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Siddhartha Sen

Publications and source records attributed to Siddhartha Sen.

At least 55 records · Page 3Linked to original sources
arXiv2014

Friedel sum rule in the presence of topological defects for graphene

The Friedel sum rule is extended to deal with topological defects for the case of a graphene cone in the presence of an external Coulomb charge. The dependence in the way the number of states change due to both the topological defect as well as the Coulomb charge are studied. Our analysis addresses both the cases of a subcritical as well as a supercritical value of the Coulomb charge. We also discuss the experimental implications of introducing a self-adjoint extension of the system Hamiltonian. We argue that the boundary conditions following from the self-adjoint extension encode the effect of short range interactions present in the system.

cond-mat.mes-hall↗
arXiv2014

A Back-to-Basics Empirical Study of Priority Queues

The theory community has proposed several new heap variants in the recent past which have remained largely untested experimentally. We take the field back to the drawing board, with straightforward implementations of both classic and novel structures using only standard, well-known optimizations. We study the behavior of each structure on a variety of inputs, including artificial workloads, workloads generated by running algorithms on real map data, and workloads from a discrete event simulator used in recent systems networking research. We provide observations about which characteristics are most correlated to performance. For example, we find that the L1 cache miss rate appears to be strongly correlated with wallclock time. We also provide observations about how the input sequence affects the relative performance of the different heap variants. For example, we show (both theoretically and in practice) that certain random insertion-deletion sequences are degenerate and can lead to misleading results. Overall, our findings suggest that while the conventional wisdom holds in some cases, it is sorely mistaken in others.

cs.DS↗
arXiv2013

Scale invariance and superfluid turbulence

We construct a Schroedinger field theory invariant under local spatial scaling. It is shown to provide an effective theory of superfluid turbulence by deriving, analytically, the observed Kolmogorov 5/3 law and to lead to a Biot-Savart interaction between the observed filament excitations of the system as well.

cond-mat.other↗
arXiv2012

Effect of topological defects and Coulomb charge on the low energy quantum dynamics of gapped graphene

We study the combined effect of a conical topological defect and a Coulomb charge impurity on the dynamics of Dirac fermions in gapped graphene. Beyond a certain strength of the Coulomb charge, quantum instability sets in, which demarcates the boundary between sub and supercritical values of the charge. In the subcritical regime, for certain values of the system parameters, the allowed boundary conditions in gapped graphene cone can be classified in terms of a single real parameter. We show that the observables such as local density of states, scattering phase shifts and the bound state spectra are sensitive to the value of this real parameter, which is interesting from an empirical point of view. For a supercritical Coulomb charge, we analyze the system with a regularized potential as well as with a zigzag boundary condition and find the effect of the sample topology on the observable features of the system.

hep-th↗
arXiv2012

An Algebraic Geometry Method for Calculating DOS for 2D tight binding models

An algebraic geometry method is used to calculate the moments of the electron density of states as a function of the energy for lattices in the tight binding approximation. Interpreting the moments as the Mellin transform of the density allows writing down a formula for the density as an inverse Mellin transform. The method is illustrated by working out the density function for the two-dimensional square and honeycomb lattices.

cond-mat.other↗
arXiv2011

Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

We present two on-line algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$ time. For sparse graphs ($m/n = O(1)$), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural {\em locality} property. Our second algorithm handles an arbitrary sequence of arc additions in $O(n^{5/2})$ time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take $Ω(n^2 2^{\sqrt{2\lg n}})$ time by relating its performance to a generalization of the $k$-levels problem of combinatorial geometry. A completely different algorithm running in $Θ(n^2 \log n)$ time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.

cs.DS↗
arXiv2010

Effect of topology on the critical charge in graphene

We show that the critical charge for the Dirac excitations in gapless graphene depends on the spatial topology of the sample. In particular, for graphene cones, the effective value of the critical charge can tend towards zero for a suitable angle of the conical sample. We discuss the nature of the scattering phase shifts, quasi-bound state energies and local density of states for a gapless graphene cone and determine the dependence of these physical quantities on the sample topology.

cond-mat.mes-hall↗
arXiv2010

Geometric Finiteness, Holography and Quasinormal Modes for the Warped AdS_3 Black Hole

We show that there exists a precise kinematical notion of holography for the Euclidean warped $AdS_3$ black hole. This follows from the fact that the Euclidean warped $AdS_3$ black hole spacetime is a geometrically finite hyperbolic manifold. For such manifolds a theorem of Sullivan provides a one-to-one correspondence between the hyperbolic structure in the bulk and the conformal structure of its boundary. Using this theorem we obtain the holographic quasinormal modes for the warped $AdS_3$ black hole.

hep-th↗
arXiv2010

Turbulent flow in graphene

We demonstrate the possibility of a turbulent flow of electrons in graphene in the hydrodynamic region, by calculating the corresponding turbulent probability density function. This is used to calculate the contribution of the turbulent flow to the conductivity within a quantum Boltzmann approach. The dependence of the conductivity on the system parameters arising from the turbulent flow is very different from that due to scattering.

cond-mat.mes-hall↗
arXiv2010

The Central Charge of the Warped AdS^3 Black Hole

The AdS/CFT conjecture offers the possibility of a quantum description for a black hole in terms of a CFT. This has led to the study of general AdS^3 type black holes with a view to constructing an explicit toy quantum black hole model. Such a CFT description would be characterized by its central charge and the dimensions of its primary fields. Recently the expression for the central charges (C_L, C_R) of the CFT dual to the warped AdS^3 have been determined using asymptotic symmetry arguments. The central charges depend, as expected, on the warping factor. We show that topological arguments, used by Witten to constrain central charges for the BTZ black hole, can be generalized to deal with the warped AdS^3 case. Topology constrains the warped factor to be rational numbers while quasinormal modes are conjectured to give the dimensions of primary fields. We find that in the limit when warping is large or when it takes special rational values the system tends to Witten's conjectured unique CFT's with central charges that are multiples of 24.

hep-th↗
arXiv2009

Effects of Quantum Vacuum Fluctuations of the Electric Field on DNA Condensation

By assuming that not only counter-ions but DNA molecules as well are thermally distributed according to a Boltzmann law, we propose a modified Poisson-Boltzmann equation at the classical level as starting point to compute the effects of quantum fluctuations of the electric field on the interaction among DNA-cation complexes. The latter are modeled here as infinite one-dimensional wires ($δ$-functions). Our goal is to single out such quantum-vacuum-driven interaction from the counterion-induced and water-related interactions. We obtain a universal, frustration-free Casimir-like (codimension 2) interaction that extensive numerical analysis show to be a good candidate to explain the formation and stability of DNA aggregates. Such Casimir energy is computed for a variety of configurations of up to 19 DNA strands in a hexagonal array. It is found to be strongly many-body.

q-bio.QM↗
arXiv2009

Scattering in graphene with impurities : A low energy effective theory

We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of the system parameters, the combined effect of the short range interactions due to the charge impurity can be modelled using a single real parameter appearing in the boundary conditions. The phase shifts and the scattering matrix depend explicitly on this parameter. We argue that this parameter for graphene can be fixed empirically, through measurements of observables that depend on the scattering data.

cond-mat.mes-hall↗
arXiv2009

Heaps Simplified

The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap implementations. From a consideration of dynamic single-elimination tournaments, we obtain the binomial queue, a classical heap implementation, in a simple and natural way. We give four equivalent ways of representing heaps arising from tournaments, and we obtain two new variants of binomial queues, a one-tree version and a one-pass version. We extend the one-pass version to support key decrease operations, obtaining the {\em rank-pairing heap}, or {\em rp-heap}. Rank-pairing heaps combine the performance guarantees of Fibonacci heaps with simplicity approaching that of pairing heaps. Like pairing heaps, rank-pairing heaps consist of trees of arbitrary structure, but these trees are combined by rank, not by list position, and rank changes, but not structural changes, cascade during key decrease operations.

cs.DS↗
arXiv2008

Bound States in Gapped Graphene with Impurities : Effective Low-Energy Description of Short-Range Interactions

We obtain a novel bound state spectrum of the low energy excitations near the Fermi points of graphene in the presence of a charge impurity. The effects of possible short range interactions induced by the impurity are modelled by suitable boundary conditions. The spectrum in the subcritical region of the effective Coulomb coupling is labelled by a parameter which characterizes the boundary conditions and determines the inequivalent quantizations of the system. In the supercritical region we obtain a renormalization group flow for the effective Coulomb coupling.

hep-th↗
arXiv2008

Scar-Driven Shape-Changes of Virus Capsids

We propose that certain patterns (scars) -- theoretically and numerically predicted to be formed by electrons arranged on a sphere to minimize the repulsive Coulomb potential (the Thomson problem) and experimentally found in spherical crystals formed by self-assembled polystyrene beads (an instance of the {\it generalized} Thomson problem) -- could be relevant to extend the classic Caspar and Klug construction for icosahedrally-shaped virus capsids. The main idea is that scars could be produced on the capsid at an intermediate stage of its evolution and the release of the bending energy present in scars into stretching energy could allow for shape-changes. The conjecture can be tested in experiments and/or in numerical simulations.

q-bio.QM↗
arXiv2008

Do quantum effects hold together DNA condensates?

The classical electrostatic interaction between DNA molecules in water in the presence of counterions is reconsidered and we propose it is governed by a modified Poisson-Boltzmann equation. Quantum fluctuations are then studied and shown to lead to a vacuum interaction that is numerically computed for several configurations of many DNA strands and found to be strongly many-body. This Casimir vacuum interaction can be the ``glue'' holding together DNA molecules into aggregates.

q-bio.QM↗
arXiv2008

Bound States in Graphene

We present a quantum analysis of the massless excitations in graphene with a charge impurity. When the effective charge exceeds a certain critical value, the spectrum is quantized and is unbounded from below. The corresponding eigenstates are square-integrable at infinity and have a rapidly oscillatory behaviour in the short distance, which can be interpreted as a fall to the centre. Using a cutoff regularization, we show that the effective Coulomb interaction strength is driven to its critical value under the renormalization group flow. In the subcritical region, we find bound states with imaginary values of the energy for certain range of the system parameters. The physical significance of these bound states with imaginary eigenvalues is discussed.

cond-mat.mes-hall↗