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Arnab Mandal

Publications and source records attributed to Arnab Mandal.

At least 19 recordsLinked to original sources

The Universal Role of Fragility on the Yielding Transition of Active Glass under Oscillatory Shear

The yielding transition marks the onset of irreversible plastic deformation in amorphous solids and plays a central role in determining the mechanical stability and failure of metallic glasses, colloidal suspensions, and biological assemblies. Despite extensive research, the microscopic factors governing the nature of yielding, particularly the transition between brittle and ductile mechanical responses, remain poorly understood. Recent studies have identified kinetic fragility as a key parameter governing yielding in passive glasses; whether this connection persists in active glasses remains open. Here, using molecular dynamics simulations of a Kob-Andersen glass former doped with Run-and-Tumble (RTP) active particles under oscillatory shear, we show that activity systematically reduces kinetic fragility and consequently alters the mechanical response. The common yield point $\gamma_c$ decreases monotonically with activity and exhibits a power-law dependence on the Arrhenius activation barrier. Increasing activity suppresses the dependence of the yield strain on thermal history and transforms the response from brittle-like to increasingly ductile, with smoother stress relaxation and reduced stress discontinuities. The timescale to reach steady state near yielding retains a critical power-law divergence, indicating that activity does not alter the underlying critical character of the transition. Active glasses also develop broader, more diffuse shear bands. Our results establish kinetic fragility as a unifying parameter governing yielding in both passive and active glasses and demonstrate that activity offers a powerful route to tune the mechanical response of amorphous materials.

cond-mat.soft

On Connectivity of Comaximal Subgroup Graph

The co-maximal subgroup graph $\Gamma(G)$ of a finite group $G$ is defined to be a graph with the set of all non-trivial proper subgroups of $G$ as the set of vertices and two distinct vertices $H$ and $K$ are adjacent if and only if $HK=G$. The deleted co-maximal subgroup graph of $G$, denoted by $\Gamma^*(G)$, is defined as the graph obtained by removing the isolated vertices from $\Gamma(G)$. In this paper, we prove that for any finite group $G$, $\Gamma^*(G)$ is connected. Furthermore, we show that $\Gamma^*(G)$ either contains a cycle or is a star. When $\Gamma^*(G)$ contains a cycle, its girth is either $3$ or $4$. Finally, we classify all finite groups $G$ for which $\Gamma^*(G)$ is a star.

math.GR

Quantum Automorphism Group of Direct Sum of Cuntz Algebras

In this article, we explore the quantum symmetry of the direct sum of a finite family of Cuntz algebras $\{\mathcal{O}_{n_i} \}_{i=1}^{m}$, viewing them as graph $C^*$-algebras associated to the graphs $\{L_{n_i}\}_{i=1}^{m}$ (where $L_n$ denotes the graph containing $n$ loops based at a single vertex), in the category introduced by Joardar and Mandal. It has been shown that the quantum automorphism group of the direct sum of non-isomorphic Cuntz algebras is ${U}_{n_1}^{+}*{U}_{n_2}^{+}* \cdots *{U}_{n_m}^{+}$ for distinct $n_i$'s, i.e. \begin{equation*} Q_τ^{Lin}(\sqcup_{i=1}^{m} ~ L_{n_i}) \cong *_{i=1}^{m} ~~ Q_τ^{Lin}(L_{n_i}) \cong {U}_{n_1}^{+}*{U}_{n_2}^{+}* \cdots *{U}_{n_m}^{+}, \end{equation*} where $Q_τ^{Lin}(Γ)$ denotes the quantum automorphism group of the graph $C^*$-algebra associated to $Γ$. Also, the quantum automorphism group of the direct sum of $m$ copies of isomorphic Cuntz algebra $\mathcal{O}_n$ is $U_n^+ \wr_* S_m^+$, i.e. \begin{equation*} Q_τ^{Lin}(\sqcup_{i=1}^{m} ~ L_n) \cong Q_τ^{Lin}(L_n) \wr_* S_m^+ \cong U_n^+ \wr_* S_m^+. \end{equation*} Furthermore, we have provided counter-examples to demonstrate that the isomorphisms mentioned above cannot be generalized to arbitrary graph $C^*$-algebras, whereas analogous relations can be extended in the context of quantum automorphism groups of graphs in the sense of Banica and Bichon.

math.OA

Some Results on Bichon's Quantum Automorphism Group of Graphs

The notion of the quantum automorphism group of a graph was introduced by J. Bichon in 2003 and T. Banica in 2005 respectively. This article explores primarily the quantum automorphism group of a graph $Γ$, denoted by $QAut_{Bic}(Γ)$, in Bichon's framework. First, we provide a sufficient condition for non-commutativity of Bichon's quantum automorphism group and discuss several applications of this criterion. Although it is known that $QAut_{Bic}(Γ) \cong QAut_{Bic}(Γ^c)$ does not hold in general, we identify a family of graphs for which this isomorphism enforces that the graph has no quantum symmetry. Moreover, we describe a few families of graphs having quantum symmetries whose quantum automorphism groups in Bichon's sense are commutative. Finally, we show that free product, tensor product and free wreath product constructions can arise as Bichon's quantum automorphism groups of connected graphs in the following sense: For a finite family of compact matrix quantum groups $\{Q_i\}_{i=1}^{m}$ arising as Bichon's quantum automorphism groups of certain graphs, there exist connected graphs $Γ_{free}$, $Γ_{ten}$ and $Γ_{wr}$ whose quantum automorphism groups are $*_{i=1}^{m} Q_{i}$, $\otimes_{i=1}^{m} Q_i$ and $Q_1 \wr_{*} Q_2$ respectively.

math.OA

The Difference Subgroup Graph of a Finite Group

The \emph{difference subgroup graph} $D(G)$ of a finite group $G$ is defined as the graph whose vertices are the non-trivial proper subgroups of $G$, with two distinct vertices $H$ and $K$ adjacent if and only if $\langle H, K \rangle = G$ but $HK \ne G$. This graph arises naturally as the difference between the join graph $Δ(G)$ and the comaximal subgroup graph $Γ(G)$. In this paper, we initiate a systematic study of $D(G)$ and its reduced version $D^*(G)$, obtained by removing isolated vertices. We establish several fundamental structural properties of these graphs, including conditions for connectivity, forbidden subgraph characterizations, and the relationship between graph parameters - such as independence number, clique number, and girth - and the solvability or nilpotency of the underlying group. The paper concludes with a discussion of open problems and potential directions for future research.

math.GR

On Independence Number of Comaximal Subgroup Graph

In this paper, we establish sharp thresholds on the independence number of the comaximal subgroup graph $\Gamma(G)$ that guarantee solvability, supersolvability, and nilpotency of the underlying group $G$. Specifically: \begin{itemize} \item For solvability, we prove that any group $G$ with independence number $\alpha(\Gamma(G))\leq 51$ must be solvable, and show that the alternating group $A_5$ is uniquely determined by its graph. \item For supersolvability, we show that $\alpha(\Gamma(G))\leq 14$ implies $G$ is supersolvable, except for three explicit exceptions. \item For nilpotency, we prove that $\alpha(\Gamma(G))\leq 6$ ensures nilpotency, except for five groups. \end{itemize} Finally, we conclude with some open issues involving domination parameters.

math.GR

Quantum Symmetries of Graph C*-algebras Having Maximal Permutational Symmetry

Quantum symmetry of a graph $C^{*}$-algebra $C^{*}(Γ)$ corresponding to a finite graph $Γ$ has been explored by several mathematicians within different categories in the past few years. In this article, we establish that there are exactly three families of compact matrix quantum groups, containing the symmetric group on the set of edges of the underlying graph $Γ$, that can be achieved as the quantum symmetries of graph $C^*$-algebras in the category introduced by Joardar and Mandal. Moreover, we demonstrate that there does not exist any graph $C^*$-algebra associated with a finite graph $Γ$ without isolated vertices having $A_{u^t}(F^Γ)$ as the quantum automorphism group of $C^*(Γ)$ for a non-scalar matrix $F^Γ$.

math.OA

Rigidity on Quantum Symmetry for a Certain Class of Graph C*-algebras

Quantum symmetry of graph $C^{*}$-algebras has been studied, under the consideration of different formulations, in the past few years. It is already known that the compact quantum group $(\underbrace{C(S^{1})*C(S^{1})*\cdots *C(S^{1})}_{|E(Γ)|-times}, Δ) $ always acts on a graph $C^*$-algebra for a finite, connected, directed graph $Γ$ in the category introduced by Joardar and Mandal, where $|E(Γ)|:=$ number of edges in $Γ$. In this article, we show that for a certain class of graphs including Toeplitz algebra, quantum odd sphere, matrix algebra etc. the quantum symmetry of their associated graph $C^*$-algebras remains $(\underbrace{C(S^{1})*C(S^{1})*\cdots *C(S^{1})}_{|E(Γ)|-times}, Δ) $ in the category as mentioned before. More precisely, if a finite, connected, directed graph $Γ$ satisfies the following graph theoretic properties : (i) there does not exist any cycle of length $\geq$ 2 (ii) there exists a path of length $(|V(Γ)|-1)$ which consists all the vertices, where $|V(Γ)|:=$ number of vertices in $Γ$ (iii) given any two vertices (may not be distinct) there exists at most one edge joining them, then the universal object coincides with $(\underbrace{C(S^{1})*C(S^{1})*\cdots *C(S^{1})}_{|E(Γ)|-times}, Δ) $. Furthermore, we have pointed out a few counter examples whenever the above assumptions are violated.

math.OA

Solvability of a group based on its number of subgroups

In this paper, we provide some conditions of (super)-solvability and nilpotency of a finite group $G$ based on its number of subgroups $Sub(G)$. Our results generalize the classification of finite groups with less than $20$ subgroups by Betz and Nash. We also provide an application of our results in studying comaximal subgroup graph of a group. Finally, we conclude with some open issues.

math.GR

On Some Intersection Properties of Finite Groups

In this article, we introduce the study of a class of finite groups $G$ which admits a subgroup which intersects all non-trivial subgroups of $G$. We also explore a subclass of it consisting of all groups $G$ in which the prime order elements commute. In particular, we discuss the relationship between these class of groups with other known classes of finite groups, like simple groups, perfect groups etc. Moreover, we also prove some results on the possible orders of such groups. Finally, we conclude with some open issues.

math.GR

Carrier thermalization and zero-point bandgap renormalization in halide perovskites from the Urbach tails of the emission spectrum

We develop techniques to study the temperature dependent localization, thermalization, and the effects of phonon scattering on the excitons in halide perovskites from the analysis of the emission spectra. The excitonic Urbach edge, when inferred from the low energy tails of the temperature dependent luminescence spectra, is shown to be sensitive to the electron distribution and thermalization. A method to observe the Urbach focus is devised for halide perovskites where the temperature dependence of the excitonic gap is anomalous. The value of the zero-point bandgap renormalization is inferred to be about 33 meV. This small value of the bandgap renormalization rules out the formation of small polarons and points to weak electron-phonon coupling. The experiments are performed on the nanosheets of the archetypal halide perovskite, CsPbBr$_3$.

cond-mat.mtrl-sci

Nonlinear optical responses of all-inorganic lead halide perovskite nanostructures by time-resolved beam-deflection technique

We have investigated nonlinear refraction in all-inorganic halide perovskites, the CsPbBr$_3$ and CsPbBr$_{1.5}$I$_{1.5}$ nanosheet and quantum dot colloids in toluene, by a novel beam deflection technique using near-resonant continuous wave lasers. The nonlinear refraction and its time-evolution measured here have originated from thermal lensing effect. Nonlinear behaviour of heat transport in terms of intensity dependent thermal diffusion rate has been observed. Effects of convective heat flow have been measured at high intensities. Quantum dots have higher nonlinear refraction as compared to the corresponding nanosheet samples, presumably due to reduced dimensionality. The effective values of nonlinear refractive index, estimated here for near-resonant excitations, exceed those reported in the literature for organic-inorganic hybrid perovskites in the nonresonant excitation regime, by several orders of magnitude.

cond-mat.mes-hall

Classification of Cayley Rose Window Graphs

Rose window graphs are a family of tetravalent graphs, introduced by Steve Wilson. Following it, Kovacs, Kutnar and Marusic classified the edge-transitive rose window graphs and Dobson, Kovacs and Miklavic characterized the vertex transitive rose window graphs. In this paper, we classify the Cayley rose window graphs.

math.CO

An example of explicit dependence of quantum symmetry on KMS states

We compute all the quantum symmetries of a graph with n- disjoint loops at the critical inverse temperature. We show that the set of non-isomorphic CQG's appearing as quantum symmetry at the critical inverse temperature has a one to one correspondence with the cardinality of the set of partitions of the number of vertices.

math.OA

Quantum symmetries of the twisted tensor products of C*-algebras

We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns out to be the generalised Drinfeld double of the quantum symmetry groups of the original filtrations. We show how these results apply to a wide class of crossed products of C*-algebras by actions of discrete groups. We also discuss an example where the hypothesis of our main theorem is not satisfied and the quantum symmetry group is not a generalised Drinfeld double.

math.OA

Invariance of KMS states on graph C*-algebras under classical and quantum symmetry

We study invariance of KMS states on graph C*-algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS state for strongly connected graphs is invariant under quantum automorphism group of the graph. For circulant graphs, it is shown that the action of classical and quantum automorphism group preserves only one of the KMS states occurring at the critical inverse temperature. We also give an example of a graph C*-algebra having more than one KMS state such that all of them are invariant under the action of classical automorphism group of the graph, but there is a unique KMS state which is invariant under the action of quantum automorphism group of the graph.

math.OA

Quantum symmetry of graph C*-algebras at critical inverse temperature

We give a notion of quantum automorphism group of graph C*-algebras without sink at critical inverse temperature. This is defined to be the universal object of a category of CQG's having a linear action in the sense of [11] and preserving the KMS state at critical inverse temperature. We show that this category for a certain KMS state at critical inverse temperature coincides with the category introduced in [11] for a class of graphs. We also introduce an orthogonal filtration on Cuntz algebra with respect to the unique KMS state and show that the category of CQG's preserving the orthogonal filtration coincides with the category introduced in this paper.

math.OA

Quantum Symmetry of Graph C*-algebras associated with connected Graphs

We define a notion of quantum automorphism group of Graph C*-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of underlying directed graph in the sense of T. banica is shown to be a quantum subgroup of quantum automorphism group in our sense. Quantum symmetries for some concrete graph C*-algebras have been computed.

math.OA