arXiv subjects

Saugata Bhattacharyya

Publications and source records attributed to Saugata Bhattacharyya.

7 recordsLinked to original sources

arXiv2021

Explicit derivation of the Fraunhofer diffraction formula for oblique incidence

We have analytically explored the Rayleigh-Sommerfeld scalar diffraction for oblique incidence. We have explicitly derived the Fraunhofer diffraction formulae for oblique incidence of plane scalar wave on various apertures, such as single-slit, circular aperture, and diffraction grating. Such derivations in the background of Rayleigh-Sommerfeld scalar diffraction theory would be important for an undergraduate course on optics.

physics.gen-ph↗

arXiv2021

Rayleigh-Sommerfeld scalar diffraction by apertures moving at relativistic speeds

We have analytically obtained the theoretical results for the Rayleigh-Sommerfeld (R-S) scalar diffraction by apertures, such as single-slit, double-slit, grating and circular aperture, moving at relativistic speeds with the velocities perpendicular to the direction of incidence. We also have studied diffraction by a single-slit of oscillatory shutter. Our study would be significant in probing the relativistic transverse Doppler effect on the intensity pattern of the diffracted field.

physics.optics↗

arXiv2015

Casimir effect for a Bose-Einstein condensate inside a cylindrical tube

We explore Casimir effect on an interacting Bose-Einstein condensate (BEC) inside a cylindrical tube. The Casimir force for the confined BEC comprises of (i) a mean-field part arising from the spatial inhomogeneity of the condensate order parameter, and (ii) a quantum fluctuation part arising from the confinement of Bogoliubov excitations in the condensate. Our analytical result predicts Casimir force on a cylindrical shallow of $^4$He well below the $λ$-point, and can be tested experimentally.

cond-mat.stat-mech↗

arXiv2015

Energy fluctuation and discontinuity of specific heat

Specific heat per particle ($c_v$) of an ideal gas, in many occasions, is interpreted as energy fluctuation per particle ($\triangleε^2$) of the ideal gas through the relation: $\triangleε^2=kT^2c_v$, where $k$ is the Boltzmann constant and $T$ is the temperature. This relationship is true only in the classical limit, and deviates significantly in the quantum degenerate regime. We have analytically explored quantum to classical crossover of this relationship, in particular, for 3-D free Bose and Fermi gases. We also have explored the same for harmonically trapped cases. We have obtained a hump of $\triangleε^2/kT^2c_v^{(\text{cl})}$ around the condensation point for 3-D harmonically trapped Bose gas. We have discussed the possibility of occurring phase transition with discontinuity of heat capacity from existence of such a hump for other Bose and Fermi systems.

cond-mat.stat-mech↗

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↗

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↗