arXiv subjects

M. L. Lekala

Publications and source records attributed to M. L. Lekala.

7 recordsLinked to original sources

arXiv2025

$R$-matrix type parametrization of the Jost function for extracting the resonance parameters from scattering data

A new method is proposed for fitting non-relativistic binary-scattering data and for extracting the parameters of possible quantum resonances in the compound system that is formed during the collision. The method combines the well-known $R$-matrix approach with the analysis based on the semi-analytic representation of the Jost functions. It is shown that such a combination has the advantages of both these approaches, namely, the number of the fitting parameters remains relatively small (as for the $R$-matrix approach) and the proper analytic structure of the $S$-matrix is preserved (as for the Jost function method). It is also shown that the new formalism, although closely related to the $R$-matrix method, has the benefit of no dependence on an arbitrary channel radius. The efficiency and accuracy of the proposed method are tested using a model single-channel potential. Artificial ``experimental'' data generated with this potential are fitted, and its known resonances are successfully recovered as zeros of the Jost function on the appropriate sheet of the Riemann surface of the energy.

quant-ph↗

arXiv2022

Dynamics of order-disorder and complexity for interacting bosons in optical lattice

The present work reports on the dynamical measures of order, disorder and complexity for the interacting bosons in optical lattice. We report results both for the relaxed state as well as quench dynamics. Our key observations are: (1) Lattice depth can be taken as order-disorder parameter. (2) The superfluid to Mott insulator transition can be treated as `order-disorder' transition. Our main motivation is to find how the system organize by itself during quench and how it optimizes the complexity. We find dynamical measures of order and disorder are more sensitive tool than entropy measures. We specifically calculate the time scale of entry and exit of different phases during time evolution. Initially the system exhibits collapse revival trend, however gradually looses its ability to turn back to superfluid phase and finally Settle to Mott insulator phase.

cond-mat.quant-gas↗

arXiv2019

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases -- due to their repulsion -- the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the $N$-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For $N$ interacting bosons, a splitting into an $N$-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that the splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

cond-mat.quant-gas↗

arXiv2017

Spectral analysis of molecular resonances in erbium isotopes: Are they close to semi-Poisson?

We perform a thorough analysis of the spectral statistics of experimental molecular resonances, of bosonic erbium $^{166}$Er and $^{168}$Er isotopes, produced as a function of magnetic field($B$) by Frisch et al. [Nature 507, (2014) 475], utilizing some recently derived surmises which interpolate between Poisson and GOE and without unfolding. Supplementing this with an analysis using unfolded spectrum, it is shown that the resonances are close to semi-Poisson distribution. There is an earlier claim of missing resonances by Molina et al. [Phys. Rev. E 92, (2015) 042906]. These two interpretations can be tested by more precise measurements in future experiments.

cond-mat.stat-mech↗

arXiv2017

Structural and quantum properties of van der Waals cluster near the unitary regime

We study the structural and several quantum properties of three-dimensional bosonic cluster interacting through van der Waals potential at large scattering length. We use Faddeev-type decomposition of the many-body wave function which includes all possible two-body correlations. At large scattering length, we observe spatially extended states which exhibit the exponential dependence on the state number. The cluster ground state energy shows universal nature at large negative scattering length. We also find the existence of generalized Tjon lines for $N$- body clusters. Signature of universal behaviour of weakly bound clusters can be observed in experiments of ultracold Bose gases. We also study the spectral statistics of the system. We calculate both the short-range fluctuation and long-range.correlation and observe semi-Poisson distribution which interpolates the Gaussian Orthogonal Ensemble (GOE) and Poisson statistics of random matrix theory. It indicates that the van der Waal cluster near the unitary becomes highly complex and correlated. However additional study of $P(r)$ distribution (without unfolding of energy spectrum) reveals the possibility of chaos for larger cluster.

cond-mat.quant-gas↗

arXiv2016

Use of two-body correlated basis functions with van der Waals interaction to study the shape-independent approximation for a large number of trapped interacting bosons

We study the ground state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small ($\sim 3$) to very large ($\sim 10^7$) particle numbers. We use the correlated two-body basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground state energy and the one-body density for different values of the van der Waals parameter $C_{6}$. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the Diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

cond-mat.quant-gas↗

arXiv2004

Triatomic Molecular Systems and Three-body forces: The Ar_3 case

We performed bound state calculations to obtain the first few vibrational states for the Ar_3 molecular system. The equations used are of Faddeev-type and are solved directly as three-dimensional equations in configuration space, i.e. without resorting to an explicit partial wave decomposition. In addition to realistic pairwise interactions, we employ long range three-body forces. Our results are in good agreement with those obtained by other methods based on partial wave expansion and show a significant contribution of the three-body forces (>10%) to the binding energy and thus their inclusion is, in general, warranted in studying similar triatomic systems.

physics.atm-clus↗