arXiv subjects

A. Bhattacharyay

Publications and source records attributed to A. Bhattacharyay.

At least 37 records · Page 2Linked to original sources

arXiv2018

Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution

Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the equilibrium solution of the corresponding Smoluchowski equation. The equilibrium distribution is a generalization of the Boltzmann distribution. This generalized Boltzmann distribution involves an effective potential which is a function of coordinate dependent diffusivity. We discuss various implications of the existence of this generalized Boltzmann distribution for equilibrium of systems with coordinate dependent diffusivity and damping.

cond-mat.stat-mech↗

arXiv2017

Probing non-locality of interactions in a Bose-Einstein Condensate using solitons

We consider a Bose-Einstein Condensate(BEC) with non-local inter-particle interactions. The local Gross-Pitaevskii(GP) equation is valid for the gas parameter $ν=: a^{3} n_{0} << 1$, but for $ν\rightarrow 1$, the BEC is described by modified GP equation(MGPE). We study the exact solutions of the MGPE describing bright and dark solitons. It turns out that the width of these non-local solitons has qualitatively similar behaviour as the modified healing length due to the non-local interactions of the MGPE. We also study the effect of the non-locality and gas parameter(ν) on the stability of the solitons using the Vakhitov Kolokolov(VK) stability criterion. We show that these soliton solutions are indeed stable. Further, the stability of these soliton solutions gets enhanced due to the non-locality of interactions.

cond-mat.quant-gas↗

arXiv2017

Effect of non-local interactions on the vortex solution in Bose-Einstein Condensates

We consider the Gross-Pitaevskii (GP) model of a Bose-Einstein Condensate (BEC) to study a single vortex line in the presence of non-local repulsive s-wave scattering. We show that in addition to the vortex solution with core width of the order of the healing length, there exists a vortex solution whose width is a microscopic length scale of the order of s-wave scattering length and is independent of the healing length. We compare the two classes of vortex solution and show the region where one can possibly observe the vortex whose width is of the order of scattering length.

cond-mat.quant-gas↗

arXiv2017

Nonlocal interactions in a BEC: an Analogue Gravity perspective

We add a minimal correction term to the local Gross-Pitaevskii equation to represent non-locality in the interactions. We show that the effective minimal non-locality can make the healing length decrease more rapidly with the increase of $s$-wave scattering length leaving the expression of the velocity of sound unaltered. We discuss the implication of this result for a Bose-Einstein Condensate (BEC) being used as an analogue gravity system. The presented result is important in the context of condensed matter physics as well because one can considerably change the size of a quantized vortex at finite $s$-wave scattering length by tuning the healing length.

cond-mat.quant-gas↗

arXiv2017

Quantum Potential induced UV-IR coupling in Analogue Hawking radiation: From Bose-Einstein Condensates to canonical acoustic black holes

Arising out of a Non-local non-relativistic BEC, we present an Analogue gravity model upto $\mathcal{O}(ξ^{2})$ accuracy in the presence of the quantum potential term for a canonical acoustic BH in $(3+1)$-d spacetime where the series solution of the free minimally coupled KG equation for the large length scale massive scalar modes is derived. We systematically address the issues of the presence of the quantum potential term being the root cause of a UV-IR coupling between short wavelength `primary' modes which are supposedly Hawking radiated through the sonic horizon and the large wavelength `secondary' modes. In the quantum gravity experiments of analogue Hawking radiation in the laboratory, this UV-IR coupling is inevitable and one can not get rid of these large wavelength excitations which would grow over space by gaining energy from the short wavelength Hawking radiated modes. We identify the characteristic feature in the growth rate(s) that would distinguish these primary and secondary modes.

gr-qc↗

arXiv2016

Equilibrium stochastic dynamics of a Brownian particle in inhomogeneous space: derivation of an alternative model

An alternative equilibrium stochastic dynamics for a Brownian particle in inhomogeneous space is derived. Such a dynamics can model the motion of a complex molecule in its conformation space when in equilibrium with a uniform heat bath. The derivation is done by a simple generalization of the formulation due to Zwanzig for a Brownian particle in homogeneous heat bath. We show that if the system couples to different number of bath degrees of freedom at different conformations then the alternative model is derived. We discuss results of an experiment by Faucheux and Libchaber which probably has indicated possible limitation of the Boltzmann distribution as equilibrium distribution of a Brownian particle in inhomogeneous space and propose experimental verification of the present theory using similar methods.

cond-mat.stat-mech↗

arXiv2015

Amplitude modulated phase in a Bose-Einstein condensate: the role of non-local interactions

We consider a Gross-Pitaevskii model of BEC with non-local interactions of range of the order of the s-wave scattering length. With this model, we study the density modulated phase in 1D and 2D, which are solutions of this modified model along with the usual uniform density state. We find an exact free energy functional for our model and show that the 1D density modulated state can have lower energy than the uniform density state. Although, the density modulated state can be made to be energetically favourable, we show also that, this state is inherently dynamically unstable due to the coupling of instabilities to the spatial order.

cond-mat.quant-gas↗

arXiv2015

Long range interaction induced density modulated state in a Bose-Einstein condensate

We consider a Gross-Pitaevskii model of BEC with non-local s-wave scattering to study the density modulated state in 1D. We resort to a perturbative Taylor series expansion for the order parameter. By perturbative calculations, we show that under long range s-wave scattering a density modulated state is energetically favourable as compared to the uniform density state. We obtain density modulated state as a solution to the perturbative non-local GP equation, rather than the conventional approach of introducing amplitude modulations on top of the uniform density state and lowering the roton minimum.

cond-mat.quant-gas↗

arXiv2014

Equilibrium of a Brownian particle in an inhomogeneous medium: An alternative approach

We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative noise. Here we show that the mapping to an additive noise gives the equilibrium distribution of the generalized Langevin dynamics of a particle with mass. The procedure does not need inclusion of any ad hoc current cancelling term in the Langevin dynamics. The result shows a modified Maxwell-Boltzmann distribution with a damping dependent amplitude.

cond-mat.stat-mech↗

arXiv2014

Quantum potential induced emergence of massive scalar fields in the analogue gravity model of a Bose-Einstein condensate

We show here a general approach to include the quantum potential term in the emergent gravity model of Bose-Einstein condensate by using multiple scales. Our main result shows the emergence of a massive scalar modulating field at larger length scales as a result of Lorentz symmetry breaking at the length scales comparable to the healing length. We also propose that, the nonlocal interactions induced tuning of healing length can be exploited experimentally to observe the systematics of small and large scale coupling as emerges in our present analysis.

gr-qc↗

arXiv2012

Generalized fluctuation-dissipation relation and statistics for the equilibrium of a system with conformation dependent damping

Liouville's theorem, based on the Hamiltonian flow (micro-canonical ensemble) for a many particle system, indicates that the (stationary) equilibrium probability distribution is a function of the Hamiltonian. A canonical ensemble corresponds to a micro-canonical one at thermodynamic limit. On the contrary, the dynamics of a single Brownian particle (BP) being explicitly non-Hamiltonian with a force and damping term in it and at the other extreme to thermodynamic limit admits the Maxwell-distribution (MD) for its velocity and Boltmann-distribution (BD) for positions (when in a potential). This is due to the fluctuation-dissipation relation (FDR), as was first introduced by Einstein, which forces the Maxwell distribution to the Brownian particles. For a structureless BP, that, this theory works is an experimentally verified fact over a century now. Considering a structured Brownian particle we will show that the BD and MD fails to ensure equilibrium. We will derive a generalized FDR on the basis of the demand of zero current on inhomogeneous space. Our FDR and resulting generalized equilibrium distributions recover the standard ones at appropriate limits.

cond-mat.stat-mech↗

arXiv2012

Conformation dependent damping and generalization of fluctuation-dissipation relation

Damping on an object generally depends on its conformation (shape size etc.). We consider the Langevin dynamics of a model system with a conformation dependent damping and generalize the fluctuation dissipation relation to fit in such a situation. We derive equilibrium distribution function for such a case which converges to the standard Boltzmann form at the limit of uniform damping. The results can have implications, in general, for barrier overcoming processes where standard Boltzmann statistics is slow.

cond-mat.stat-mech↗

arXiv2011

Directed transport in equilibrium : analysis of the dimer model with inertial terms

We have previously shown an analysis of our dimer model in the over-damped regime to show directed transport in equilibrium. Here we analyze the full model with inertial terms present to establish the same result. First we derive the Fokker-Planck equation for the system following a Galilean transformation to show that a uniformly translating equilibrium distribution is possible. Then, we find out the velocity selection for the centre of mass motion using that distribution on our model. We suggest generalization of our calculations for soft collision potentials and indicate to interesting situation with possibility of oscillatory non-equilibrium state within equilibrium.

cond-mat.stat-mech↗

arXiv2011

Directed transport in equilibrium

We investigate a symmetry broken dimer constrained to move in a particular direction when in contact with a heat-bath at a constant temperature. The dimer is not driven by any external force. The system gains kinetic energy from the heat-bath. The symmetry broken system can use this energy in directed transport. At the hard core collision limit between the particles of the dimer, we show by exact analytic calculations and complementary numerical results that the dimer undergoes steady directed transport. Our observation, being consistent with the {\it second law of thermodynamics}, {\it detailed balance} etc leads to new physical understanding to which much attention has not been paid.

cond-mat.stat-mech↗

arXiv2011

Revisiting Langer-Ambegaokar-McCumber-Halperin theory of resistive transitions in one-dimensional superconductors with exact solutions

We present an important correction to the Langer-Ambegaokar-McCumber-Halperin theory for the resistive state of a 1D superconductor. We establish that the identification of the saddle on the free energy surface over which Langer and Ambegaokar had claimed the system to move in order to form thermally excited phase slip centres is wrong. With the help of an exact solution we show that the system has to overcome a similar free energy barrier but can actually have vanishing amplitude of superconducting phase at a point unlike the Langer-Ambegaokar solution.

cond-mat.supr-con↗

arXiv2010

Directional transport induced by elasticity and volume exclusion

We investigate an exactly solvable model for directional transport in 1D. The structured system, which has strong elastic interactions in its parts, explicitly demonstrates the role of volume exclusion in producing directional transport. We capture the complementary role of the elasticity and volume exclusion as the basic ingredient for showing up of broken microscopic symmetry at the scale of macroscopic motions. We compare the analytic results with the numerical simulation.

cond-mat.stat-mech↗

arXiv2009

Model of amplitude modulations induced by phase slips in one-dimensional superconductors

We propose a linear model for the dynamics of amplitudes associated with formation of phase slip centers in a one-dimensional superconductor. The model is derived taking into account the fact that, during the formation of phase slip centers the wave number of the superconducting phase remains practically constant. The model captures various forms of amplitude modulations associated with PSCs in closed analytic forms.

cond-mat.supr-con↗

arXiv2009

Parametric internal waves in a compressible fluid

We describe the effect of vibration on a confined volume of fluid which is density stratified due to its compressibility. We show that internal gravity-acoustic waves can be parametrically destabilized by the vibration. The resulting instability is similar to the classic Faraday instability of surface waves, albeit modified by the compressible nature of the fluid. It may be possible to observe experimentally near a gas-liquid critical point.

physics.flu-dyn↗