arXiv subjects

J. K. Bhattacharjee

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

At least 37 records · Page 2Linked to original sources

arXiv2007

Global Persistence Exponent in Critical Dynamics: Finite Size induced Crossover

We extend the definition of a global order parameter to the case of a critical system confined between two infinite parallel plates separated by a finite distance $L$. For a quench to the critical point we study the persistence property of the global order parameter and show that there is a crossover behaviour characterized by a non universal exponent which depends on the ratio of the system size to a dynamic length scale.

cond-mat.stat-mech↗

arXiv2006

Asymmetry of the work probability distribution

We show, both analytically and numerically, that for a nonlinear system making a transition from one equilibrium state to another under the action of an external time dependent force, the work probability distribution is in general asymmetric.

cond-mat.stat-mech↗

arXiv2006

Finite Size Effect in Persistence

We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially decaying function.The particle here is trapped with in a box of size $L$ . We have also considered the problem when the particle in trapped in a potential. Direct calculation and numerical result show that the scaling function here also an exponentially decaying function. We also present numerical works on harmonically trapped randomly accelerated particle and randomly accelerated particle with viscous drag.

cond-mat.stat-mech↗

arXiv2005

A dynamical systems approach to a thin accretion disc and its time-dependent behaviour on large length scales

Modelling the flow in a thin accretion disc like a dynamical system, we analyse the nature of the critical points of the steady solutions of the flow. For the simple inviscid disc there are two critical points, with the outer one being a saddle point and the inner one a centre type point. For the weakly viscous disc, there are four possible critical points, of which the outermost is a saddle point, while the next inner one is a spiral. Coupling the nature of the critical points with the outer boundary condition of the flow, gives us a complete understanding of all the important physical features of the flow solutions in the subsonic regions of the disc. In the inviscid disc, the physical realisability of the transonic solution passing through the saddle point is addressed by considering a temporal evolution of the flow, which is a very likely non-perturbative mechanism for selecting the transonic inflow solution from among a host of other possible stable solutions. For the weakly viscous disc, while a linearised time-dependent perturbation imposed on the steady mass inflow rate causes instability, the same perturbative analysis reveals that for the inviscid disc, there is a very close correspondence between the equation for the propagation of the perturbation and the metric of an acoustic black hole. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity-limited length scale is defined for the spatial extent of the inward rotational drift of matter.

astro-ph↗

arXiv2005

Fokker-Planck Equation : Long-Time Dynamics in Approach to Equilibrium

We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers' time. We also describe the connection between stochastic processes and quantum mechanics.

cond-mat.stat-mech↗

arXiv2005

A Dynamical Systems Approach to an Inviscid and Thin Accretion Disc

The inviscid and thin accretion disc is a simple and well understood model system in accretion studies. In this work, modelling such a disc like a dynamical system, we analyse the nature of the fixed points of the stationary solutions of the flow. We show that of the two fixed points, one is a saddle and the other is a centre type point. We then demonstrate, using a simple but analogous mathematical model, that a temporal evolution of the flow is a very likely non-perturbative mechanism for the selection of an inflow solution that passes through the saddle type critical point.

astro-ph↗

arXiv2005

Growth Models and Models of Turbulence : A Stochastic Quantization Perspective

We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization scheme.

cond-mat.stat-mech↗

arXiv2005

Large scale properties in turbulent spherically symmetric accretion

The role of turbulence in a spherically symmetric accreting system has been studied on very large spatial scales of the system. This is also a highly subsonic flow region and here the accreting fluid has been treated as nearly incompressible. It has been shown here that the coupling of the mean flow and the turbulent fluctuations, gives rise to a scaling relation for an effective "turbulent viscosity". This in turn leads to a dynamic scaling for sound propagation in the accretion process. As a consequence of this scaling, the sonic horizon of the transonic inflow solution is shifted inwards, in comparison with the inviscid flow.

astro-ph↗

arXiv2005

Non equilibrium statistical physics with fictitious time

Problems in non equilibrium statistical physics are characterized by the absence of a fluctuation dissipation theorem. The usual analytic route for treating these vast class of problems is to use response fields in addition to the real fields that are pertinent to a given problem. This line of argument was introduced by Martin, Siggia and Rose. We show that instead of using the response field, one can, following the stochastic quantization of Parisi and Wu, introduce a fictitious time. In this extra dimension a fluctuation dissipation theorem is built in and provides a different outlook to problems in non equilibrium statistical physics.

cond-mat.stat-mech↗

arXiv2004

Approach to equilibrium in adiabatically evolving potentials

For a potential function (in one dimension) which evolves from a specified initial form $V_{i}(x)$ to a different $V_{f}(x)$ asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibeium.There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form $V(x,t)=V_{f}(x)+(V_{i}-V_{f})e^{-λt}$. For a $V_{f}(x)$, which is double welled and a $V_{i}(x)$ which is simple harmonic, we show that, in particular, if the evolution is adiabatic, the results in a decrease in the Kramers time characteristics of $V_{f}(x)$. Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when $V_{i}(x)$ and $V_{f}(x)$ are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterising the potential variation and the Kramers time.

cond-mat.stat-mech↗

arXiv2004

Realizability of stationary spherically symmetric transonic accretion

The spherically symmetric stationary transonic (Bondi) flow is considered a classic example of an accretion flow. This flow, however, is along a separatrix, which is usually not physically realizable. We demonstrate, using a pedagogical example, that it is the dynamics which selects the transonic flow.

astro-ph↗

arXiv2002

Photoemission From A Two Electron Quantum Dot

We consider photoemission from a two-electron quantum dot and find analytic expression for the cross-section. We show that the emission cross-section from the ground state as a function of magnetic field has sharp discontinuities corresponding to the singlet-triplet transitions for low magnetic fields and the transitions between magic numbers (2J+1) for high magnetic field. We also find the corrections to the photoemission cross-section from a more realistic quantum dot having a finite thickness due to nonvanishing extent of electron wave function in the direction perpendicular to the plane in which 2-D dot electrons are usually confined.

cond-mat.mes-hall↗

arXiv2002

Two Electron Quantum Dot - A Variational Treatment For The Ground State

A variational treatment for a two-electron quantum dot (the artificial helium atom) is proposed which leads to exact answer for the ground state energy. Depending on the magnetic field value the singlet-triplet and triplet-triplet transitions of the ground state take place, which are captured in our solution. Using the same variational technique we find corrections to wave function and energy and the transition field strengths in a realistic dot where electron wave function has a finite extent in the direction perpendicular to the x-y plane in which usually 2-D dot electrons are confined. Using the variational wave function we show that photoemission cross-section as a function of magnetic field has sharp discontinuities, which can be used for experimental verification of the singlet-triplet transitions.

cond-mat.mes-hall↗

arXiv2001

Chaos in the Quantum Double Well Oscillator: The Ehrenfest View Revisited

We treat the double well quantum oscillator from the standpoint of the Ehrenfest equation but in a manner different from Pattanayak and Schieve. We show that for short times there can be chaotic motion due to quantum fluctuations, but over sufficiently long times the behaviour is normal.

quant-ph↗

arXiv1998

Critical Ultrasonics Near the Superfluid Transition : Finite Size Effects

The suppression of order parameter fluctuations at the boundaries causes the ultrasonic attenuation near the superfluid transition to be lowered below the bulk value. We calculate explicitly the first deviation from the bulk value for temperatures above the lambda point. This deviation is significantly larger than for static quantities like the thermodynamic specific heat or other transport properties like the thermal conductivity. This makes ultrasonics a very effective probe for finite size effects.

cond-mat↗

arXiv1998

Scaling Function for the Critical Specific Heat in a Confined Geometry : Spherical Limit

The scaling function for the critical specific heat is obtained exactly for temperatures above the bulk transition temperature by working in the spherical limit. Generalization of the function to arbitrary $α$ (the specific heat exponent), gives an excellent account of the experimental data of Mehta and Gasparini near the superfluid transition.

cond-mat↗

arXiv1997

Smoothing of sandpile surfaces after intermittent and continuous avalanches: three models in search of an experiment

We present and analyse in this paper three models of coupled continuum equations all united by a common theme: the intuitive notion that sandpile surfaces are left smoother by the propagation of avalanches across them. Two of these concern smoothing at the `bare' interface, appropriate to intermittent avalanche flow, while one of them models smoothing at the effective surface defined by a cloud of flowing grains across the `bare' interface, which is appropriate to the regime where avalanches flow continuously across the sandpile.

cond-mat.soft↗

arXiv1997

ESS and Dissipation Range Dynamics of 3-D Turbulence

We carry out a self consistent calculation of the structure functions in the dissipation range using Navier Stokes equation. Combining these results with the known structures in the inertial range, we actually propose crossover functions for the structure functions that takes one smoothly from the inertial to the dissipation regime. In the process the success of the extended self similarity is explicitly demonstrated.

chao-dyn↗