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Satish Ramakrishna

Publications and source records attributed to Satish Ramakrishna.

11 recordsLinked to original sources
arXiv2025

IR/UV mixing from higher-order interactions in a Scalar Field

The observed vacuum energy lies far below quantum-field-theoretic estimates. Weinberg's theorem shows that no field can dynamically relax the cosmological constant to zero in a local theory with a translationally invariant vacuum. Approaching this question from a different point of view, the Cohen-Kaplan-Nelson (CKN) bound ties an effective theory's ultraviolet cutoff to its infrared size - however, it has lacked a concrete field-theoretic realization. Our central idea is that anharmonic field oscillations with a supra-linear per-mode ground-state energy reach the Planck scale at a much smaller wavenumber than linearly dispersing modes. Under the standard single-pole assumptions stated below, a supra-linear one-particle pole law cannot arise from a Lorentz-invariant self-energy. We start with a Lorentz-invariant, nonlocal action that breaks Weinberg's locality assumption. We then assume a vacuum that spontaneously breaks boost invariance and preserves spatial isotropy in a preferred frame. A smooth-kernel nonlocal quartic interaction, inserted as our ansatz, yields an instantaneous (in the preferred frame) diagonal reduced Hamiltonian whose high-wavenumber modes are quartic oscillators with ground-state energy $\mathcal{E}_0(k)\sim|\vec k|^{8/3}$. The interaction is diagonal at leading order in the operative regime, with its single coupling's magnitude fixed by a CKN-inspired closure. We establish stability of the reduced theory and the regime of controlled unitary evolution. Imposing the per-mode Planck ceiling together with CKN saturation gives a closure scale $k_{ cutoff}\sim k_{ Pl}^{1/3}\,k_{ box}^{2/3}$, independent of the mode-energy power up to an order-one prefactor. We carry this forward to deduce an equation of state parameter for this vacuum energy.

hep-th↗
arXiv2023

An observer's perspective of the Unruh and Hawking effects -- using coherent signals to extract information from a black hole

The Unruh effect is one of the first calculations of what one would see when transiting between an inertial reference frame with its quantum field vacuum state and a non-inertial (specifically, uniformly accelerating) reference frame. The inertial reference frame's vacuum state would not correspond to the vacuum state of the non-inertial frame and the observer in that frame would see radiation, with a corresponding Bose distribution and a temperature proportional to the acceleration (in natural units). In this paper, I compute the response of this non-inertial observer to a single frequency mode in the inertial frame and deduce that, indeed, the cumulative distribution (over the observer's proper time) of frequencies observed by the accelerating observer would be the Bose distribution with a temperature proportional to the acceleration. The conclusion is that the Unruh effect (and the related Hawking effect) is generic, in that it would appear with any incoming incoherent state and the Bose distribution is obtained as a consequence of the non-inertial frame's motion, rather than some special property of the quantum vacuum. As a consequence of the analysis of a coherent set of signals, I show to extract information from the spectrum that an accelerated observer would see (as well as from the radiation from a black hole).

gr-qc↗
arXiv2022

Implications of a holographic density of states on inflation

There is theoretical evidence that the number of degrees of freedom in quantum fields decreases as one studies them at extremely short distances. This emerges from the study of entropy of black holes, as well as from holographic theories in AdS geometries. Presumably a theory of quantum gravity will provide an explicit description of how the number of degrees of freedom thin out as one studies high energy scales. We do not have a comprehensive theory of how such a thinning of degrees of freedom would occur. It is likely that there might be residual (and measurable) effects at larger length scales, though this might be significant only near the Planck scale. There are very few instances in Nature where one might be able to see effects of this thinning. One promising venue is in the phenomenon of inflation, produced in the simplest models through a scalar inflaton field in a potential with a flat ("slow-roll") part as well as a potential well. We compute the effect of such a thinning of degrees of freedom upon the running of the spectral index of quantum fluctuations of the inflaton and deduce that this will lead to a positive power of wave-vector (opposite to the usual $\sim -ε$, i.e., negative power correction). Some comments are then made about the impact on observations (or non-observations) of such fluctuations \cite{Martin}.

hep-th↗
arXiv2022

A thermodynamic origin for the Cohen-Kaplan-Nelson bound

The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. We do so by defining an appropriate Helmholtz free energy which when extremized relative to a key parameter (the Hubble radius L) provides a scaling formula for the entropy with the Hubble radius (an exponent 'r' used in the text). We deduce that the CKN bound is one solution to this extremization problem (with r=3/2), but there are others consistent with r=2. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

hep-th↗
arXiv2021

A microscopic model of wave-function dephasing and decoherence in the double-slit experiment

The act of measurement on a quantum state is supposed to "collapse" the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. There are two general approaches to the study of wave-function collapse: one called the "consistent" or "decoherent" histories approach and the other, the "environmental decoherence" approach, which studies the effect of the environment upon the quantum system, to explain wave-function collapse. In the "environmental decoherence" approach, one usually studies a Markovian-approximated Master equation to study the time-evolution of reduced density matrix and obtains the long-term dependence of the off-diagonal elements of this matrix. We do not make a Markovian assumption and study a particularly simple and calculable example. We find, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential, which is a new result (the long-term behavior is, of course, still exponential). This allows one to connect the Fermi-golden rule quadratic-in-time behavior of a transition probability to the exponential long-time behavior of a collapsing wave-function.

quant-ph↗
arXiv2021

Relativistic Equations for Fractional-Spin particles

This paper generalizes the method of deducing Dirac's equation to constructing a family of equations that represent the $N$-th root of the basic Energy-Momentum relation for a free particle \cite{Dattoli1, Dattoli2, Dattoli3, Dattoli4}. Then these equations are recast in a form that allows one to interpret them as the fundamental dynamical equations for particles with fractional spin, which we study in detail for the case of $N=4$ and $N=3$. We explicitly prove that the equation is invariant to rotations and boosts and indeed represents spin-$\frac{3}{8}$ and spin-$\frac{1}{8}$ particles for $N=4$ and spin-$\frac{1}{6}$ and $0$ for $N=3$.

physics.gen-ph↗
arXiv2020

Coherent States and Generalized Hermite Polynomials for fractional statistics -- interpolating from fermions to bosons

This article develops the algebraic structure that results from the $θ$-commutator $αβ- e^{i θ} βα= 1 $ that provides a continuous interpolation between the Clifford and Heisenberg algebras. We first demonstrate the most general geometrical picture, applicable to all values of $N$. After listing the properties of this Hilbert space, we study the generalized coherent states that result when $ξ^N=0$, for $N \ge 2$. We also solve the generalized harmonic oscillator problem and derive generalized versions of the Hermite polynomials for general $N$. Some remarks are made to connect this study to the case of anyons. This study represents the first steps towards developing an anyonic field theory.

physics.gen-ph↗
arXiv2020

Algebra for Fractional Statistics -- interpolating from fermions to bosons

This article constructs the Hilbert space for the algebra $αβ- e^{i θ} βα= 1 $ that provides a continuous interpolation between the Clifford and Heisenberg algebras. This particular form is inspired by the properties of anyons. We study the eigenvalues of a generalized number operator (${\cal N} = βα$) and construct the Hilbert space, classified by values of a complex coordinate ($λ_0$): the eigenvalues lie on a circle. For $θ$ being an irrational multiple of $2 π$, we get an infinite-dimensional representation, however for a rational multiple ($\frac{M}{N}$) of $2 π$, it is finite-dimensional, parametrized by the complex coordinate $λ_0$. The case for $N=2 \: ; \: θ=π$ is the usual Clifford algebra for fermions, while the case for $N=\infty \: ; \: θ=0$ is the Heisenberg algebra of bosons, albeit with two copies for positive and negative eigenvalues. We find a smooth transition from the fermion to the boson situation as $N \rightarrow \infty$ from $N=2$. After constructing the Hilbert space from the algebra, the cases for $N=2,3$ can be mapped to $SU(2)$. Then, we motivate the study of coherent states, rather generally. The coherent states are eigenstates of $α$, the annihilation operator and are labeled by complex numbers for non-zero $λ_0$.

hep-th↗
arXiv2017

The curious case of the double-slit experiment and a black hole

This experiment was conceived of as a method of transmitting information from inside a black hole to the outside. As it turns out, it doesn't work in the form described (and possibly not in any form), but the way in which Nature prevents quantum-mechanical effects from transmitting usable information using quantum correlations is illuminating. In the process, one can learn some quantum theory, as well as quantum optics. The proposed scheme uses a double-slit experiment, in the manner of the Delayed Choice set up (see Kim et. al.), where the region where the interference takes place (between "signal" photons) is spatially separated from the region where the Delayed Choice (with "idler" photons) is made. Indeed, this Double-Delayed Choice, which is this thought experiment, has one of the idler photons slip inside the event horizon and serves as the method to attempt to communicate from the inside to the outside.

quant-ph↗
arXiv2011

Common-View Mode Synchronization as a source of error in Measurement of Time of Flight of neutrinos at the CERN-LNGS experiment

The CERN-LNGS time-of-flight experiment (of neutrinos) represents a significant challenge to the special theory of relativity and needs to be addressed either as a source of new physics, or as an un-remedied experimental error. There have been several attempts at using new physics to explain the results, while a few unpublished results exist that address the experimental errors that might lead to the same result. In particular, a recent calculation by van Elburg [2] indicates a potential flaw in the OPERA experiment [1] that represents a source of potential error, i.e., that the motion of the synchronizing GPS satellites causes the clocks to go out of synchronization. Unfortunately, there are several misconceptions about how GPS satellites work that pervade the paper. In addition, the principal contention of the paper, that the experiment is being timed by a moving clock is not substantiated in the analysis. This paper substantiates the point, as well as introduces a new source of error in the "common-view" method of synchronization of clocks.

physics.gen-ph↗