argue that a quantum aether is consistent with the principle of relativity and can provide an economical way of having an invariant quantum gravity or Planck scale. We also show that it may change the effective scale at which quantum gravity effects may be observable.

gr-qc↗
arXiv2011

Planck scale effects on some low energy quantum phenomena

Almost all theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). Recently it was shown that the GUP gives rise to corrections to the Schrodinger and Dirac equations, which in turn affect all non-relativistic and relativistic quantum Hamiltonians. In this paper, we apply it to superconductivity and the quantum Hall effect and compute Planck scale corrections. We also show that Planck scale effects may account for a (small) part of the anomalous magnetic moment of the muon. We obtain (weak) empirical bounds on the undetermined GUP parameter from present-day experiments.

hep-th↗
arXiv2011

A proposal for testing Quantum Gravity in the lab

Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.

hep-th↗
arXiv2011

Relativistic particle in a three-dimensional box

We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle confined in a 3-dimensional box. The non-relativistic and ultra-relativistic limits are considered and it is shown that the size of the box determines how relativistic the low-lying states are. The consequences for the density of states of a relativistic fermion gas are briefly discussed.

quant-ph↗
arXiv2010

Quantum Gravity Corrections and Entropy at the Planck time

We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as the Planck time, length, mass and energy become larger by a factor of order 10-10^{4} compared to those quantities which result from the Heisenberg Uncertainty Principle. However, we prove that the dimensionless entropy enclosed in the cosmological horizon at the Planck time remains unchanged. These results, though preliminary, indicate that we should anticipate modifications in the set-up of cosmology since changes in the Planck era will be inherited even to the late universe through the framework of Quantum Gravity (or Quantum Field Theory) which utilizes the Planck scale as a fundamental one. More importantly, these corrections will not affect the entropic content of the universe at the Planck time which is a crucial element for one of the basic principles of Quantum Gravity named Holographic Principle.

hep-th↗
arXiv2010

Discreteness of Space from GUP II: Relativistic Wave Equations

Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to corrections to the Schrodinger equation, which in turn affect all quantum mechanical Hamiltonians. In particular, by applying it to a particle in a one dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself. In this paper, we extend the above results to a relativistic particle in a rectangular as well as a spherical box, by solving the GUP-corrected Klein-Gordon and Dirac equations, and for the latter, to two and three dimensions. We again arrive at quantization of box length, area and volume and an indication of the fundamentally grainy nature of space. We discuss possible implications.

hep-th↗
arXiv2010

Entanglement and corrections to Bekenstein-Hawking entropy

In this talk, we focus on the corrections to Bekenstein-Hawking entropy by associating it with the entanglement between degrees of freedom inside and outside the horizon. Using numerical techniques, we show that the corrections proportional to fractional power of area result when the field is in a superposition of ground and excited states. We explain this result by identifying that the degrees of freedom contributing to such corrections are different from those contributing to Bekenstein-Hawking entropy.

gr-qc↗
arXiv2010

The Generalized Uncertainty Principle and Quantum Gravity Phenomenology

In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this affects all Hamiltonians, and in particular those which describe low energy experiments. We discuss possible observational consequences. Further, we also show that this indicates that space may be discrete at the fundamental level.

hep-th↗
arXiv2009

Discreteness of Space from the Generalized Uncertainty Principle

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that space itself is discrete, and that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this signals the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale.

hep-th↗
arXiv2009

Multiple kinetic k-essence, phantom barrier crossing and stability

We investigate models of dark energy with purely kinetic multiple k-essence sources that allow for the crossing of the phantom divide line, without violating the conditions of stability. It is known that with more than one kinetic k-field one can possibly construct dark energy models whose equation of state parameter $\wx$ crosses -1 (the phantom barrier) at recent red-shifts, as indicated by the Supernova Ia and other observational probes. However, such models may suffer from cosmological instabilities, as the effective speed of propagation $\cx$ of the dark energy density perturbations may become {\it imaginary} while the $\wx = -1$ barrier is crossed. Working out the expression for $\cx$ we show that multiple kinetic k-essence fields do indeed lead to a $\wx = -1$ crossing dark energy model, satisfying the stability criterion $\cx^2 \geq 0$ as well as the condition $\cx \leq 1$ (in natural units), which implies that the dark energy is not super-luminal. As a specific example, we construct a phantom barrier crossing model involving three k-fields for which $\cx$ is a constant, lying between 0 and 1. The model fits well with the latest Supernova Ia Union data, and the best fit shows that $\wx$ crosses -1 at red-shift $z \sim 0.2$, whereas the dark energy density nearly tracks the matter density at higher red-shifts.

astro-ph↗
arXiv2009

Phenomenological Implications of the Generalized Uncertainty Principle

Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to βp^4 and β^2 p^6 respectively, where β\sim 1/(M_{Pl}c)^2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these, and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a Scanning Tunnel Microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.

hep-th↗
arXiv2008

Universality of Quantum Gravity Corrections

We show that the existence of a minimum measurable length and the related Generalized Uncertainty Principle (GUP), predicted by theories of Quantum Gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. We compute such corrections to the Lamb Shift, the Landau levels and the tunnelling current in a Scanning Tunnelling Microscope (STM). We show that these corrections can be interpreted in two ways: (a) either that they are exceedingly small, beyond the reach of current experiments, or (b) that they predict upper bounds on the quantum gravity parameter in the GUP, compatible with experiments at the electroweak scale. Thus, more accurate measurements in the future should either be able to test these predictions, or further tighten the above bounds and predict an intermediate length scale, between the electroweak and the Planck scale.

hep-th↗
arXiv2008

Stability and hierarchy problems in string inspired braneworld scenarios

We generalise the RS braneworld model by taking into account a general stringy bulk containing the scalar dilaton field and the two-form Kalb-Ramond field, apart from gravity. Assuming small fluctuations around a RS background, the back-reacted warp factor is obtained. It is shown that the fine tuning problem in connection with the Higgs mass reappears in a new guise and the effective modular potential fails to stabilise the braneworld.

hep-th↗
arXiv2008

Cosmological constant, brane tension and large hierarchy in a generalized Randall-Sundrum braneworld scenario

We consider a generalized Randall Sundrum (RS) brane world scenario with a cosmological constant $Ω$ induced on the visible brane. We show that for $Ω<0$, resolution of the hierarchy problem requires an upper bound on the magnitude of $Ω$. The corresponding tension on the visible brane can be positive or negative. On the other hand, there is no such bound for $Ω>0$. However, in this case, the resolution of the hierarchy problem along with the tuning of the value of the cosmological constant to its observed value closed to $+10^{-124}$ (in Planck units) naturally lead to the tuning of the modulus to a small value of inverse Planck length as estimated in the original RS scenario.

hep-th↗