arXiv subjects

Pankaj K. Mishra

Publications and source records attributed to Pankaj K. Mishra.

14 recordsLinked to original sources

arXiv2025

Vortex configuration dependent equilibrium and non-equilibrium states in two-dimensional quantum turbulence

In this work, we analyze the evolution of four vortex configurations, namely, dipole, plasma, cluster, and lattice, using the two-dimensional mean-field Gross-Pitaevskii equation, focusing on their dynamical decay and approach to the equilibrium. Our analysis reveals that the cluster vortex configuration reaches equilibrium more rapidly than the others, while the dipole, plasma, and lattice configurations exhibit persistent non-equilibrium behavior, tending toward non-thermal fixed points. Specifically, the cluster configuration follows Kolmogorov-like scaling ($\varepsilon^{i}(k)\sim k^{-5/3}$) in the incompressible spectrum, while the other configurations follow Vinen-like scaling ($\varepsilon^{i}(k)\sim k^{-1}$). In the compressible spectrum, the cluster case exhibits a $k$ scaling, indicating full mode equilibration, while for the other configurations, the modes thermalize only above a critical wave number. Additionally, the transfer function for the cluster configuration displays a Gaussian distribution, typical of equilibrium states, while the other configurations exhibit skewed Gaussian or exponential distributions, indicative of their non-equilibrium nature. Finally, the particle number spectra show that the cluster case follows dynamical scaling closer to equilibrium, while the dipole, plasma, and lattice configurations evolve towards non-thermal fixed points. Our findings provide new insights into the dynamics of vortex configurations and their approach to equilibrium or non-equilibrium states, offering guidance for future studies on quantum turbulence and its control.

cond-mat.quant-gas↗

arXiv2025

Rabi-induced localization and resonant delocalization of a binary condensate in a spin-asymmetric quasiperiodic potential

We theoretically investigate the ground state and dynamics of a Rabi-coupled pseudospin-1/2 Bose-Einstein condensate, where only one spin component is subjected to an external potential. We show that in the quasiperiodic potential the Rabi coupling induces localization between the components as it is raised above the threshold value. Interestingly, the localization is mutually induced by both components for the quasiperiodic confinement, whereas for a harmonic trap the localization is induced in the potential-free component by interaction with that confined in the potential. Further, we explore the condensate dynamics by implementing a periodic driving of the Rabi frequency, where various frequency-dependent delocalization patterns, such as double (triple)-minima, tree-(parquet)-like, and frozen distributions with a correlated propagation of different spin populations are observed in the condensate density. These features pave the way to control the condensate mass and spin density patterns, both in the stationary and dynamical realizations.

cond-mat.quant-gas↗

arXiv2025

Signature of localization-delocalization in collisional inhomogeneous spin-orbit coupled condensates

We study the localization transition in spin-orbit (SO) coupled binary Bose-Einstein condensates (BECs) with collisional inhomogeneous interaction trapped in a one-dimensional quasiperiodic potential. Our numerical analysis shows that the competition between the quasiperiodic disorder and inhomogeneous interaction leads to a localization-delocalization transition as the interaction strength is tuned from attractive to repulsive in nature. Furthermore, we analyse the combined effect of the SO and Rabi coupling strengths on the localization transition for different interaction strengths and obtain signatures of similar localization-delocalization transition as a function of SO coupling in the regime of weak interactions. We complement our numerical observation with the analytical model using the Gaussian variational approach. In the end, we show how the localization-delocalization is manifested in the quench dynamics of the condensate. Our study provides an indirect approach to achieve localization transition without tuning the quasiperiodic potential strength, but rather by tuning the inhomogeneity in the interaction.

cond-mat.quant-gas↗

arXiv2025

Spin-dependent localization of spin-orbit and Rabi-coupled Bose-Einstein condensates in a random potential

We investigate the effect of the spin-orbit (SO) and Rabi couplings on the localization of the spin-1/2 condensate trapped in a one-dimensional random potential. Our studies reveal that the spin-dependent couplings create distinct localization regimes, resulting in various relations between localization and spin-related properties. First, we examine the localization in the linear condensate and find that the SO coupling can lead to a transition of the localized state from the "basin-like" to the "void" region of the potential. For a weak random potential upon an increase in the SO coupling, we find a re-entrant transition from a broad to narrow localized state and back at a higher SO coupling. Further, we analyze the competing role of inter-species and intra-species interactions on the localization of the condensate. We find the appearance of spin-dependent localization as the interactions increase beyond threshold values for a sufficiently strong disorder. Our findings on controlling spin-dependent localization may be useful for future ultracold atomic experiments and corresponding spin-related quantum technologies.

cond-mat.quant-gas↗

arXiv2024

Impurities induced vortex lattice melting and turbulence in rotating Bose-Einstein condensates

We investigate the impact of various impurities on rotating Bose-Einstein condensates confined within two-dimensional harmonic and optical lattice potentials. Without impurities, the rotating condensates display an organized square lattice pattern of vortices due to the influence of a square optical lattice. The introduction of impurity potentials disrupts this lattice structure, inducing a phase transition from an ordered state to a disordered state. Our analysis encompasses both static and dynamic types of impurities. The static impurities are implemented using a randomly varying potential with a spatially random amplitude. The transformation of the vortex lattice structure, in this case, relies on the strength and lattice constant of the impurity potential. For dynamical impurities, we employ a Gaussian obstacle that orbits around the condensate at a specific distance from its center. In this scenario, the vortex lattice melting occurs beyond a certain threshold radius and frequency of oscillation of the rotating obstacle. We characterize the melting of the vortex lattice due to impurities using various quantities, such as the structure factor and angular momentum. Notably, in the vortex-melted state, the angular momentum follows a power-law dependence with an exponent of approximately $1.73$, regardless of the type of impurity. Finally, we demonstrate the signature of the presence of a turbulent state within the vortex-melted state generated by both static and dynamical impurities.

cond-mat.quant-gas↗

arXiv2024

Evidence of Kolmogorov like scalings and multifractality in the rainfall events

In this paper we present a detailed statistical analysis related to the characterization of the spatial and temporal fluctuations present in the rainfall patterns of North-East region ($26.05^{\circ}N-26.95^{\circ}N$, $88.05^{\circ}E-94.95^{\circ}E$) of India using half hourly rainfall data over the last 20 years for the range 2001-2020. We analyze the nature of the distribution by computing the mean, second moment of the fluctuation, skewness and kurtosis of the temporal rainfall data that indicate the presence of heavy tail in the right skewed distribution a typical feature of the presence of rare events. We find that the temporal distribution of the rainfall data follow the multiplicative Log-Normal probability distribution. Further we compute the spatial and temporal correlation of the rainfall in this region indicate that the rainfall events are correlated in the spatial direction of about 70 Km. The Power spectral density of temporal rainfall shows power law behaviour with frequency with an exponent $\sim -1.5$ close to the Kolmogorov exponent ($-1.67$) exhibited for the turbulent passive scalar driven by the mean flow. Our wavelet analysis reveals the evidence of multiple frequencies in the rainfall pattern which can attributed to different short and long range factors responsible for the rainfall. We have also used the Hilbert Huang transformation to identify the frequencies corresponding fluctuating part of the rainfall time series. Using multifractal detrended fluctuation analysis, finally we establish the multifractal nature of the rainfall pattern with Hurst exponent close to $0.65$ .

physics.ao-ph↗

arXiv2023

Quench induced chaotic dynamics of Anderson localized interacting Bose-Einstein condensates in one dimension

We study the effect of atomic interaction on the localization and the associated dynamics of Bose-Einstein condensates in a one-dimensional quasiperiodic optical lattice and random Gaussian disordered potentials. When the interactions are absent, the condensates exhibit localization, which weakens as we increase the interaction strength beyond a threshold value for both potential types. We inspect the localized and delocalized states by perturbing the system via quenching the interaction strength instantaneously to zero and studying the dynamics of the condensate, which we further corroborate using the out-of-time-order correlator. The temporal behaviour of the time correlator displays regular dynamics for the localized state, while it shows temporal chaos for the delocalized state. We confirm this dynamical behaviour by analyzing the power spectral density of the time correlator. We further identify that the condensate admits a quasiperiodic route to chaotic dynamics for both potentials. Finally, we present the variation of the maximal Lyapunov exponents for different nonlinearity and disorder strengths that have a positive value in the regime where the time correlator function shows chaotic behaviour. Through this, we establish the strong connection between the spatially delocalized state of the condensate and its temporal chaos.

cond-mat.quant-gas↗

arXiv2017

Scalings of heat transport and energy spectra of turbulent Rayleigh-Benard convection in a large-aspect-ratio box

Direct Numerical Simulations of turbulent convection in a large aspect-ratio box are carried out in the range of Rayleigh number $7 \times 10^4 \le Ra \le 2 \times 10^6$ at Prandtl number Pr=0.71. A strong correlation between the vertical velocity and temperature is observed in the turbulent regime at almost all the length scales. Frequency spectra of all the velocities and temperature show a $-5/3$ law for a wide band of frequencies. The variances of horizontal velocities at different points in the flow yield a single power-law. Probability density functions of velocities and temperature are close to Gaussian only at higher Rayleigh numbers. The mean and variance of temperature clearly show boundary layers, surface layers and a near-homogeneous bulk region. The boundary layer thickness decreases and bulk-homogeneity is enhanced on increasing the Rayleigh numbers. The wave number spectra of the turbulent kinetic energy exhibit Kolmogorov like ($E(k)\sim k^{-5/3}$) and Bolginao-Obukhov like ($E(k)\sim k^{-11/5}$) behaviour respectively in the central and near-wall regions of the container. An approximate balance between the production due to buoyancy and the dissipation is found in the turbulent kinetic energy budget. Taylor's approximate equation of the production due to turbulent stretching and the dissipation of turbulent enstrophy is modified by the inclusion of buoyancy production in the enstrophy budget. The present results support the previously proposed $2/7$ power-law dependence of the average Nusselt number on the Rayleigh number by yielding an exponent of 0.272, but do not necessarily support the proposed classification of "soft" and "hard" turbulence on the basis of this exponent.

physics.flu-dyn↗

arXiv2014

Elasticity and Plasticity in Stiff and Flexible Oligomeric Glasses

In this paper we focus on the mechanical properties of oligomeric glasses (waxes), employing a microscopic model that provides, via numerical simulations, information about the shear modulus of such materials, the failure mechanism via plastic instabilities and about the geometric responses of the oligomers themselves to a mechanical load. We present a microscopic theory that explains the numerically observed phenomena, including an exact theory of the shear modulus and of the plastic instabilities, both local and system spanning. In addition we present a model to explain the geometric changes in the oligomeric chains under increasing strains.

cond-mat.soft↗

arXiv2014

Scaling of heat flux and energy spectrum for "very large" Prandtl number convection

Under the limit of infinite Prandtl number, we derive analytical expressions for the large-scale quantities, e.g., Péclet number Pe, Nusselt number Nu, and rms value of the temperature fluctuations $θ_\mathrm{rms}$. We complement the analytical work with direct numerical simulations, and show that $\mathrm{Nu} \sim \mathrm{Ra}^γ$ with $γ\approx (0.30-0.32)$, $\mathrm{Pe} \sim \mathrm{Ra}^η$ with $η\approx (0.57-0.61)$, and $θ_\mathrm{rms} \sim \mathrm{const}$. The Nusselt number is observed to be an intricate function of $\mathrm{Pe}$, $θ_\mathrm{rms}$, and a correlation function between the vertical velocity and temperature. Using the scaling of large-scale fields, we show that the energy spectrum $E_u(k)\sim k^{-13/3}$, which is in a very good agreement with our numerical results. The entropy spectrum $E_θ(k)$ however exhibits dual branches consisting of $k^{-2}$ and $k^0$ spectra; the $k^{-2}$ branch corresponds to the Fourier modes $\hatθ(0,0,2n)$, which are approximately $-1/(2n π)$. The scaling relations for Prandtl number beyond $10^2$ match with those for infinite Prandtl number.

physics.flu-dyn↗

arXiv2013

Role of Bulk flow in Turbulent Convection

In this paper we present scaling of large-scale quantities like Peclét and Nusselt numbers, and the dissipation rates of kinetic energy and entropy. Our arguments are based on the scaling of bulk quantities and earlier experimental and simulation results. We also present the inertial-range properties of spectra and fluxes of kinetic energy and entropy.

physics.flu-dyn↗

arXiv2012

Field correlations and the ultimate regime of turbulent convection

Using direct numerical simulations of Rayleigh-Bénard convection (RBC) under free-slip boundary condition, we show that the normalized correlation function between the vertical velocity field and the temperature field, as well as the normalized viscous dissipation rate, scales as $Ra^{-0.22}$ for moderately large Rayleigh number $Ra$. This scaling accounts for the Nusselt number ($Nu$) exponent to be around 0.3 observed in experiments. Numerical simulations also reveal that the above normalized correlation functions are constants for the convection simulation under periodic boundary conditions.

physics.flu-dyn↗

arXiv2009

Bifurcation and chaos in zero Prandtl number convection

We present the detailed bifurcation structure and associated flow patterns near the onset of zero Prandtl number Rayleigh Bénard convection. We employ both direct numerical simulation and a low-dimensional model ensuring qualitative agreement between the two. Various flow patterns originate from a stationary square observed at a higher Rayleigh number through a series of bifurcations starting from a pitchfork followed by a Hopf and finally a homoclinic bifurcation as the Rayleigh number is reduced to the critical value. Global chaos, intermittency, and crises are observed near the onset.

nlin.CD↗

arXiv2009

Order and chaos in two-dimensional Rayleigh-Bénard convection

A detailed study of the Rayleigh-Bénard convection in two-dimensions with free-slip boundaries is presented. Pseudo-spectral method has been used to numerically solve the system for Rayleigh number up to $3.3 \times 10^7$. The system exhibits various convective states: stationary, oscillatory, chaotic and soft-turbulent. The `travelling rolls' instability is observed in the chaotic regime. Scaling of Nusselt number shows an exponent close to 0.33. Studies on energy spectrum and flux show an inverse cascade of kinetic energy and a forward cascade of entropy. This is consistent with the shell-to-shell energy transfer in wave number space. The shell-to-shell energy transfer study also indicates a local energy transfer from one shell to the other.

physics.flu-dyn↗