arXiv subjects

Abhishek Banerjee

Publications and source records attributed to Abhishek Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2025

Momentum and Matter Matter for Axion Dark Matter Matters on Earth

We investigate the implications of matter effects to searches for axion Dark Matter on Earth. The finite momentum of axion Dark Matter is crucial to elucidating the effects of Earth on both the axion Dark Matter field value and its gradient. We find that experiments targeting axion couplings compatible with canonical solutions of the strong CP puzzle are likely not affected by Earth's matter effects. However, experiments sensitive to lighter axions with stronger couplings can be significantly affected, with a significant part of the parameter space suffering from a reduced axion field value, and therefore decreased experimental sensitivity. In contrast, the spatial gradient of the axion field can be enhanced along Earth's radial direction, with important implications for ongoing and planned experiments searching for axion Dark Matter.

hep-ph↗

arXiv2024

Chow groups of ind-schemes and extensions of Saito's filtration

Let $K$ be a field of characteristic zero and let $Sm/K$ be the category of smooth and separated schemes over $K$. For an ind-scheme $\mathcal X$ (and more generally for any presheaf of sets on $Sm/K$), we define its Chow groups $\{CH^p(\mathcal X)\}_{p\in \mathbb Z}$. We also introduce Chow groups $\{\mathcal{CH}^p(\mathcal G)\}_{p\in \mathbb Z}$ for a presheaf with transfers $\mathcal G$ on $Sm/K$. Then, we show that we have natural isomorphisms of Chow groups $$ CH^p(\mathcal X)\cong \mathcal{CH}^p(Cor(\mathcal X))\qquad\forall\textrm{ }p \in \mathbb Z$$ where $Cor(\mathcal X)$ is the presheaf with transfers that associates to any $Y\in Sm/K$ the collection of finite correspondences from $Y$ to $\mathcal X$. Additionally, when $K=\mathbb C$, we show that Saito's filtration on the Chow groups of a smooth projective scheme can be extended to the Chow groups $CH^p(\mathcal X)$ and more generally, to the Chow groups of an arbitrary presheaf of sets on $Sm/\mathbb C$. Similarly, there exists an extension of Saito's filtration to the Chow groups of a presheaf with transfers on $Sm/\mathbb C$. Finally, when the ind-scheme $\mathcal X$ is ind-proper, we show that the isomorphism $CH^p(\mathcal X)\cong \mathcal{CH}^p(Cor(\mathcal X))$ is actually a filtered isomorphism.

math.AG↗

arXiv2024

Text2Gestures: A Transformer-Based Network for Generating Emotive Body Gestures for Virtual Agents

We present Text2Gestures, a transformer-based learning method to interactively generate emotive full-body gestures for virtual agents aligned with natural language text inputs. Our method generates emotionally expressive gestures by utilizing the relevant biomechanical features for body expressions, also known as affective features. We also consider the intended task corresponding to the text and the target virtual agents' intended gender and handedness in our generation pipeline. We train and evaluate our network on the MPI Emotional Body Expressions Database and observe that our network produces state-of-the-art performance in generating gestures for virtual agents aligned with the text for narration or conversation. Our network can generate these gestures at interactive rates on a commodity GPU. We conduct a web-based user study and observe that around 91% of participants indicated our generated gestures to be at least plausible on a five-point Likert Scale. The emotions perceived by the participants from the gestures are also strongly positively correlated with the corresponding intended emotions, with a minimum Pearson coefficient of 0.77 in the valence dimension.

cs.HC↗

arXiv2024

Dynamical Axion Misalignment from the Witten Effect

We propose a relaxation mechanism for the initial misalignment angle of the pre-inflationary QCD axion with a large decay constant. The proposal addresses the challenges posed to the axion dark matter scenario by an overabundance of axions overclosing the Universe, as well as by isocurvature constraints. Many state-of-the-art experiments are searching for QCD axion dark matter with a decay constant as large as $10^{16}\,\mathrm{GeV}$, motivating the need for a theoretical framework such as ours. In our model, hidden sector magnetic monopoles generated in the early Universe give the axion a large mass via the Witten effect, causing early oscillations that reduce the misalignment angle and axion abundance. As the hidden gauge symmetry breaks, its monopoles confine via cosmic strings, dissipating energy into the Standard Model and leading to monopole-antimonopole annihilation. This removes the monopole-induced mass, leaving only the standard QCD term. We consider the symmetry breaking pattern of $\mathrm{SU}(2)' \to \mathrm{U}(1)' \to 1$, leading to monopole and string formation respectively. We calculate the monopole abundance, their interactions with the axion field, and the necessary conditions for monopole-induced axion oscillations, while accounting for UV instanton effects. We present three model variations based on different symmetry breaking scales and show that they can accommodate an axion decay constant of up to $10^{16}\,\mathrm{GeV}$ with an inflationary scale of $10^{15}\,\mathrm{GeV}$. The required alignment between monopole-induced and QCD axion potentials is achieved through a modest Nelson-Barr mechanism, avoiding overclosure without anthropic reasoning.

hep-ph↗

arXiv2024

Entwined comodules and contramodules over coalgebras with several objects: Frobenius, separability and Maschke theorems

We study module like objects over categorical quotients of algebras by the action of coalgebras with several objects. These take the form of ``entwined comodules'' and ``entwined contramodules'' over a triple $(\mathscr C,A,ψ)$, where $A$ is an algebra, $\mathscr C$ is a coalgebra with several objects and $ψ$ is a collection of maps that ``entwines'' $\mathscr C$ with $A$. Our objective is to prove Frobenius, separability and Maschke type theorems for functors between categories of entwined comodules and entwined contramodules.

math.CT↗

arXiv2024

Probing (Ultra-) Light Dark Matter Using Synchrotron Based Mössbauer Spectroscopy

We propose to search for (ultra)-light scalar dark matter (DM) using synchrotron radiation based Mössbauer spectroscopy technique. Such DM induces temporal variation in various fundamental constants, which in turn causes time modulation of the nuclear transition energies. When a Mössbauer source and absorber is separated by a large baseline, the DM induced shift between their energy levels can be tested by the modulation of the photon absorption spectrum. The narrow Mössbauer transitions allow the setup to efficiently probe DM in the high frequency range. We show that the reach of a Mössbauer experiment with the existing synchrotron beams is at par with the bounds from various equivalence principle violation searches. An improvement of the synchrotron setup would enable us to probe the hitherto uncharted territory of the DM parameter space upto MHz frequency. The proposed method would extend the DM search beyond the EP limit by several orders of magnitude, and would provide the best bound on DM interaction strength with various standard model fields in the high ($>$kHz) frequency region.

hep-ph↗

arXiv2024

Superfluid stiffness of twisted multilayer graphene superconductors

The robustness of the macroscopic quantum nature of a superconductor can be characterized by the superfluid stiffness, $ρ_s$, a quantity that describes the energy required to vary the phase of the macroscopic quantum wave function. In unconventional superconductors, such as cuprates, the low-temperature behavior of $ρ_s$ drastically differs from that of conventional superconductors due to quasiparticle excitations from gapless points (nodes) in momentum space. Intensive research on the recently discovered magic-angle twisted graphene family has revealed, in addition to superconducting states, strongly correlated electronic states associated with spontaneously broken symmetries, inviting the study of $ρ_s$ to uncover the potentially unconventional nature of its superconductivity. Here we report the measurement of $ρ_s$ in magic-angle twisted trilayer graphene (TTG), revealing unconventional nodal-gap superconductivity. Utilizing radio-frequency reflectometry techniques to measure the kinetic inductive response of superconducting TTG coupled to a microwave resonator, we find a linear temperature dependence of $ρ_s$ at low temperatures and nonlinear Meissner effects in the current bias dependence, both indicating nodal structures in the superconducting order parameter. Furthermore, the doping dependence shows a linear correlation between the zero temperature $ρ_s$ and the superconducting transition temperature $T_c$, reminiscent of Uemura's relation in cuprates, suggesting phase-coherence-limited superconductivity. Our results provide strong evidence for nodal superconductivity in TTG and put strong constraints on the mechanisms of these graphene-based superconductors.

cond-mat.supr-con↗

arXiv2024

Activation of entanglement in generalized entanglement swapping

We study entanglement activation in a generalized entanglement swapping process involving two Bell pairs and generalized measurements. The conventional understanding posits entangled measurements as both necessary and sufficient for establishing entanglement between distant parties. In this study, we reassess the role of measurement operators in entanglement generation within a generalized entanglement swapping process. We focus on maximally entangled two-qubit initial states and generalized measurements, investigating the necessity and sufficiency conditions for entangled measurement operators. By utilizing two Bell pairs, (1, 2) shared between Alice and Bob, and (3, 4) shared between Bob and Charlie, we demonstrate that while entangled measurements are sufficient, they are not indispensable for establishing entanglement between spatially separated observers. Through a sequential approach, if Bob performs an initial measurement which is not able to establish entanglement then followed by another measurement after post-processing the first measurement it is possible to establish entanglement. We identify specific criteria for different measurement operators that enable the potential for performing a second measurement to establish entanglement. Our findings highlight the feasibility of generating entanglement between distant parties through a combination of measurements, shedding light on entanglement distribution in quantum networks. Additionally, we showcase through illustrative examples how successive measurements enhance entanglement compared to single measurements, underscoring the practical benefits of our approach in enhancing entanglement. Moreover, our protocol extends beyond bipartite qubit states to higher-dimensional maximally entangled states, emphasizing its versatility and applicability.

quant-ph↗

arXiv2024

On representation categories of $A_\infty$-algebras and $A_\infty$-coalgebras

In this paper, we use the language of monads, comonads and Eilenberg-Moore categories to describe a categorical framework for $A_\infty$-algebras and $A_\infty$-coalgebras, as well as $A_\infty$-modules and $A_\infty$-comodules over them respectively. The resulting formalism leads us to investigate relations between representation categories of $A_\infty$-algebras and $A_\infty$-coalgebras. In particular, we relate $A_\infty$-comodules and $A_\infty$-modules by considering a rational pairing between an $A_\infty$-coalgebra $C$ and an $A_\infty$-algebra $A$. The categorical framework also motivates us to introduce $A_\infty$-contramodules over an $A_\infty$-coalgebra $C$.

math.CT↗

arXiv2024

Hilbert spaces over $C^*$-tensor categories, Fredholm modules and cyclic cohomology

We construct Fredholm modules over an algebra taking values in generalized Hilbert spaces over a rigid $C^*$-tensor category. Using methods of Connes, we obtain Chern characters taking values in cyclic cohomology. These Chern characters are well behaved with respect to the periodicity operator, and depend only on the homotopy class of the Fredholm module.

math.OA↗

arXiv2024

Thermalization of isolated quantum many-body system and the role of entanglement

Thermalization of an isolated quantum system has been a nontrivial problem since the early days of quantum mechanics. In generic isolated quantum systems, nonequilibrium dynamics is expected to result in thermalization, indicating the emergence of statistical mechanics from quantum dynamics. However, what feature of a many-body quantum system facilitates quantum thermalization is still not well understood. Recent experimental advancements have shown that entanglement may act as a thermalizing agent, not universally but particularly. Here, we theoretically show that the thermal averages of an observable in an isolated many-body quantum system with a large number of degrees of freedom emerge from the entangled energy eigenstates of the system. In particular, we show that the expectation values of an observable in entangled energy eigenstates and its marginals are equivalent to the microcanonical and canonical averages of the observable.

quant-ph↗

arXiv2024

Quantum change point and entanglement distillation

In a quantum change point problem, a source emitting particles in a fixed quantum state (default) switches to a different state at some stage, and the objective is to identify when the change happened by measuring a sequence of particles emitted from such a source. Motivated by entanglement-sharing protocols in quantum information, we study this problem within the paradigm of local operations and classical communication (LOCC). Here, we consider a source that emits entangled pairs in a default state, but starts producing another entangled state (mutation) at a later stage. Then, a sequence of entangled pairs prepared from such a source and shared between distant observers cannot be used for quantum information processing tasks as the identity of each entangled pair remains unknown. We show that identifying the change point using LOCC leads to the distillation of free entangled pairs. In particular, if the default and the mutation are mutually orthogonal, there exists an efficient LOCC protocol that identifies the change point without fail and distills a sufficiently large number of pairs. However, if they are nonorthogonal, there is a probability of failure. In this case, we compute the number of entangled pairs that may be obtained on average. We also consider a relaxation of the two-state problem where the mutation is not known a priori, but instead belongs to a known set. Here we show that local distinguishability plays a crucial role: if the default and the possible mutations are locally distinguishable, the problem reduces to the two-state problem with orthogonal states, but if not, one may still identify the mutation, the change point, and distill entanglement, as we illustrate with a concrete example.

quant-ph↗

arXiv2023

When Mei-Gu Guan's 1960 Postmen Get Empowered with Bell's 1964 Nonlocal Correlations, or, Nonlocal Advantage in Vehicle Routing Problem

Vehicle routing problems, a comprehensive problem category originated from the seminal Chinese Postman Problem (first investigated by Chinese mathematician Mei-Gu Guan), entail strategic and tactical decision making for efficient scheduling and routing of vehicles. While Chinese postman problem is aimed at finding the minimum length cycle for a single postman, the broader challenges encompass scenarios with multiple postmen. Making cost-effective decisions in such cases depends on various factors, including vehicle sizes and types, vehicle usage time, road tax variations across routes, and more. In this work, we delve into a class of such problems wherein Bell nonlocal correlations provide advantages in optimizing the costs for non-communicating postmen, and thus establish a nascent utilization of quantum entanglement in traffic routing problem. Our investigation unveils promising applications for nonlocal correlations within combinatorial optimization and operational research problems, which otherwise have predominantly been explored within the quantum foundation and quantum information theory community.

quant-ph↗

arXiv2023

The Phenomenology of Quadratically Coupled Ultra Light Dark Matter

We discuss models of ultralight scalar Dark Matter (DM) with linear and quadratic couplings to the Standard Model (SM). In addition to studying the phenomenology of linear and quadratic interactions separately, we examine their interplay. We review the different experiments that can probe such interactions and present the current and expected future bounds on the parameter space. In particular, we discuss the scalar field solution presented in [A. Hees, O. Minazzoli, E. Savalle, Y. V. Stadnik and P. Wolf, Phys.Rev.D 98 (2018) 6, 064051], and extend it to theories that capture both the linear and the quadratic couplings of the DM field to the SM. Furthermore, we discuss the theoretical aspects and the corresponding challenges for natural models in which the quadratic interactions are of phenomenological importance.

hep-ph↗

arXiv2023

Noncommutative supports, local cohomology and spectral sequences

The purpose of this paper is to study local cohomology in the noncommutative algebraic geometry framework of Artin and Zhang. The noncommutative spaces are obtained by base change of a Grothendieck category that is locally noetherian or strongly locally noetherian. Using what we call elementary objects and their injective hulls, we develop a theory of supports and associated primes in these categories. We apply our theory to study a general functorial setup that requires certain conditions on the injective hulls of elementary objects and gives us spectral sequences for derived functors associated to local cohomology objects, as well as generalized local cohomology and also generalized Nagata ideal transforms.

math.CT↗

arXiv2023

Robust Decentralized Secondary Control Scheme for Inverter-based Power Networks

Inverter-dominated microgrids are quickly becoming a key building block of future power systems. They rely on centralized controllers that can provide reliability and resiliency in extreme events. Nonetheless, communication failures due to cyber-physical attacks or natural disasters can make autonomous operation of islanded microgrids challenging. This paper examines a unified decentralized secondary control scheme that is robust to inverter clock synchronization errors and can be seamlessly applied to grid-following or grid-forming control architectures. The proposed scheme overcomes the well-known stability problem that arises from parallel operation of local integral controllers. Theoretical guarantees for stability are provided along with criteria to appropriately tune the secondary control gains to achieve good frequency regulation performance while ensuring fair power sharing. The efficacy of our approach in eliminating the steady-state frequency deviation is demonstrated through simulations on a 5-bus microgrid with four grid-forming inverters.

eess.SY↗

arXiv2023

Measurings of Hopf algebroids and morphisms in cyclic (co)homology theories

In this paper, we consider measurings between Hopf algebroids and show that they induce morphisms on cyclic homology and cyclic cohomology. We also consider comodule measurings between SAYD modules over Hopf algebroids. These give an enrichment of the global category of SAYD modules over comodules. These measurings also induce morphisms on cyclic (co)homology of Hopf algebroids with SAYD coefficients, which are compatible with Hopf-Galois maps. Finally, we consider non-$Σ$ operads with multiplication. We obtain an enrichment of cyclic unital comp modules over non-$Σ$ operads, as well as morphisms on cyclic homology induced by measurings of comp modules over operads with multiplication.

math.CT↗

arXiv2023

Heavily separable functors of the second kind and applications

We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modules over small preadditive categories. The second is with free functors taking values in Eilenberg-Moore categories associated to a monad or a comonad. Finally, we consider entwined modules and give if and only if conditions for heavy separability of the second kind for functors forgetting either the comodule action or the module action.

math.RA↗