arXiv subjects

Dhruba Banerjee

Publications and source records attributed to Dhruba Banerjee.

12 recordsLinked to original sources

arXiv2022

Subharmonic entrainment and limit cycle modulation by high frequency excitation: A Renormalization group approach

In this article, we explore the possibility of a sub-harmonic $(1{:}2)$ entrainment and supercritical Hopf bifurcation in a van der Pol-Duffing oscillator that has been excited by two frequencies, comprising a slow parametric drive and a fast external forcing, through the variation of the amplitude of the external fast signal. We also deduce the condition for the threshold parametric strength required to generate sub-harmonic oscillation. The Blekhman perturbation (direct partition of motion) and the Renormalization group technique have been employed to study how the signal amplitude plays a pivotal role in modulating the limit cycle dynamics as well as the subharmonic generation. Studies of nonlinear responses and bifurcations of such driven nonlinear systems are usually done by treating the strength of the fast drive as the control parameter. Here we show that, beyond its role in allowing one to study the dynamics with the slow and fast components nicely separated, the amplitude of the high-frequency signal can also be treated as an independent control parameter for controlling both the limit cycle behavior and the onset of subharmonic oscillation in the oscillator. Our analytical estimations are well supported by numerical simulations.

nlin.CD↗

arXiv2018

Classical Open Systems coupled to Nonlinear Baths: Noise Spectrum and Dynamical Correlations

Open system dynamics in a classical setting is microscopically governed by the structure of the thermal environment which influences the dynamics of the probe particle (free or in an external potential). Nonlinear baths have recently been shown to impart interesting nonequilibrium correlations in the dissipative dynamics affecting Generalised Langevin Equations and the Fluctuation Dissipation Relations. In the following work, we investigate some aspects of nonlinear baths with rigour relying on perturbative expansions to deal with nonlinear equations. Firstly, the question of noise spectrum emerging from such nonlinearities are addressed and the Markovian limit is explored; super-Ohmic corrections to the linear Ohmic spectrum is deduced. Velocity correlations of a probe system under such approximations are studied in detail. In a second part to the paper, a quenched initial thermal bath is modelled via nonlinearities and Louivillean evolution is applied to evaluate subsequent correlations out of equilibrium. In all these problems, weak system-bath coupling is assumed and quartic baths are used for specific calculations.

cond-mat.stat-mech↗

arXiv2016

Generating a perfect quantum optical vortex

In this article we introduce a novel quantum state, the perfect quantum optical vortex state which exhibits a highly localised distribution along a ring in the quadrature space. We examine its nonclassical properties using the Wigner function and the negativity volume. Such a quantum state can be a useful resource for quantum information processing and communication.

quant-ph↗

arXiv2015

System-reservoir theory with anharmonic baths: a perturbative approach

In this paper we present a study of a general system coupled to a reservoir consisting of nonlinear oscillators, based on perturbation theory at the classical level. We extend the standard Zwanzig approach of elimination of bath degrees of freedom order by order in perturbation. We observe that the Fluctuation Dissipation Relation (FDR) in its standard form for harmonic baths gets modified due to the nonlinearity and this is manifested through higher powers of kBT in the expression for two-time noise correlation.As an aside, we also observe that the first moment of the noise arising from a nonlinear bath can be non-zero, even in absence of any external drive, if the reservoir potential is asymmetric with respect to one of its minima, about which one builds up the perturbation theory.

cond-mat.stat-mech↗

arXiv2015

Entanglement propagation of a quantum optical vortex state

We study the entanglement evolution of a quantum optical vortex state propagating through coupled lossless waveguides. We consider states generated by coupling two squeezed modes using a sequence of beam splitters and also by subtracting photons from the signal in spontaneous parametric down conversion. We reconstruct the Wigner function at a later time to study the correlation and quantify the entanglement after propagation using \emph{logarithmic negativity}.

quant-ph↗

arXiv2014

Stochastic dynamics of two-step processes with harmonic potential

In this paper we address the one-dimensional problem of stochastic renewal in different damping environments. An ensemble of particles with some specified initial distribution in phase space are allowed to evolve stochastically till a certain instant of time (say,$tau$), when a restoring force is applied to bring them back to some point in configuration space. The physical quantities of interest that have been studied are the Survival Probability and the First Passage distribution for return to the specified target point. We observe nontrivial dependence of these quantities on $tau$ as well as on the width of the initial distribution, which has been taken to be Gaussian in position and velocity.

cond-mat.stat-mech↗

arXiv2013

Super-Critical and Sub-Critical Hopf bifurcations in two and three dimensions

Hopf bifurcations have been studied perturbatively under two broad headings, viz., super-critical and sub-critical. The criteria for occurrences of such bifurcations have been investigated using the renormalization group. The procedure has been described in details for both two and three dimensions and has been applied to several important models, including those by Lorenz and Rossler.

nlin.CD↗

arXiv2010

Center or Limit Cycle: Renormalization Group as a Probe

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have a non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center. Moreover, the methodology has a definite advantage over linear stability analysis in analyzing centers.

nlin.CD↗

arXiv2003

A numerical method for generation of quantum noise and solution of generalized c-number quantum Langevin equation

Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E {\bf 65}, 021109 (2002); {\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to derive the equations for time evolution of {\it true} probability distribution functions in $c$-number phase space. We extend the treatment to develop a numerical method for generation of $c$-number noise with arbitrary correlation and strength at any temperature, along with the solution of the associated generalized quantum Langevin equation. The method is illustrated with the help of a calculation of quantum mean first passage time in a cubic potential to demonstrate quantum Kramers turnover and quantum Arrhenius plot.

cond-mat.stat-mech↗

arXiv2002

Quantum Kramers' equation for energy diffusion and barrier crossing dynamics in the low friction regime

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers' equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers' equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.

cond-mat.stat-mech↗

arXiv2002

Quantum Smoluchowski equation: Escape from a metastable state

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.

cond-mat↗

arXiv2001

Approach to Quantum Kramers' Equation and Barrier Crossing Dynamics

We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical mean values of their co-ordinates and momenta we have derived a $c$-number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of temperature and friction. While almost all the earlier theories rest on quasi-probability distribution functions (like Wigner function) and path integral methods, the present work is based on {\it true probability distribution functions} and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermal activated processes and tunneling.

quant-ph↗