arXiv subjects

Pragya Shukla

Publications and source records attributed to Pragya Shukla.

At least 37 records · Page 2Linked to original sources

arXiv2018

Disorder perturbed Flat Bands II: a search for criticality

We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing disorder, insensitive to disorder strength, in weak disorder limit; the spectral statistics at the critical point corresponds to a critical Brownian ensemble, a non-equilibrium universality class of random matrix ensembles, intermediate to Poisson and Gaussian orthogonal ensemble. With increasing disorder, the statistics again approaches Poisson limit indicating a localization -> extended -> localization transition of the wave-dynamics. Our analysis also reveals a hidden connection of weakly disordered flat bands to a wide-range of other complex systems including standard Anderson Hamiltonian.

cond-mat.stat-mech↗

arXiv2018

Statistical analysis of chiral structured ensembles: role of matrix constraints

We numerically analyze the statistical properties of complex system with conditions subjecting the matrix elements to a set of specific constraints besides symmetry, resulting in various structures in their matrix representation. Our results reveal an important trend: while the spectral statistics is strongly sensitive to the number of independent matrix elements, the eigenfunction statistics seems to be affected only by their relative strengths. This is contrary to previously held belief of one to one relation between the statistics of the eigenfunctions and eigenvalues (e.g. associating Poisson statistics to the localized eigenfunctions and Wigner-Dyson statistics to delocalized ones).

cond-mat.dis-nn↗

arXiv2018

Disorder perturbed Flat Bands I: Level density and Inverse Participation Ratio

We consider the effect of disorder on the tight-binding Hamiltonians with a flat band and derive a common mathematical formulation of the average density of states and inverse participation ratio applicable for a wide range of them. The system information in the formulation appears through a single parameter which plays an important role in search of the critical points for disorder driven transitions in flat bands [1]. In weak disorder regime, the formulation indicates an insensitivity of the statistical measures to disorder strength, thus confirming the numerical results obtained by our as well as previous studies.

cond-mat.dis-nn↗

arXiv2017

Eigenfunction statistics of Laguerre Brownian ensemble

We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Laguerre type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the pertubation parameter along with a drift due to level-repulsion. The energy-dependences of the fluctuations for the Laguerre case is in general different from the Gaussian case but locally they can be expressed in a same mathematical form.

cond-mat.stat-mech↗

arXiv2017

Criticality in Brownian ensembles

The local statistical fluctuations in Brownian ensembles, the intermediate state of perturbation of one classical ensemble by another one, are system-size invariant if the perturbation parameter has the same size-dependence as that of the ensemble averaged local level density. The sensitivity to local spectral density however makes the measures for the critical statistics non-stationary along the spectrum.

cond-mat.stat-mech↗

arXiv2017

Extended states with Poisson spectral statistics

Contrary to prevailing notion we find that the spectrum associated with the extended states in a complex system may belong to the Poisson universality class if the system is subjected to a specific set of constraints. Our results are based on an exact theoretical as well as numerical analysis of column constrained chiral ensembles with circulant off-diagonal blocks and are relevant for a complete understanding of the eigenfunction localization and related physical properties.

cond-mat.stat-mech↗

arXiv2015

Anderson transitions in disordered two-dimensional lattices

We numerically analyze the energy level statistics of the Anderson model with Gaussian site disorder and constant hopping. The model is realized on different two-dimensional lattices, namely, the honeycomb, the kagomé, the square, and the triangular lattice. By calculating the well-known statistical measures viz., nearest neighbor spacing distribution, number variance, the partition number and the dc electrical conductivity from Kubo-Greenwood formula, we show that there is clearly a delocalization to localization transition with increasing disorder. Though the statistics in different lattice systems differs when compared with respect to the change in the disorder strength only, we find there exists a single complexity parameter, a function of the disorder strength, coordination number, localization length, and the local mean level spacing, in terms of which the statistics of the fluctuations matches for all lattice systems at least when the Fermi energy is selected from the bulk of the energy levels.

cond-mat.mes-hall↗

arXiv2015

Random matrix ensembles with column/row constraints: part I

We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new correlations among eigenfunctions, hinders their complete delocalization and affects the eigenvalues too. Our results reveal a rich behavior hidden beneath the spectral statistics and also indicate the presence of a new universality class analogous to that of a Brownian ensemble appearing between Poisson and Gaussian orthogonal ensemble.

cond-mat.stat-mech↗

arXiv2015

Random matrix ensembles with column/row constraints. II

We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath the spectral statistics and also confirm our analytical predictions, presented in part I of this paper, about the analogy of their spectral fluctuations with those of a critical Brownian ensemble which appears between Poisson and Gaussian orthogonal ensemble.

cond-mat.stat-mech↗

arXiv2010

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows however that the evolution of the statistical measures e.g Gibbs free energy, heat capacity, entropy is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.

cond-mat.soft↗

arXiv2010

Anderson localisation in tight-binding models with flat bands

We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands that are dispersionless throughout the Brillouin zone. We show that states derived from these flat bands are generically critical in the presence of weak disorder, being neither Anderson localised nor spatially extended. Further, we establish a mapping between this localisation problem and the one of resonances in random impedance networks, which previous work has suggested are also critical. Our conclusions are illustrated using numerical results for a two-dimensional lattice, known as the square lattice with crossings or the planar pyrochlore lattice.

cond-mat.dis-nn↗

arXiv2008

Criticality in the Quantum Kicked Rotor with a Smooth Potential

We investigate the possibility of an Anderson type transition in the quantum kicked rotor with a smooth potential due to dynamical localization of the wavefunctions. Our results show the typical characteristics of a critical behavior i.e multifractal eigenfunctions and a scale-invariant level-statistics at a critical kicking strength which classically corresponds to a mixed regime. This indicates the existence of a localization to delocalization transition in the quantum kicked rotor. Our study also reveals the possibility of other type of transitions in the quantum kicked rotor, with a kicking strength well within strongly chaotic regime. These transitions, driven by the breaking of exact symmetries e.g. time-reversal and parity, are similar to weak-localization transitions in disordered metals.

cond-mat.dis-nn↗

arXiv2008

Towards a common thread in Complexity: an accuracy-based approach

The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external potential due to existing system conditions. The fluctuation of accuracy due to varying system-conditions leads to a diffusion of the matrix elements. We show that, for the single well potentials, the diffusion can be described by a common mathematical formulation where system information enters through a single parameter. This further leads to a characterization of physical properties by an infinite range of single parametric universality classes.

cond-mat.stat-mech↗

arXiv2007

Eigenfunction Statistics of Complex Systems: A Common Mathematical Formulation

We derive a common mathematical formulation for the eigenfunction statistics of Hermitian operators, represented by a multi-parametric probability density. The system-information in the formulation enters through two parameters only, namely, system size and the complexity parameter, a function of all system parameter including size. The behavior is contrary to the eigenvalue statistics which is sensitive to complexity parameter only and shows a single parametric scaling. The existence of a mathematical formulation, of both eigenfunctions and eigenvalues, common to a wide range of complex systems indicates the possibility of a similar formulation for many physical properties. This also suggests the possibility to classify them in various universality classes defined by complexity parameter.

cond-mat.stat-mech↗

arXiv2005

Level-statistics in Disordered Systems: A single parametric scaling and Connection to Brownian Ensembles

We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles \cite{dy}. The latter appear during a Poisson $\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling of the level-correlations in disordered systems as well as a tool to obtain them at the critical point for a wide range of disorders.

cond-mat.stat-mech↗

arXiv2005

Multi-Channel Transport in Disordered Medium under Generic Scattering Conditions

Our study of the evolution of transmission eigenvalues, due to changes in various physical parameters in a disordered region of arbitrary dimensions, results in a generalization of the celebrated DMPK equation. The evolution is shown to be governed by a single complexity parameter which implies a deep level of universality of transport phenomena through a wide range of disordered regions. We also find that the interaction among eigenvalues is of many body type that has important consequences for the statistical behavior of transport properties.

cond-mat.mes-hall↗

arXiv2005

Random Matrices with Correlated Elements: A Model for Disorder with Interactions

The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations of these matrices can be described by the single parametric Brownian ensembles. The analogy helps us to reveal many important features of the level-statistics in interacting systems e.g. a critical point behavior different from that of non-interacting systems, the possibility of extended states even in one dimension and a universal formulation of level correlations.

cond-mat.dis-nn↗

arXiv2002

Level-Statistics of Disordered Systems: a Single Parametric Formulation

We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders behaves in a way similar to that of the single parametric Brownian ensembles. The latter appear during aPoisson $\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling behaviour in disordered systems as well as a tool to obtain the level-correlations at the critical point for a wide range of disorders.

cond-mat.dis-nn↗