arXiv subjects

Indubala I. Satija

Publications and source records attributed to Indubala I. Satija.

36 records · Page 2Linked to original sources

arXiv2006

Quantum coherence of Hard-Core-Bosons and Fermions : Extended, Glassy and Mott Phases

We use Hanbury-Brown-Twiss interferometry (HBTI) to study various quantum phases of hard core bosons (HCBs) and ideal fermions confined in a one-dimensional quasi-periodic (QP) potential. For HCBs, the QP potential induces a cascade of Mott-like band-insulator phases in the extended regime, in addition to the Mott insulator, Bose glass, and superfluid phases. At critical filling factors, the appearance of these insulating phases is heralded by a peak to dip transition in the interferogram, which reflects the fermionic aspect of HCBs. On the other hand, ideal fermions in the extended phase display various complexities of incommensurate structures such as devil's staircases and Arnold tongues. In the localized phase, the HCB and the fermion correlations are identical except for the sign of the peaks. Finally, we demonstrate that HBTI provides an effective method to distinguish Mott and glassy phases.

cond-mat.other↗

arXiv2004

Geometric Phase and Classical-Quantum Correspondence

We study the geometric phase factors underlying the classical and the corresponding quantum dynamics of a driven nonlinear oscillator exhibiting chaotic dynamics. For the classical problem, we compute the geometric phase factors associated with the phase space trajectories using Frenet-Serret formulation. For the corresponding quantum problem, the geometric phase associated with the time evolution of the wave function is computed. Our studies suggest that the classical geometric phase may be related to the the difference in the quantum geometric phases between two neighboring eigenstates.

nlin.CD↗

arXiv2001

Localization, Dirac Fermions and Onsager Universality

Disordered systems exhibiting exponential localization are mapped to anisotropic spin chains with localization length being related to the anisotropy of the spin model. This relates localization phenomenon in fermions to the rotational symmetry breaking in the critical spin chains. One of the intriguing consequence is that the statement of Onsager universality in spin chains implies universality of the localized fermions where the fluctuations in localized wave functions are universal. We further show that the fluctuations about localized nonrelativistic fermions describe relativistic fermions. This provides a new approach to understand the absence of localization in disordered Dirac fermions. We investigate how disorder affects well known universality of the spin chains by examining the multifractal exponents. Finally, we examine the effects of correlations on the localization characteristics of relativistic fermions.

cond-mat.dis-nn↗

arXiv2000

Localization Transition in Incommensurate non-Hermitian Systems

A class of one-dimensional lattice models with incommensurate complex potential $V(θ)=2[λ_r cos(θ)+i λ_i sin(θ)]$ is found to exhibit localization transition at $|λ_r|+|λ_i|=1$. This transition from extended to localized states manifests in the behavior of the complex eigenspectum. In the extended phase, states with real eigenenergies have finite measure and this measure goes to zero in the localized phase. Furthermore, all extended states exhibit real spectrum provided $|λ_r| \ge |λ_i|$. Another novel feature of the system is the fact that the imaginary part of the spectrum is sensitive to the boundary conditions {\it only at the onset to localization}.

cond-mat.dis-nn↗

arXiv1999

Quantized Orbits and Resonant Transport

A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples of $π/2$. Commensurability relations between the orbit frequencies are shown to correlate with the emergence of accelerator modes in the classical phase space of the original kicked problem. The signature of this resonant transport is seen in both classical and quantum behavior. An important feature of our analysis is the emergence of a natural scaling relating classical and quantum couplings which is necessary for establishing correspondence.

chao-dyn↗

arXiv1999

Collision and symmetry-breaking in the transition to strange nonchaotic attractors

Strange nonchaotic attractors (SNAs) can be created due to the collision of an invariant curve with itself. This novel ``homoclinic'' transition to SNAs occurs in quasiperiodically driven maps which derive from the discrete Schrödinger equation for a particle in a quasiperiodic potential. In the classical dynamics, there is a transition from torus attractors to SNAs, which, in the quantum system is manifest as the localization transition. This equivalence provides new insights into a variety of properties of SNAs, including its fractal measure. Further, there is a {\it symmetry breaking} associated with the creation of SNAs which rigorously shows that the Lyapunov exponent is nonpositive. By considering other related driven iterative mappings, we show that these characteristics associated with the the appearance of SNA are robust and occur in a large class of systems.

chao-dyn↗

arXiv1999

Breakup of a Dimer: a New Approach to Localization Transition

Within the framework of tight binding models, aperiodic systems are mapped to a renormalized lattice with a dimer defect. In models exhibiting metal-insulator transition, the dimer acts like a resonant cavity and explains the existence of the ballistic transport in the system. The localization in the model can be attributed to the vanishing of the coupling between the two sites of the dimer. Our approach unifies Anderson transition and resonance transition and provides a new formulation to understand localization and its absence in aperiodic systems.

cond-mat↗

arXiv1999

Dimer-Type Correlations and Band Crossings in Fibonacci Lattices

Fibonacci system with both diagonal and off-diagonal disorder is mapped to a model with dimer type 'defects'. The model exhibit resonance transition corresponding to zero reflectance condition resulting in extended states in the system. These Bloch-type states reside on the line of inversion symetry of the energy spectrum and include states at the band crossings. The resonant states at the band crossings are related to the harmonics of the sine wave and have transmission coefficient equal to unity in quasiperiodic limit. This is in contrast to other resonant states where the transmission coeffiecient oscillates. An exact renormalization scheme confirms the fact that all resonant states are Bloch type waves as they are described by trivial attractors of the renormalization flow.

cond-mat↗

arXiv1999

Localization and Fluctuations in Quantum Kicked Rotors

We address the issue of fluctuations, about an exponential lineshape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical localization. An exact renormalization scheme establishes the fractal character of the fluctuations and provides a new method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuations are independent of the kicking parameter $k$ and exhibit self-similarity for certain values of the quasienergy. For given $k$, the asymptotic localization length is a good characteristic of the localized lineshapes for all quasienergies. This is in stark contrast to the quadratic rotor, where the fluctuations depend upon the strength of the kicking and exhibit local "resonances". These resonances result in strong deviations of the localization length from the asymptotic value. The consequences are particularly pronounced when considering the time evolution of a packet made up of several quasienergy states.

chao-dyn↗

arXiv1998

Phase Diagram of strongly correlated one-dimensional fermions in incommensurate potentials

We study the interplay between strong correlations and incommensurability on fermions using mean field as well as exact many-body Lanczos diagonalization techniques. In a two-dimensional parameter space, mean field phase diagram of infinite system shows a critical phase with multifractal characteristics sandwiched between a Bloch-type extended and a localized phase. Exact numerical computation on finite size systems of the Kohn charge stiffness Dc, characterizing transport properties, and the charge exponent Krho, characterizing the superconducting pairing fluctuations, shows the existence of a phase with superconducting correlations. This phase may be characterized by a power law scaling of the charge stiffness constant in contrast to the Anderson localized phase where Dc scales exponentially with the size of the system. We argue that this intermediate phase may be a dressed up analog of the critical phase of the noninteracting fermions in an incommensurate potential.

cond-mat.str-el↗

arXiv1998

Hidden Dimer in the Frenkel-Kontorova model

The incommensurability of the supercritical Frenkel-Kontorova model is decomposed into a family of dimer type "defects" by appropriate decimations. Interestingly, this hidden dimer results in Bloch-wave type excitations of the renormalized chain which appear in the disguised form of multi-step phonon modes for the original system. We call these intriguing excitations stepon modes and conjecture that they play a key role in determining the localization boundary in systems exhibiting Anderson localization.

cond-mat.dis-nn↗

arXiv1996

Critical and Supercritical Dynamics of Quasiperiodic Systems

The almost periodic eigenvalue problem described by the Harper equation is connected to other classes of quasiperiodic behaviour: the dissipative dynamics on critical invariant tori and quasiperiodically driven maps. Firstly, the strong coupling limit of the supercritical Harper equation and the strong dissipation limit of the critical standard map play equivalent role in the renormalization analysis of the self-similar fluctuations of localized eigenfunctions and the universal slope of the projected map on the invariant circle. Secondly, we use a simple transformation to relate the Harper equation to a quasiperiodically forced one-dimensional map. In this case, the localized eigenstates of the supercritical Harper equation correspond to strange but nonchaotic attractors of the driven map. Furthermore, the existence of localization in the eigenvalue problem is associated with the appearance of homoclinic points in the corresponding map.

chao-dyn↗

arXiv1996

``Critical'' phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams

The phonon modes of the Frenkel-Kontorova model are studied both at the pinning transition as well as in the pinned (cantorus) phase. We focus on the minimal frequency of the phonon spectrum and the corresponding generalized eigenfunction. Using an exact decimation scheme, the eigenfunctions are shown to have nontrivial scaling properties not only at the pinning transition point but also in the cantorus regime. Therefore the phonons defy localization and remain critical even where the associated area-preserving map has a positive Lyapunov exponent. In this region, the critical scaling properties vary continuously and are described by a line of renormalization limit cycles. Interesting renormalization bifurcation diagrams are obtained by monitoring the cycles as the parameters of the system are varied from an integrable case to the anti-integrable limit. Both of these limits are described by a trivial decimation fixed point. Very surprisingly we find additional special parameter values in the cantorus regime where the renormalization limit cycle degenerates into the above trivial fixed point. At these ``degeneracy points'' the phonon hull is represented by an infinite series of step functions. This novel behavior persists in the extended version of the model containing two harmonics. Additional richnesses of this extended model are the one to two-hole transition line, characterized by a divergence in the renormalization cycles, nonexponentially localized phonons, and the preservation of critical behavior all the way upto the anti-integrable limit.

chao-dyn↗

arXiv1995

Reentrant Phase Diagram of Two-Dimensional Electron Gas

We study the phase diagram of an electron on a square lattice in a transverse magnetic field. Using a renormalization scheme, we show that the inequality of the two next-nearest neighbor couplings destroys the fat critical regime above the bicritical line and replaces it with another reentrant extended phase. Furthermore, the universal strange attractor describing self-similar fluctuations of the localized phase is replaced by a new fixed point. The reentrant extended phase and the new fixed point of the localized phase belong to the universality class of an anisotropic triangular lattice.

cond-mat↗

arXiv1995

Bloch Electron on a Triangular Lattice and Quantum Ising Model in a Transverse Field

The tight binding model for an electron on an anisotropic triangular lattice in a uniform magnetic field is studied using a decimation scheme. The model exhibits a transition from critical to localized phase and the phase diagram is described in terms of three nontrivial renormalization fixed points for the band edges. These subcritical, critical, and supercritical universality classes also describe the corresponding states of the quantum Ising chain in a modulating transverse field. The only exception is the conformally invariant point of the Ising model which has no analog in the electron problem.

cond-mat↗

arXiv1995

Self-Similarity and Localization

The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is characterized by a single strong coupling fixed point of the renormalization equations. This fixed point also describes the generalized Harper model with next nearest neighbor interaction below a certain threshold. Above the threshold, the fluctuations in the generalized Harper model are described by a strange invariant set of the renormalization equations.

cond-mat↗

arXiv1995

Conformal, Subconformal and Spectral Universality in Incommensurate Spin Chains

A renormalization scheme is developed to study an anisotropic quantum XY spin chain in a quasiperiodic transverse field. The critical phase of the quasi-particle excitations of the model with fractal wave functions exists in a finite parameter interval and is sandwiched between the extended and localized phases. The scaling properties of the critical phase fall into four distinct universality classes referred as spectral, subconformal, conformal and Harper. The spectral and conformal classes respectively describe the onsets of extended to critical and critical to localized transitions while the subconformal class describes the part of the phase diagram sandwiched between the conformal and spectral transitions. The Harper universality class describes the isotropic limit of the XY model. A decimation scheme is developed to compute the infinite sets of universal scaling ratios characterizing the wave functions in the four universality classes. The renormalization flow equations exhibit a limit cycle at the band center and at the band edges providing a new method for determining these energies with extremely high precision.

cond-mat↗

arXiv1995

Decimation Studies of Bloch Electrons in a Magnetic Field: Higher Order Limit Cycles Underlying the Phase Diagram

A decimation method is applied to the tight binding model describing the two dimensional electron gas with next nearest neighbor interaction in the presence of an inverse golden mean magnetic flux. The critical phase with fractal spectrum and wave function exists in a finite window in two-dimensional parameter space. There are special points on the boundaries as well as inside the critical phase where the renormalization flow exhibits higher order limit cycles. Our numerical results suggest that most of the critical phase is characterized by a strange attractor of the renormalization equations.

cond-mat↗