arXiv subjects

Aritra Banerjee

Publications and source records attributed to Aritra Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2024

Strings near black holes are Carrollian

We demonstrate that strings near the horizon of a Schwarzschild black hole, when viewed by a stationary observer at infinity, probe a string Carroll geometry, where the effective lightspeed is given by the distance from the horizon. We expand the Polyakov action in powers of this lightspeed to find a theory of Carrollian strings. We show that the string shrinks to a point to leading order near the horizon, which follows a null geodesic in a two-dimensional Rindler space. At the next-to-leading order the string oscillates in the embedding fields associated with the near-horizon two-sphere.

hep-th↗

arXiv2024

Beyond Wilson? Carroll from current deformations

At extreme energies, both low and high, the spacetime symmetries of relativistic quantum field theories (QFTs) are expected to change with Galilean symmetries emerging in the very low energy domain and, as we will argue, Carrollian symmetries appearing at very high energies. The formulation of Wilsonian renormalisation group seems inadequate for handling these changes of the underlying Poincare symmetry of QFTs and it seems unlikely that these drastic changes can be seen within the realms of relativistic QFT. We show that contrary to this expectation, changes in the spacetime algebra occurs at the very edges of parameter space. In particular, we focus on the very high energy sector and show how bilinears of $U(1)$ currents added to a two dimensional (massless) scalar field theory deform the relativistic spacetime conformal algebra to conformal Carroll as the effective coupling of the deformation is dialed to infinity. We demonstrate this using both a symmetric and an antisymmetric current-current deformation for theories with multiple scalar fields. These two operators generate distinct kinds of quantum flows in the coupling space, the symmetric driven by Bogoliubov transformations and the antisymmetric by spectral flows, both leading to Carrollian CFTs at the end of the flow.

hep-th↗

arXiv2023

Tensionless Tales of Compactification

We study circle compactifications of tensionless bosonic string theory, both at the classical and the quantum level. The physical state condition for different representations of BMS$_3$, the worldsheet residual gauge symmetry for tensionless strings, admits three inequivalent quantum vacua. We obtain the compactified mass spectrum in each of these vacua using canonical quantization and explicate their properties.

hep-th↗

arXiv2023

Transport phenomena of TiCoSb: Defects induced modification in structure and density of states

TiCoSb1+x (x=0.0, 0.01, 0.02, 0.03, 0.04, 0.06) samples have been synthesized, employing solid state reaction method followed by arc menting. Theoretical calculations, using Density Functional Theory (DFT) have been performed to estimate band structure and density of states (DOS). Further, energitic calculations, using first principle have been carried out to reveal the formation energy for vacancy, interstitial, anti-site defects. Detail structural calculation, employing Rietveld refinement reveals the presence of embedded phases, vacancy and interstitial atom, which is also supported by the theoretical calculations. Lattice strain, crystalline size and dislocation density have been estimated by Williamson-Hall and modified Williamson-Hall methods. Thermal variation of resistivity [\r{ho}(T)] and thermopower [S(T)] have been explained using Mott equation and density of states (DOS) modification near the Fermi surface due to Co vancancy and embedded phases. Figure of merit (ZT) has been calculated and 4 to 5 times higher ZT for TiCoSb than earlier reported value is obtained at room temperature.

cond-mat.mtrl-sci↗

arXiv2023

Quantum state complexity meets many-body scars

Scar eigenstates in a many-body system refers to a small subset of non-thermal finite energy density eigenstates embedded into an otherwise thermal spectrum. This novel non-thermal behaviour has been seen in recent experiments simulating a one-dimensional PXP model with a kinetically-constrained local Hilbert space realized by a chain of Rydberg atoms. We probe these small sets of special eigenstates starting from particular initial states by computing the spread complexity associated to time evolution of the PXP hamiltonian. Since the scar subspace in this model is embedded only loosely, the scar states form a weakly broken representation of the Lie Algebra. We demonstrate why a careful usage of the Forward Scattering Approximation (or similar strategies thereof) is required to extract an appropriate set of Lanczos coefficients in this case as the consequence of this approximate symmetry. This leads to a well defined notion of a closed Krylov subspace and consequently, that of spread complexity. We show how the spread complexity shows approximate revivals starting from both $|\mathbb{Z}_2\rangle$ and $|\mathbb{Z}_3\rangle$ states and how these revivals can be made more accurate by adding optimal perturbations to the bare Hamiltonian. We also investigate the case of the vacuum as the initial state, where revivals can be stabilized using an iterative process of adding few-body terms.

quant-ph↗

arXiv2023

Carroll covariant scalar fields in two dimensions

Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons and tensionless strings. In this paper, we focus on two dimensional (2d) null manifolds and hence on the 2d Conformal Carroll or equivalently the 3d Bondi-Metzner-Sachs (BMS) algebra. Using Carroll covariance, we write the most general free massless Carroll scalar field theory and discover three inequivalent actions. Of these, two viz. the time-like and space-like actions, have made their appearance in literature before. We uncover a third that we call the mixed-derivative theory. As expected, all three theories enjoy off-shell BMS invariance. Interestingly, we find that the on-shell symmetry of mixed derivative theory is a single Virasoro algebra instead of the full BMS. We discuss potential applications to tensionless strings and flat holography.

hep-th↗

arXiv2022

Bootstrapping the Kronig-Penney Model

Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the Schrödinger equation with periodic potentials, paying particular attention to the Kronig-Penney model of a particle in a one-dimensional lattice. With an appropriate choice of operator basis involving position and momenta, we find that the bootstrap approach efficiently computes the band gaps of the energy spectrum but has trouble effectively constraining the minimum energy. We show how applying more complex constraints involving higher powers of momenta can potentially remedy such a problem. We also propose an approach for analytically constructing the dispersion relation associated with the Bloch momentum of the system.

quant-ph↗

arXiv2022

From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators

We probe the contraction from $2d$ relativistic CFTs to theories with Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, using diagnostics of quantum chaos. Starting from an Ultrarelativistic limit on a relativistic scalar field theory and following through at the quantum level using an oscillator representation of states, one can show the CFT$_2$ vacuum evolves smoothly into a BMS$_3$ vacuum in the form of a squeezed state. Computing circuit complexity of this transmutation using the covariance matrix approach shows clear divergences when the BMS point is hit or equivalently when the target state becomes a boundary state. We also find similar behaviour of the circuit complexity calculated from methods of information geometry. Furthermore, we discuss the hamiltonian evolution of the system and investigate Out-of-time-ordered correlators (OTOCs) and operator growth complexity, both of which turn out to scale polynomially with time at the BMS point.

hep-th↗

arXiv2022

Magic Fermions: Carroll and Flat Bands

The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null surfaces. Due to the availability of two different (degenerate) metrics on Carroll spacetimes, there is the possibility of two different versions of Carroll Clifford algebras. We consider both possibilities and construct explicit representations of Carrollian gamma matrices and show how to build higher spacetime dimensional representations out of lower ones. Actions for Carroll fermions are constructed with these gamma matrices and the properties of these actions are investigated. We show that in condensed matter systems where the dispersion relation becomes trivial i.e. the energy is not dependent on momentum and bands flatten out, Carroll symmetry generically appears. We give explicit examples of this including that of twisted bi-layer graphene, where superconductivity appears at so called magic angles and connect this to Carroll fermions.

hep-th↗

arXiv2022

Carroll fermions in two dimensions

Carroll symmetry is a very powerful characteristic of generic null surfaces, as it replaces the usual Poincaré algebra with a vanishing speed of light version thereof. These symmetries have found universal applications in the physics of null manifolds as they arise in diverse situations ranging from black hole horizons to condensed matter systems with vanishing Fermi velocities. In this work, we concentrate on fermions living on two dimensional ($2d$) null manifolds and explore the Carroll invariant structure of the associated field theories in a systematic manner. The free massless versions of these fermions are shown to exhibit $2d$ Conformal Carroll or equivalently the $3d$ Bondi-Metzner-Sachs (BMS) algebra as their symmetry. Due to the degenerate nature of the manifold, we show the presence of two distinct classes of Clifford Algebras. We also find that in two dimensions there are two distinct fermion actions. We study discrete and continuous symmetries of both theories, and quantize them using highest weight representation of the vacuum. We also discuss how the symmetries of $2d$ free fermion CFTs can be continually deformed by infinite boosts or degenerate linear transformations on coordinates, leading to the corresponding BMS invariant theory at singular points.

hep-th↗

arXiv2022

ModMax meets GCA

A maximally symmetric non-linear extension of Maxwell's theory in four dimensions called ModMax has been recently introduced in the literature. This theory preserves both electromagnetic duality and conformal invariance of the linear theory. In this short paper, we introduce a Galilean cousin of the ModMax theory, written in a covariant formalism, that is explicitly shown to be invariant under Galilean Conformal Symmetries. We discuss the construction of such a theory involving Galilean electromagnetic invariants, and show how the classical structure of the theory is invariant under the action of Galilean Conformal Algebra (GCA).

hep-th↗

arXiv2022

Boosting to BMS

Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, are intrinsically associated to null manifolds and in two dimensions can be obtained as an In{ö}n{ü}-Wigner contraction of the two-dimensional ($2d$) relativistic conformal algebra. Instead of performing contractions, we demonstrate in this paper how this transmutation of symmetries can be achieved by infinite boosts or degenerate linear transformations on coordinates. Taking explicit cues from the worldsheet theory of null strings, we show boosting the system is equivalent to adding a current-current deformation term to the Hamiltonian. As the strength of this deformation term reaches a critical value, the classical symmetry algebra "flows" from two copies of Virasoro to the BMS algebra. We further explore the situation where the CFT coordinates are asymmetrically transformed, and degenerate limits lead to chiral theories.

hep-th↗

arXiv2022

zkHawk: Practical Private Smart Contracts from MPC-based Hawk

Cryptocurrencies have received a lot of research attention in recent years following the release of the first cryptocurrency Bitcoin. With the rise in cryptocurrency transactions, the need for smart contracts has also increased. Smart contracts, in a nutshell, are digitally executed contracts wherein some parties execute a common goal. The main problem with most of the current smart contracts is that there is no privacy for a party's input to the contract from either the blockchain or the other parties. Our research builds on the Hawk project that provides transaction privacy along with support for smart contracts. However, Hawk relies on a special trusted party known as a manager, which must be trusted not to leak each party's input to the smart contract. In this paper, we present a practical private smart contract protocol that replaces the manager with an MPC protocol such that the function to be executed by the MPC protocol is relatively lightweight, involving little overhead added to the smart contract function, and uses practical sigma protocols and homomorphic commitments to prove to the blockchain that the sum of the incoming balances to the smart contract matches the sum of the outgoing balances.

cs.CR↗

arXiv2022

Observation of Griffiths-like phase in the quaternary Heusler compound NiFeTiSn

The quaternary Heusler compound NiFeTiSn can be considered to be derived from the exotic pseudogap-compound Fe2TiSn by the replacement of one Fe atom by Ni. In contrast to Fe2TiSn, which shows a disorder-induced ferromagnetic phase, the ground state of NiFeTiSn is antiferromagnetic with the signature of spin canting. Interestingly, NiFeTiSn shows a Griffiths-like phase characterized by isolated ferromagnetic clusters before attaining the antiferromagnetic state. The Griffiths-like phase is possibly associated with the antisite disorder between Fe and Ti sites as evident from our powder X-ray diffraction study. The compound also shows rather an unusual temperature dependence of resistivity, which can be accounted for by the prevailing structural disorder in the system. NiFeTiSn turned out to be a rare example where a Griffiths-like phase is observed in a semiconducting 3d transition metal-based intermetallic compound with an antiferromagnetic ground state.

cond-mat.str-el↗

arXiv2022

A Rindler Road to Carrollian Worldsheets

The tensionless limit of string theory has recently been formulated in terms of worldsheet Rindler physics. In this paper, by considering closed strings moving in background Rindler spacetimes, we provide a concrete exemplification of this phenomenon. We first show that strings probing the near-horizon region of a generic non-extremal blackhole become tensionless thereby linking a spacetime Carroll limit to a worldsheet Carroll limit. Then, considering strings in $d$-dimensional Rindler spacetime we find a Rindler structure induced on the worldsheet. Novelties, including folds, appear on the closed string worldsheet pertaining to the formation of the worldsheet horizon. The closed string becomes segmented at these folding points and different segments go into the formation of closed strings in the different Rindler wedges. The Bondi-Metzner-Sachs (BMS) or the Conformal Carroll algebra emerges from the closed string Virasoro algebra as the horizon is hit. Quantum states on these accelerated worldsheets are discussed and we show the formation of boundary states from gluing conditions of the different segments of the accelerated closed string.

hep-th↗

arXiv2021

Sb concentration dependent Structural and Transport properties of Polycrystalline (Bi1-xSbx)2Te3 Mixed crystal

(Bi1-xSbx)2Te3 (x=0.60, 0.65, 0.68, 0.70, 0.75 and 0.80) mixed crystals have been synthesized by solid state reaction. In depth structural, thermal, transport and electronic properties are reported. Defect and disorder play a crucial role in structural and transport behaviour. Disorder induced iso-structural phase transition is observed at x=0.70, which is supported by the structural and transport properties data. Debye temperature has been estimated from the powder diffraction data. Differential scanning calorimetry (DSC) data confirms the glass transition in the material. Low temperature resistivity data shows Variable range hopping mechanism whereas high temperature data follows activated behaviour. Activation energy is calculated from the semiconducting region of resistivity data. Both Hall measurement and temperature dependent thermopower data (S(T)) confirms that samples are p-type in nature. Density of state effective mass has been estimated from Pisarenko relation and corroborated with resistivity data. Thermal conductivity (k) is estimated using experimentally obtained data. Figure of Merit (ZT) of the synthesized samples are calculated using resistivity, S(T) and k. Structural and transport properties are correlated, confirms the transition from disorder to order state. Defect and disorder are corroborated with structural and Thermoelectric properties of the synthesized samples.

physics.app-ph↗

arXiv2021

Lost in the Log-Polynomial Expansion: Comment on arXiv:2101.08278

In [1] we highlighted the fact that the log polynomial expansion employed in Nature Astron. 3, no.3, 272-277 (2019) [2] is a poor approximation to flat $Λ$CDM, so using it to infer deviations from flat $Λ$CDM is not well-motivated. The "orthogonalized logarithmic polynomials" recently presented in arXiv:2101.08278 [3] are an attempt to respond to the earlier criticism [1]. Here we demonstrate that this new technique [3] - interesting though it may be - fails to address the fundamental problem raised in [1]. Unfortunately, the claim made in [2] may still be lost in the expansion.

astro-ph.CO↗

arXiv2021

On Problems with Cosmography in Cosmic Dark Ages

Quasars show considerable promise as standard candles in a high-redshift window beyond Type Ia supernovae. Recently, Risaliti, Lusso \& collaborators \cite{Risaliti:2018reu, Lusso:2019akb, Lusso:2020pdb} have succeeded in producing a high redshift Hubble diagram ($ z \lesssim 7$) that supports "a trend whereby the Hubble diagram of quasars is well reproduced by the standard flat $Λ$CDM model up to $z \sim 1.5-2$, but strong deviations emerge at higher redshifts". This conclusion hinges upon a log polynomial expansion for the luminosity distance. In this note, we demonstrate that this expansion (or "improvements" thereof) typically can only be trusted up to $z \sim 1.5-2$. As a result, a breakdown in the validity of the expansion may be misinterpreted as a (phantom) deviation from flat $Λ$CDM. We further illustrate the problem through mock data examples.

astro-ph.CO↗