arXiv subjects

Sumita Datta

Publications and source records attributed to Sumita Datta.

12 recordsLinked to original sources

arXiv2026

Structural Distinction in ODE and PDE Chaos:Lorenz vs Kuramoto--Sivashinsky Equation

We study the nature of chaos in finite and infinite dimensional systems through a comparison between the Kuramoto Sivashinsky (KS) equation, the Lorenz system, and a Lorenz type reduction of the KS equation proposed by Wilczak. Numerical simulations of the KS equation reveal intrinsic spatio temporal chaos, with disorder evolving simultaneously in space and time. In contrast, the Lorenz system and the Wilczak reduction exhibit low dimensional temporal chaos lacking spatial complexity. Lyapunov exponent analysis highlights the finite-dimensional convergence properties of the reduced systems and underscores the fundamentally different dynamical nature of chaos in the KS equation. In particular, we demonstrate that low-dimensional reductions may reproduce transient chaotic signatures but do not necessarily retain the structural properties of infinite-dimensional dissipative systems.

nlin.CD↗

arXiv2026

Melnikov Analysis of Deterministic and Stochastic Manifold Splitting in the Kuramoto--Sivashinsky Equation

We develop a Melnikov framework for the Kuramoto Sivashinsky (KS) equation under weak deterministic and stochastic forcing. By treating KS as an infinite dimensional dynamical system, we derive a Melnikov functional that measures splitting of stable and unstable manifolds of a homoclinic orbit. Periodic forcing leads to phase dependent transverse intersections, while stochastic forcing produces random manifold splitting characterized by a variance determined by the adjoint solution. This provides a geometric mechanism linking invariant manifold theory to spatiotemporal chaos in dissipative partial differential equations.

math.DS↗

arXiv2026

On the Connection Between Chaos Assisted Tunneling and Coherent Destruction of Tunneling

The interplay between classical chaos and quantum tunneling is examined in driven nonlinear systems, with emphasis on how semi classical phase space structures influence purely quantum transport phenomena. We show that, in the presence of external driving and stochastic perturbations, tunneling rates acquire an activated form determined by effective classical barriers, providing a transparent link between chaotic dynamics and quantum tunneling. Within this framework, chaos assisted tunneling and coherent destruction of tunneling emerge as closely related manifestations of the same underlying phase space restructuring and interference effects induced by driving. The results offer a unified perspective on tunneling control in non integrable systems and remain relevant for modern studies of driven quantum dynamics and decoherence resistant transport.

nlin.CD↗

arXiv2026

Quantum Simulation of Hyperbolic Equations and the Nonexistence of a Dirac Path Measure

We revisit the longstanding issue of why no well defined probability measure exists corresponding to a classical (Kolmogorov) path integral representation of the Dirac equation in Minkowski space. Two complementary perspectives are compared: (i) Zastawniak's observation that the distributional character of the Dirac propagator (presence of derivatives of the delta distribution) obstructs the construction of a nonnegative transition kernel, and (ii) the indefinite signature of the Minkowski metric which prevents positivity of the action and yields oscillatory integrals. We show how these viewpoints can be unified as different manifestations of a single mathematical obstruction from measure theoretical point of view, and we discuss consequences for stochastic representations of relativistic first-order equations.

quant-ph↗

arXiv2026

Mpemba Effect in an Expanding Lieb-Liniger Bose gas in a hard wall box

The Mpemba effect, broadly understood as the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than a system closer to equilibrium, has been widely studied in classical stochastic systems and, more recently, in quantum settings. However, its manifestation is strongly dependent on the choice of observable and the dynamical constraints of the system. In this work, we investigate the emergence of a Mpemba-type effect in the density redistribution dynamics of a strongly interacting one-dimensional Bose gas in the Tonks-Girardeau regime undergoing a sudden box expansion from length L_0 to L. By defining a physically motivated distance function based on the difference of densities between spatial regions, we provide evidence that -the relaxation dynamics of the ground and excited symmetry sectors exhibit a clear crossing in time, indicating a reversal in relaxation ordering. We emphasize that the Mpemba effect is not a universal law but rather an observable-dependent phenomenon that arises under specific dynamical conditions. In particular, we show that the interplay between initial state structure, integrability, and spatial redistribution leads to distinct relaxation pathways that enable the effect. Our results clarify common misconceptions linking the Mpemba effect to Newton's law of cooling and highlight the conditions under which such anomalous relaxation behavior can emerge in integrable quantum systems.

cond-mat.quant-gas↗

arXiv2024

Dynamical Fermionization and Emergent Bethe Rapidity Structure in the Spatial Density of Cold quenched Lieb-Liniger gas

We demonstrate that the nonequilibrium spatial density of a one-dimensional interacting Bose gas, following a geometric quench, directly encodes information about the underlying momentum (rapidity) distribution of the system. Starting from the interacting ground state of a Lieb--Liniger gas confined in a hard-wall box of length $L_0$, we study its expansion into a larger box of length $L > L_0$ at fixed interaction strength. Using an ab initio quantum Monte Carlo approach based on the generalized Feynman--Kac representation, we compute the time evolution of the many-body density. We show that, in the long-time limit, the density profile acquires a scaling form in the velocity variable $x/t$, approaching a stationary distribution whose shape reflects the underlying rapidity structure. The velocity-space density broadens systematically with increasing interaction strength and exhibits rapid convergence in the strongly interacting (Tonks--Girardeau) regime. These results provide numerical evidence that ballistic expansion enables a direct mapping between spatial density profiles and the momentum-space structure of the integrable Lieb--Liniger model, offering a practical route to accessing Bethe rapidities through real-space observables.

cond-mat.quant-gas↗

arXiv2023

On the path integral simulation of space-time fractional Schroedinger equation with time independent potentials

In this work a Feynman-Kac path integral method based on Levy measure has been proposed for solving the Cauchy problems associated with the space-time fractional Schroedinger equations arising in interacting systems in fractional quantum mechanics. The Continuous Time Random Walk(CTRW) model is used to simulate the underlying Levy process-a generalized Wiener process. Since we are interested to capture the lowest energy state of quantum systems, we use Pareto distribution as opposed to Mittag-Leffler random variables, which are more suitable for finite time. Adopting the CTRW model we have been able to simulate the space-time fractional diffusion process with comparable simplicity and convergence rate as in the case of a standard diffusion. We hope this paves an elegant way to solve space-time diffusion equations numerically through Fractional Feynman-Kac path integral technique as an alternative to fractional calculus.

quant-ph↗

arXiv2023

Quantum Simulation of non-Born-Oppenheimer dynamics in molecular systems by path integrals

A numerical algorithm based on the probabilistic path integral approach for solving Schroedinger equation has been devised to treat molecular systems without Born-Oppenheimer approximation in the non relativistic limit at zero temperature as an alternative to conventional Variational and perturbation methods. Using high quality variational trial functions and path integral method based on Generalized Feynman-Kac method, we have been able to calculate the non-Born-Oppenheimer energy for hydrogen molecule for the sigma state and hydrogen molecular ion. Combining these values and the value for ionization potential for atomic hydrogen, dissociation energy and ionization potential for hydrogen molecule have been determined to be 36 113.672(3) cm inverse and 124.446.066(10) cm inverse.respectively. Our results favorably compare with other theoretical and experimental results and thus show the promise of being a nonperturbative alternative for testing fundamental physical theories.

quant-ph↗

arXiv2022

Computing quantum correlation functions by Importance Sampling method based on path integrals

An importance sampling method based on Generalized Feynman-Kac method has been used to calculate the mean values of quantum observables from quantum correlation functions for many body systems both at zero and finite temperature. Specifically, the expectation of $\langle r_i^n\rangle$, $\langle r_{ij}^n\rangle$, $\langle r_i^{-n}\rangle$ and $\langle r_{ij}^{-n}\rangle$ for the ground state of the lithium and beryllium and the density matrix, the partition function, the internal energy and the specific heat of a system of quantum harmonic oscillators are computed, in good agreement with the best nonrelativistic values for these quantities. Although the initial results are encouarging, more experimentation will be needed to improve the other existing numerical results beyond chemical accuracies specially for the last two properties for lithium and beryllium. Also more work needs to be done to improve the trial functions for finite temperature calculations.

quant-ph↗

arXiv2022

Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitevskii Breather

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored,indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculations, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

quant-ph↗

arXiv2018

Metastability versus collapse following a quench in attractive Bose-Einstein condensates

We consider a Bose-Einstein condensate (BEC) with attractive two-body interactions in a cigar-shaped trap, initially prepared in its ground state for a given negative scattering length, which is quenched to a larger absolute value of the scattering length. Using the mean-field approximation, we compute numerically, for an experimentally relevant range of aspect ratios and initial strengths of the coupling, two critical values of quench: one corresponds to the weakest attraction strength the quench to which causes the system to collapse before completing even a single return from the narrow configuration ("perihelion") in its breathing cycle. The other is a similar critical point for the occurrence of collapse before completing two returns. In the latter case, we also compute the limiting value, as we keep increasing the strength of the post-quench attraction towards its critical value, of the time interval between the first two perihelia. We also use a Gaussian variational model to estimate the critical quenched attraction strength below which the system is stable against the collapse for long times. These time intervals and critical attraction strengths---apart from being fundamental properties of nonlinear dynamics of self-attractive BECs---may provide clues to the design of upcoming experiments that are trying to create robust BEC breathers.

cond-mat.quant-gas↗

arXiv2017

Numerical Realization of Bethe Rapidities in cold quenched systems by Feynman-Kac path integral method

We apply Quantum Monte Carlo technique to analyze the non equlibrium state of a trapped 1d Bose gas just after the quenching of the confining potential. As a matter of fact we solve the time dependent Schroedinger equation for the system of one-dimensional bosons interacting via delta potential in an infinite square well (namely Lieb-Liniger model) using Feynman-Kac path integral Monte Carlo technique. These 1d systems are extremely interesting and worth investigating in the context of non-equilibrium dynamics of interacting many body systems. Even though the systems can be realized experimentally and are exactly solvable by Bethe Ansatz, the diffusion Monte Carlo is proven to be more efficient in most circumstances than other mean value techniques as the numerical method can incorporate the finite interaction very easily. Using N particle ground state wavefunction for one-dimensional hard core bosons in a harmonic trap, we develop an algorithm to calculate density. We also observe the change in the density distribution by changing the length of the hard wall box. After an increase in the box length, we still get a self-similar density distribution.

cond-mat.quant-gas↗