arXiv subjects

Indubala I Satija

Publications and source records attributed to Indubala I Satija.

22 records · Page 2Linked to original sources

arXiv2005

Gauge Invariant Geometry of Closed Space Curves: Applications to Boundary Curves of Mobius-type Strips

We derive gauge-invariant expressions for the twist $Tw$ and the linking number $Lk$ of a closed space curve, that are independent of the frame used to describe the curve, and hence characterize the intrinsic geometry of the curve. We are thus led to a {\it frame-independent} version of the Călugăreanu-White-Fuller theorem $Lk =Tw + Wr$ for a curve, where $Wr$ is the writhe of the curve. The gauge-invariant twist and writhe are related to two types of geometric phases associated with the curve. As an application, we study the geometry of the boundary curves of closed twisted strips. Interestingly, the Möbius strip geometry is singled out by a characteristic maximum that appears in the geometric phases, at a certain critical width of the strip.

math-ph↗

arXiv2001

$\hbar \to 0$ in Kicked Harper Model: Reassurances and Surprises

We investigate classical-quantum correspondence for kicked Harper model for extremely small values of the Planck constant $\hbar$. In the asymmetric case a pure quantum state shows clear signature of classical diffusive as well as super diffusive transitions asymptotically independent of $\hbar$. However, for the symmetric case, the $\hbar$ independent behavior occurs only for renormalized parameter $\bar{K}=K/(2\hbar)$ with intriguing features such as a sharp transition from integrable to non-integrable transport at $\bar{K}=π/2$, a series of transitions at multiples of $π$ and periodicity of the transmission probability. These results add new puzzles to the frontiers of quantum chaos.

nlin.CD↗

arXiv2001

Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper

Dimer decimation scheme is introduced in order to study the kicked quantum systems exhibiting localization transition. The tight-binding representation of the model is mapped to a vectorized dimer where an asymptotic dissociation of the dimer is shown to correspond to the vanishing of the transmission coefficient thru the system. The method unveils an intricate nesting of extended and localized phases in two-dimensional parameter space. In addition to computing transport characteristics with extremely high precision, the renormalization tools also provide a new method to compute quasienergy spectrum.

nlin.CD↗

arXiv2000

Localization Characteristics of Relativistic vs Nonrelativistic Fermions on a Lattice

Relativistic fermions on a lattice are shown to correspond to the $fluctuations$ in the localized nonrelativistic fermions. Therefore, in contrast to nonrelativistic case, the relativistic fermions are critical with universal exponents described by the strong coupling limit of the nonrelativistic problem. The fluctuations also describe $anisotropic$ spin chain at the onset to {\it long range magnetic order} whose universality class is the Ising model. This generalizes the universality in spin models to include multifractal exponents. Finally, analogous to the nonrelativistic case, the relativistic fermions may exhibit ballistic character due to correlations.

cond-mat.dis-nn↗