246 research outputs found
Long Time Results for a Weakly Interacting Particle System in Discrete Time
We study long time behavior of a discrete time weakly interacting particle
system, and the corresponding nonlinear Markov process in ,
described in terms of a general stochastic evolution equation. In a setting
where the state space of the particles is compact such questions have been
studied in previous works, however for the case of an unbounded state space
very few results are available. Under suitable assumptions on the problem data
we study several time asymptotic properties of the -particle system and the
associated nonlinear Markov chain. In particular we show that the evolution
equation for the law of the nonlinear Markov chain has a unique fixed point and
starting from an arbitrary initial condition convergence to the fixed point
occurs at an exponential rate. The empirical measure of the
-particles at time is shown to converge to the law of the
nonlinear Markov process at time , in the Wasserstein-1 distance, in
, as , uniformly in . Several consequences of this
uniform convergence are studied, including the interchangeability of the limits
and and the propagation of chaos property at . Rate of convergence of to is studied by
establishing uniform in time polynomial and exponential probability
concentration estimates
Generic 3-point Statistics with Tensor Modes in Light of Swampland and TCC
Recently proposed Swampland Criteria (SC) and Trans-Planckian Censorship
Conjecture (TCC) together put stringent theoretical constraints on slow roll
inflation, raising a question on future prospects of detection of Primordial
Gravitational Waves (PGW). As it appears, the only option to relax the
constraints is by considering Non Bunch Davies (NBD) initial states, that in
turn brings back the observational relevance of PGW via its 2-point function.
In this article we develop consistent 3-point statistics with tensor modes for
all possible correlators (auto and mixed) for NBD initial states in the light
of SC and TCC in a generic, model independent framework of Effective Field
Theory of inflation. We also construct the templates of the corresponding
nonlinearity parameters for different shapes of relevance and
investigate if any of the 3-point correlators could be of interest for future
CMB missions. Our analysis reveals that the prospects of detecting the tensor
auto correlator are almost nil whereas the mixed correlators might be relevant
for future CMB missions.Comment: 20 pages, 1 figur
Enhanced tensor non-Gaussianities in presence of a source
We address the possibility of having an enhanced signal for tensor
non-Gaussianities in presence of a source, as a signature of Primordial
Gravitational Waves. We employ a nearly model-independent framework based on
Effective Field Theory of inflation and compute tensor non-Gaussianities
therefrom sourced by particle production during (p)reheating to arrive at an
enhanced signal strength. We obtain the model-independent non-linearity
parameters and also find that squeezed limit bispectra are more enhanced than
equilateral limit.Comment: 8 pages, 2 figures, Typos corrected, Minor modification
An efficient quantum-classical hybrid algorithm for distorted alphanumeric character identification
An algorithm for image processing is proposed. The proposed algorithm, which
can be viewed as a quantum-classical hybrid algorithm, can transform a
low-resolution bitonal image of a character from the set of alphanumeric
characters (A-Z, 0-9) into a high-resolution image. The quantum part of the
proposed algorithm fruitfully utilizes a variant of Grover's search algorithm,
known as the fixed point search algorithm. Further, the quantum part of the
algorithm is simulated using CQASM and the advantage of the algorithm is
established through the complexity analysis. Additional analysis has also
revealed that this scheme for optical character recognition (OCR) leads to high
confidence value and generally works in a more efficient manner compared to the
existing classical, quantum, and hybrid algorithms for a similar task.Comment: A quantum-assisted algorithm for optical character recognition (OCR)
is proposed using fixed point Grover's algorith
- …