arXiv subjects

J. K. Bhattacharjee

Publications and source records attributed to J. K. Bhattacharjee.

At least 19 recordsLinked to original sources

arXiv2021

Activity induced turbulence in driven active matter

Turbulence in driven stratified active matter is considered. The relevant parameters characterizing the problem are the Reynolds number Re and an active matter Richardson-like number,R. In the mixing limit,Re>>1, R<<1, we show that the standard Kolmogorov energy spectrum 5/3 law is realized. On the other hand, in the stratified limit, Re>>1,R>>1, there is a new turbulence universality class with a 7/5 law. The crossover from one regime to the other is discussed in detail. Experimental predictions and probes are also discussed.

cond-mat.soft↗

arXiv2020

Exotic Pairing Structures in Population-Imbalanced Fermionic Systems: Dynamics as a Probe

We investigate a population-imbalanced two-species fermionic system where the resonantly-paired fermions combine to form bosonic molecules via Feshbach interaction. We study the dynamics of the intrinsic quantum fluctuations of the system. It is shown that the natural fluctuations of the condensate fraction consists of a fixed number of periodic components : indicating that these oscillations do not die out, and are sustained in the mean field dynamics of the system. These frequency components bear distinct signatures of the nature of pairing present in the system. We describe how a time dependent external magnetic field can be used to locate these oscillation frequencies, and thus to explore the momentum space structure of the population imbalanced system. We propose that this method can be used as an indirect experimental probe for detecting exotic phases like the breached pair state, FFLO state, and a phase-separated state comprising of BCS and normal regions.

cond-mat.quant-gas↗

arXiv2019

Transition to Turbulence in Driven Active Matter

A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term comes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.

physics.flu-dyn↗

arXiv2017

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations

Work fluctuations and work probability distributions are fundamentally different in systems with short- ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with shortranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet , well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short-ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behaviour of the work probability distribution and the associated fluctuations is presented.

cond-mat.stat-mech↗

arXiv2015

Stability and The Existence of Coherent Structure in Demixed State of Binary BEC

From a linear stability analysis of the Gross Pitaevskii equation for binary Bose Einstein condensates, it is found that the uniform state becomes unstable to a periodic perturbation of wave number k if k exceeds a critical value kc. However we find that a stationary spatially periodic state does not exist. We show the existence of pulse type solutions, when the pulse structure for one condensate is strongly influenced by the presence of the other condensate.

cond-mat.quant-gas↗

arXiv2014

Wave packet dynamics for a non-linear Schrodinger equation: Qualitative changes with changes in the initial width

The propagation of an initially Gaussian wave packet of width $Δ_0$ in a cubic non-linear Schrodinger equation with a negative coupling constant for the nonlinear term is considered . It is predicted analytically and verified numerically that for a free particle if $Δ_0$ is less than a critical value $Δ_c$, then the packet will propagate in time with linearly growing width but for $Δ>Δ_c$, the packet will start becoming narrow and cease to be a Gaussian . For a simple harmonic oscillator, we find that for $Δ_0$ smaller than a critical value, there always exist a coupling strength for which the packet simply oscillates about the mean position without changing its shape.

quant-ph↗

arXiv2012

Competing order parameters and a tricritical point with a difference

We propose a mean-field, phenomenological Ginzburg-Landau free energy functional with two competing order parameters for a two-component, spin-polarized Fermi gas. This free energy supports a tricritical point which is different from the conventional one and this change offers a correct understanding of the experimental phase diagram of imbalanced Fermi systems (Shin et al, Nature, 2008). The specific heat also happens to be different than in standard theory.

cond-mat.supr-con↗

arXiv2011

Bohr Sommerfeld quantisation and molecular potentials

We use the Bohr Sommerfeld quantization rule along with a perturbative evaluation of the action intergral to find exact energy levels for the Pöschl-Teller potential (both hyperbolic and trigonometric forms), the Morse potential, and the Rosen Morse potential. Combining perturbation theory with the simplest asymptotic evaluation of the action integral allows us to obtain all the energy levels of the Lennard-Jones potential with an accuracy greater than 0.1 per cent and serves to confirm that the perturbation results for Pöschl-Teller and Morse Potentials are exact.

math-ph↗

arXiv2011

Renormalization group and isochronous oscillations

We show how the condition of isochronicity can be studied for two dimensional systems in the renormalization group (RG) context. We find a necessary condition for the isochronicity of the Cherkas and another class of cubic systems. Our conditions are satisfied by all the cases studied recently by Bardet et al \cite{bard} and Ghose Choudhury and Guha

nlin.CD↗

arXiv2011

Eigenvalue Problem in Two Dimension for An Irregular Boundary

An analytical perturbative method is suggested for solving the Helmholtz equation (\bigtriangledown^{2} + k^{2})ψ = 0 in two dimensions where ψ vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed.

math-ph↗

arXiv2010

Critical Casimir force in the superfluid phase: effect of fluctuations

We have considered the critical Casimir force on a $^4$He film below and above the bulk $λ$ point. We have explored the role of fluctuations around the mean field theory in a perturbative manner, and have substantially improved the mean field result of Zandi et al [Phys. Rev. E {\bf 76}, 030601(R) (2007)]. The Casimir scaling function obtained by us approaches a universal constant ($-\frac{ζ(3)}{8π}$) for $T\lesssim 2.13~\text{K}$.

cond-mat.stat-mech↗

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↗

arXiv2010

Casimir force on interacting Bose-Einstein condensate

We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wave function as well as for the phonon field. We have shown that, the condensate wave function (which obeys the Gross-Pitaevskii equation) is responsible for the mean field part of Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.

cond-mat.stat-mech↗

arXiv2009

Approximation Techniques for Non Linear Oscillators

We show that the Lindstedt-Poincare perturbation theory is always a reliable technique in the region of small coupling constant. The harmonic balance result, on the other hand, if expanded in the perturbation parameter may lead to incorrect results.

nlin.CD↗

arXiv2008

Resonance and limit cycle in a noise driven Lorenz model

The effect of an external noise on the Lorenz model is investigated near the onset of convection and near the Hopf bifurcation. We show the existence of a diverging time scale near the onset of convection and a resonance near the Hopf bifurcation. Our calculation provides an understanding of the noise induced stabilization of the limit cycle that had been observed numerically.

cond-mat.stat-mech↗

arXiv2007

Standing and travelling waves in the shallow-water circular hydraulic jump

A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the flow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the flow in the vicinity of the jump, for which experimental support has been given.

cond-mat.other↗

arXiv2007

Effects of non-denumerable fixed points in finite dynamical systems

The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point that a point on the fixed point in the phase space should remain there forever, for, a fixed point can evolve as well! Under such considerations one can argue that a free-kicked football should be non-chaotic.

nlin.CD↗

arXiv2007

On the third order structure function for rotating 3D homogeneous turbulent flow

A form for the two-point third order structure function has been calculated for three dimensional homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalisation of the 3D incompressible turbulence owing to rotation.

physics.flu-dyn↗