arXiv subjects

R. Ganesh

Publications and source records attributed to R. Ganesh.

At least 19 recordsLinked to original sources

arXiv2026

Self-excited oscillations in multi-degree-of-freedom systems subjected to discontinuous forcing

This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and slow-flow phase-plane analysis, analytical expressions are derived for the amplitudes and stability boundaries of limit cycles in a two-degree-of-freedom system. The analysis demonstrates that stable limit cycles may exist in all natural modes, with the steady-state response governed by initial conditions in regimes of multistability. A central contribution of this work is the identification and analytical characterization of the stability-axis-flipping (SAF) bifurcation, which serves as the governing mechanism for the exchange of stability between modes. The framework is then systematically extended to systems with higher degrees of freedom, confirming that the SAF bifurcation remains a universal feature, even under varying feedback configurations. The steady-state dynamics, summarized through stability maps and validated by numerical simulations, delineate the existence and stability regions of modal limit cycles as functions of key system parameters. These results provide efficient criteria for guiding optimization studies to mitigate or generate limit cycles at targeted frequencies in flexible mechanical structures.

nlin.CD↗

arXiv2026

Transport in close-packed solids with stacking defects

Lithium and sodium are the only solids that are known to lose crystalline order upon cooling. The seemingly-disordered low-temperature phase shows signatures of various close-packed structures. The lack of order has been attributed to a hidden gauge symmetry that arises when electrons from one layer can hop to a neighbouring layer but not further. It makes all close-packed structures nearly degenerate and leads to ``structural frustration''. In this article, we examine whether this symmetry is reflected in transport signatures. Taking advantage of in-plane translational periodicity, we map the bulk Bloch Hamiltonian to an effective one-dimensional chain, with stacking disorder mapping to random phases of the hopping amplitudes. We derive an explicit analytic form for the Green's function of electrons and use it to calculate conductance of a bulk crystal. When hopping in the effective one-dimensional chain is restricted to nearest neighbours, conductance is completely insensitive to phase disorder, which indicates that all close-packed structures exhibit the same conductance. We show that the leading correction that can differentiate between close-packed structures arises from hopping to the next-nearest-neighbour layer, equivalent to second-neighbour hopping in the chain model. This process appears when a pair of next-neighbour layers are aligned in a certain way, e.g., at an hcp-like stacking fault within an fcc background. With this hopping included, conductance becomes sensitive to the precise arrangement of layers. When multiple stacking faults are present, the conductance decreases with increasing system size, as expected from Anderson localization. Our results are applicable to pressurized lithium and sodium, where conductance measurements can identify and characterize stacking faults.

cond-mat.mes-hall↗

arXiv2025

Exact Fractionalized Ground States in an Extended Spin-1 Kitaev Chain

Inspired by the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, we present exact solutions for a spin-1 chain with Kitaev-like couplings. We consider an expanded Kitaev model with bilinear and biquadratic terms. At an exactly solvable point, the Hamiltonian can be reexpressed as a sum of projection operators. Unlike the AKLT model where projectors act on total spin, we project onto components of spin along the bond direction. This leads to exponential ground state degeneracy, expressed in terms of fractionalized spin-$\frac{1}{2}$ objects. Each ground state can be expressed concisely as a matrix product state. We construct a phase diagram by varying the relative strength of bilinear and biquadratic terms. The fractionalized states provide a qualitative picture for the spin-1 Kitaev model, yielding approximate forms for the ground state and low-lying excitations.

cond-mat.str-el↗

arXiv2025

Spin-basis wavefunctions for the one-dimensional Kitaev model

Magnetic phases with quantum entanglement are often expressed in terms of parton wavefunctions. Relatively few examples are known where wavefunctions can be directly written down in the spin basis. In this article, we consider the spin-$S$ Kitaev model in one dimension. For $S=1/2$, its eigenstates can be written using a Jordan-Wigner fermionic representation. Here, we present ground state wavefunctions for any $S$ directly in the spin basis. The states we propose are valence bond arrangements, with bonds having singlet or triplet character for $S=1/2$. For $S>1/2$, we use bond-states that serve as analogues of singlets and triplets. We establish the validity of our wavefunctions using a perturbative approach starting from an anisotropic limit, with key features surviving to all orders in perturbation theory. For half-integer $S$ and periodic boundaries, we have exponential ground state degeneracy. The ground states are subject to a nonlocal constraint. They have `triplets' superposed on a background of singlets, but with the total number of triplets constrained to be even. For integer $S$, a unique ground state emerges, composed purely of `triplets'. Our spin-basis wavefunctions, while not exact, capture the dominant weight of the ground state(s). We obtain good agreement against exact diagonalization wavefunctions and Jordan-Wigner spectra.

cond-mat.str-el↗

arXiv2025

Structures of group-15 elemental solids from an effective boundary theory

We present an effective description for the crystal structures of pnictogen elemental solids. In these materials, each atom contains three valence electrons in $p$ orbitals. They are shared between neighbouring atoms to form valence bonds. We propose a trivalent network model on the simple cubic lattice. As a generalization of a dimer model, we impose a constraint that three dimers must touch every site. We argue that intra-orbital Coulomb repulsion prohibits the formation of two adjacent, parallel dimers. This leads to a tripod-like local configuration at every site. More importantly, it forces every line of the cubic lattice to have alternating dimers and blanks. There is no dynamics as dimers cannot be locally rearranged. A bulk-boundary mapping emerges whereby bonds in the interior are fully described by Ising variables on three bounding planes -- a simple example of holography that may be realized in real materials. To describe the energetics of bonding, we formulate a minimal model in terms of boundary Ising spins. Symmetries reduce the problem to that of three identical, independent, two-dimensional Ising models. An antiferromagnetic Ising-ground-state corresponds to the A7 structure seen in antimony and grey arsenic. An antiferromagnetic phase within a bilayer describes the structure of phosphorene. By stacking such bilayers, we obtain the A17 structure of black phosphorus. The stripe phase of the Ising models describes the cubic gauche structure of nitrogen. As a testable signature, we demonstrate that single impurities will induce long-ranged domain walls.

cond-mat.str-el↗

arXiv2025

Measuring dark state number in the Tavis-Cummings model

Quantum mechanics allows for light-matter setups that hold excitations without releasing them as light. Arising from destructive interference processes, they are best seen in a Tavis-Cummings-like setup where two-level atoms (or qubits) are placed within a lossy cavity. If the system is initialized with some qubits excited and some in the ground state, there is a non-zero probability that no photons will be emitted. This can be framed as a Stern-Gerlach measurement, with a detector to measure if one or more photons leave the cavity. If no photons are detected, the qubits collapse onto a dark state. This can be viewed as heralding of a dark state based on zero photon detection. Building upon this idea, we propose a protocol to measure the number of independent dark states. Moreover, we show that this quantity is robust to arbitrary levels of disorder in the qubit-photon coupling constants. We then discuss a phase transition where the number of dark states plays the role of an order parameter. This provides an exciting example of a phase transition that is completely insensitive to disorder.

quant-ph↗

arXiv2025

Trivalent network model for d$^3$ transition metal dichalcogenides in the 1T structure: Holography from local constraints

Dimer models are well known as prototypes for locally constrained physics. They describe systems in which every site on a lattice must be attached to one dimer. Loop models are an extension of this idea, with the constraint that two dimers must touch at each site. Here, we present a further generalization where every site must have three dimers attached -- a trivalent network model. As concrete physical realizations, we discuss d$^3$ transition metal dichalcogenides in the 1T structure -- materials with the structural formula MX$_2$ (M = Tc, Re) or AM$'$X$_2$ (A = Li or Na; M$'$ = Mo, W), where X is a chalcogen atom. These materials have a triangular layer of transition metal atoms, each with three valence electrons in $t_{2g}$ orbitals. Each atom forms valence bonds with three of its nearest neighbours. The geometry of the 1T structure imbues each bond with sharp orbital character. We argue that this enforces a ``bending constraint'' so that two dimers attached to the same site cannot be parallel. This leads to a highly structured space of configurations, with alternating bonds along each line of the underlying triangular lattice. There is no dynamics, as constraints forbid local rearrangements of dimers. We construct a phase diagram, identifying configurations that minimize potential energy. We find a rhombus-stripe phase that explains a distortion pattern seen across several materials. Remarkably, the local constraints in this model lead to a simple example of holography. The bonding configuration in the bulk is completely determined by the configuration at the boundary. We recast the model in terms of three Ising chains that are defined on the boundaries of a triangular cluster. As a testable prediction, we propose that a single impurity will generate long-ranged domain walls.

cond-mat.str-el↗

arXiv2025

Berry curvature-induced transport signature for altermagnetic order

Altermagnetism has been detected in several materials using spin-sensitive probes. These measurements require rather complex setups that make it challenging to track variations in altermagnetic order, e.g., to identify a temperature-tuned altermagnetic phase transition. We propose a simple transport measurement that can probe the order parameter for $d$-wave altermagnetism. We suggest magnetoconductivity anisotropy -- the difference between the two principal values of the magnetoconductivity tensor. This quantity can be easily measured as a function of temperature, without any spin-selective apparatus. It acquires a nonzero value in a $C_4K$ phase, where $C_4$ rotations and time reversal $K$ are not symmetries but their combination is. This effect can be traced to the modification of phase space density due to Berry curvature, which we demonstrate using semiclassical equations of motion for band electrons. As an illustration, we build a minimal tight-binding model with altermagnetic order that breaks $C_4$ and $K$ symmetries while preserving $C_4K$.

cond-mat.mes-hall↗

arXiv2024

Quantum loops in the 1T transition metal dichalcogenides

Loop arrangements and their quantum superpositions describe several interesting many-particle states. We propose that they also describe bonding in a class of transition metal dichalcogenides. We present an effective quantum loop model for monolayers with 1T structure and a d$^2$ valence electron configuration: materials of the form MX$_2$ (M = Mo, W and X=S, Se, Te) and AM$'$Y$_2$ (A = Li, Na; M$'$ = V, Nb and Y = O, S, Se). Their t$_{2g}$ orbitals exhibit strongly directional overlaps between neighbouring atoms, favouring the formation of valence bonds. A transition metal atom forms two valence bonds, each with one of its neighbours. When connected, these bonds form loops that cover the triangular lattice. We construct a minimal Rokhsar-Kivelson-like model with resonance processes that cut and reconnect loops that run in proximity. The resulting dynamics is more constrained than in traditional quantum dimer models, with a `bending' constraint that arises from orbital structure. In the resulting phase diagram, we find phases that resemble distorted phases seen in materials, viz., the 1T$'$ and trimerized phases. As a testable prediction, we propose that a single d$^1$ or d$^3$ impurity will terminate a loop and give rise to a long-ranged texture. For example, a Ti/Cr defect in LiVO$_2$ will produce one or more domain walls that propagate outward from the impurity. We discuss the possibility of a loop liquid phase that can emerge in these materials.

cond-mat.str-el↗

arXiv2024

Ice on curved surfaces: defect rings and differential local dynamics

Ice systems are prototypes of locally constrained dynamics. This is exemplified in Coulomb-liquid phases where a large space of configurations is sampled, each satisfying local ice rules. Dynamics proceeds through `flipping' rings, i.e., through reversing arrows running along the edges of a polygon. We examine the role of defect rings in such phases, with square-ice as a testing ground. When placed on a curved surface, the underlying square lattice will form defects such as triangles or pentagons. We show that triangular defects are statistically more `flippable' than the background. In contrast, pentagons and larger polygons are less flippable. In fact, flippability decreases monotonically with ring size, as seen from a Pauling-like argument. As an explicit demonstration, we wrap the square ice model on a sphere. We start from an octahedron and perform repeated rectifications, producing a series of clusters with sphere-like geometry. They contain a fixed number of defect triangles in an otherwise square lattice. We numerically enumerate all ice-rule-satisfying configurations. Indeed, triangles are flippable in a larger fraction of configurations than quadrilaterals. The obtained flippabilities are in broad agreement with the Pauling-like estimates. As a minimal model for dynamics, we construct a Hamiltonian with quantum tunnelling terms that flip rings. The resulting ground state is a superposition of all ice configurations. The dominant contribution to its energy comes from localized resonance within triangles. Our results suggest local dynamics as a promising observable for experiments in spin ice and artificial ice systems. They also point to hierarchical dynamics in materials such as ice V that contain rings of multiple sizes.

cond-mat.stat-mech↗

arXiv2024

Metallic bonding in close packed structures: structural frustration from a hidden gauge symmetry

Based on its simple valence electron configuration, we may expect lithium to have straightforward physical properties that are easily explained. However, solid lithium, when cooled below 77 K, develops a complex structure that has been debated for decades. A close parallel is found in sodium below 36 K where the crystal structure still remains unresolved. In this letter, we explore a possible driving force behind this complexity. We begin with the observation that Li and Na form close-packed structures at low temperatures. We demonstrate a gauge symmetry that forces \textit{all} close-packed structures to have the same electronic energy and, in fact, the very same band structure. This symmetry requires two conditions: (a) bands must arise from $s$ orbitals, and (b) hoppings beyond second-nearest neighbours must be negligible. We argue that both can be reasonably invoked in Li and Na. When these conditions are satisfied, we have extensive degeneracy with the number of competing iso-energetic structures growing exponentially with linear system size. Weak effects, such as $p$-orbital admixture, long-range hopping and phonon zero-point energy, can break this symmetry. These can play a decisive role in `selecting' one particular ordered structure. This point of view may explain the occurrence of ordered structures in Li and Na under pressure. Our results suggest that martensitic transitions may also occur in heavier alkali metals such as potassium.

cond-mat.str-el↗

arXiv2024

Light-induced charge and spin Hall currents in materials with $C_4K$ symmetry

Berry curvature, a momentum space property, can manifest itself in current responses. The well-known anomalous Hall effect in time-reversal-breaking systems arises from a Berry curvature monopole. In time-reversal-invariant materials, a second-order Hall conductivity emerges from a Berry curvature dipole. Recently, it has been shown that a Berry curvature quadrupole induces a third-order ac Hall response in systems that break time reversal ($K$) and a fourfold rotational ($C_{4}$) symmetry, while remaining invariant under the combination of the two ($C_{4}K$). In this letter, we demonstrate that incident light can induce a $\rm dc$ Hall current in such systems, driven by the Berry curvature quadrupole. We consider a combination of a static $\rm dc$ electric field and an ac light-induced electric field. We calculate the current perpendicular to both the static electric field and the fourfold axis. Remarkably, the induced current is generically spin-polarized. A net charge current appears for light that is linearly or elliptically polarized, but not for circular polarization. In contrast, the spin current remains unchanged when the polarization of light is varied. This allows for rich possibilities such as generating a spin current by shining circularly polarized light on an altermagnetic material. We demonstrate this physics using a two-dimensional toy model for altermagnets.

cond-mat.mes-hall↗

arXiv2024

The high-density regime of dusty plasma: Coulomb plasma

It is shown that the dust density regimes in dusty plasma are characterized by two complementary screening processes, (a) the low dust density regime where the Debye screening is the dominant process and (b) the high dust density regime where the Coulomb screening is the dominant process. The Debye regime is characterized by a state where all dust particles carry an equal and constant charge. The high-density regime or the Coulomb plasma regime is characterized by (a) Coulomb screening where the dust charge depends on the spatial location and is screened by other dust particles in the vicinity by charge reduction, (b) quark like asymptotic freedom where dust particles, which on an average carry minimal electric charge (q tends to 0), are asymptotically free, (c) uniform dust charge density and plasma potential, (d) dust charge neutralization by a uniform background of hot ions. Thus, the Coulomb plasma is essentially a one-component plasma (OCP) with screening as opposed to electron plasma which is OCP without screening. Molecular dynamics (MD) simulations verify these properties. The MD simulations are performed, using a recently developed Hamiltonian formalism, to study the dynamics of Yukawa particles carrying variable electric charge. A hydrodynamic model for describing the collective properties of Coulomb plasma and its characteristic acoustic mode called the Coulomb acoustic wave is given.

physics.plasm-ph↗

arXiv2023

Localization of vibrational modes in high-entropy oxides

The recently-discovered high-entropy oxides offer a paradoxical combination of crystalline arrangement and high disorder. They differ qualitatively from established paradigms for disordered solids such as glasses and alloys. In these latter systems, it is well known that disorder induces localized vibrational excitations. In this article, we explore the possibility of disorder-induced localization in (MgCoCuNiZn)O, the prototypical high-entropy oxide with rock-salt structure. To describe phononic excitations, we model the interatomic potentials for the cation-oxygen interactions by fitting to the physical properties of the parent binary oxides. We validate our model against the experimentally determined crystal structure, bond lengths, and optical conductivity. The resulting phonon spectrum shows wave-like propagating modes at low energies and localized modes at high energies. Localization is reflected in signatures such as participation ratio and correlation amplitude. Finally, we explore the possibility of increased mass disorder in the oxygen sublattice. Admixing sulphur or tellurium atoms with oxygen enhances localization. It even leads to localized modes in the middle of the spectrum. Our results suggest that high-entropy oxides are a promising platform to study Anderson localization of phonons.

cond-mat.dis-nn↗

arXiv2023

Entropic sampling in frustrated magnets: role of self-intersecting spaces

Frustrated magnets typically possess a large space of classical ground states. If this degeneracy is not protected by symmetry, thermal fluctuations may `select' certain states via order-by-disorder. In this article, we examine a precursor effect where all ground states are sampled, but with different weights. Geometry plays a key role in determining the weight distribution and its behaviour. We demonstrate this with two examples -- both clusters with four spins coupled by XY interactions. In the first, the classical ground states form a smooth space. In the second, they form a self-intersecting non-manifold space. Ground state sampling is very different in these two cases. We first consider the microcanonical ensemble picture, where fluctuations conserve energy. Phase space arguments suggest that the first model exhibits energy-independent probabilities. The second shows a dramatic energy-dependence with relative probability increasing as $\epsilon^{-1/2}$, where $\epsilon$ is the energy of the system. We simulate low-energy dynamics in both models, confirming the expected behaviour. We next consider the canonical ensemble, where the first model produces temperature-independent probabilities. In the second, relative probability rises sharply as $T^{-1/2}$, where $T$ is the temperature. Our results bring out a classical analogue of order-by-singularity, a mechanism that has been recently proposed in the context of quantum spin clusters. The sampling of classical orders is qualitatively different in systems with self-intersecting ground state spaces. It grows at low energies and becomes singular as $\epsilon \rightarrow 0$ (microcanonical ensemble) or $T\rightarrow 0$ (canonical ensemble). We discuss relevance for disordered phases in macroscopic magnets, particularly for spiral liquids.

cond-mat.str-el↗

arXiv2023

Correlations in randomly stacked solids

Packing of spheres is a problem with a long history dating back to Kepler's conjecture in 1611. The highest density is realized in face-centred-cubic (FCC) and hexagonal-close-packed (HCP) arrangements. These are only limiting examples of an infinite family of maximal-density structures called Barlow stackings. They are constructed by stacking triangular layers, with each layer shifted with respect to the one below. At the other extreme, Torquato-Stillinger stackings are believed to yield the lowest possible density while preserving mechanical stability. They form an infinite family of structures composed of stacked honeycomb layers. In this article, we characterize layer-correlations in both families when the stacking is random. To do so, we take advantage of the H\"agg code -- a mapping between a Barlow stacking and a one-dimensional Ising magnet. The layer-correlation is related to a moment-generating function of the Ising model. We first determine the layer-correlation for random Barlow stacking, finding exponential decay. We next introduce a bias favouring one of two stacking-chiralities -- equivalent to a magnetic field in the Ising model. Although this bias favours FCC ordering, there is no long-ranged order as correlations still decay exponentially. Finally, we consider Torquato-Stillinger stackings, which map to a combination of an Ising magnet and a three-state Potts model. With random stacking, the correlations decay exponentially with a form that is similar to the Barlow problem. We discuss relevance to ordering in clusters of stacked solids and for layer-deposition-based synthesis methods.

cond-mat.stat-mech↗

arXiv2023

Scattering off a junction

Scattering off a potential is a fundamental problem in quantum physics. It has been studied extensively with amplitudes derived for various potentials. In this article, we explore a setting with no potentials, where scattering occurs off a junction where many wires meet. We study this problem using a tight-binding discretization of a star graph geometry -- one incoming wire and $M$ outgoing wires intersecting at a point. When an incoming wave scatters, one part is reflected along the same wire while the rest is transmitted along the others. Remarkably, the reflectance increases monotonically with $M$, i.e., the greater the number of outgoing channels, the more the particle bounces back. In the $M \rightarrow \infty$ limit, the wave is entirely reflected back along the incoming wire. We rationalize this observation by establishing a quantitative mapping between a junction and an on-site potential. To each junction, we assign an equivalent potential that produces the same reflectance. As the number of wires ($M$) increases, the equivalent potential also increases. A recent article by one of us has drawn an equivalence between junctions and potentials from the point of view of bound state formation. Our results here show that the same equivalence also holds for scattering amplitudes. We verify our analytic results by simulating wavepacket motion through a junction. We extend the wavepacket approach to two dimensions where analytic solutions cannot be found. An incoming wave travels on a sheet and scatters off a point where many sheets intersect. Unlike in 1D, the equivalent potential is momentum-dependent. Nevertheless, for any given momentum, the equivalent potential grows monotonically with the number of intersecting sheets. Our findings can be tested in ultracold atom setups and semiconductor structures.

cond-mat.quant-gas↗

arXiv2023

Spreading entanglement through pairwise exchange interactions

The spread of entanglement is a problem of great interest. It is particularly relevant to quantum state synthesis, where an initial direct-product state is sought to be converted into a highly entangled target state. In devices based on pairwise exchange interactions, such a process can be carried out and optimized in various ways. As a benchmark problem, we consider the task of spreading one excitation among $N$ two-level atoms or qubits. Starting from an initial state where one qubit is excited, we seek a target state where all qubits have the same excitation-amplitude -- a generalized-W state. This target is to be reached by suitably chosen pairwise exchange interactions. For example, we may have a a setup where any pair of qubits can be brought into proximity for a controllable period of time. We describe three protocols that accomplish this task, each with $N-1$ tightly-constrained steps. In the first, one atom acts as a flying qubit that sequentially interacts with all others. In the second, qubits interact pairwise in sequential order. In these two cases, the required interaction times follow a pattern with an elegant geometric interpretation. They correspond to angles within the spiral of Theodorus -- a construction known for more than two millennia. The third protocol follows a divide-and-conquer approach -- dividing equally between two qubits at each step. For large $N$, the flying-qubit protocol yields a total interaction time that scales as $\sqrt{N}$, while the sequential approach scales linearly with $ N$. For the divide-and-conquer approach, the time has a lower bound that scales as $\log N$. With any such protocol, we show that the phase differences in the final state cannot be independently controlled. For instance, a W-state (where all phases are equal) cannot be generated by pairwise exchange.

quant-ph↗