arXiv subjects

S. Bera

Publications and source records attributed to S. Bera.

15 recordsLinked to original sources

arXiv2026

Advanced Virgo Plus for O5 -- Design Report Overview

This document presents an overview of the design, implementation, and expected performance of the Advanced Virgo Plus (AdV+) upgrades in view of the O5 observing run. Following the experience gained during the O4 commissioning and operations, the Virgo Collaboration has revised the upgrade strategy to address limitations associated with marginally stable recycling cavities. The O5 upgrade program combines elements from the original AdV+ Phase II project with new design solutions, including the implementation of stable recycling cavities, a major modification to the central interferometer layout, and a comprehensive renewal of critical subsystems. The planned upgrades are organized in two steps, targeting progressive improvements in operational stability, noise reduction, and detector sensitivity. Key developments include new vacuum infrastructures, suspensions, mirrors, optical configurations, quantum noise reduction systems, and high-power laser technologies. The resulting configuration is expected to significantly enhance the interferometer performance, enabling a substantial increase in astrophysical reach and scientific return during O5.

astro-ph.IM↗

arXiv2026

Subnormality of the quotients of $\mathbb T^d$-invariant Hilbert modules

In this paper, we investigate $\mathbb T^d$-invariant Hilbert modules $\mathscr H$ over the polynomial ring $\mathbb C[z_1, \ldots, z_d]$ and their quotients, with primary emphasis on the classification of subnormal quotient modules of the form $\mathscr H/[p],$ where $p$ is a homogeneous polynomial in $d$ complex variables. The motivation for this classification arises from the case $p(z_1, z_2)=z_1-z_2,$ in which the subnormality of the quotient module $\widehat{\mathscr H_{\kappa_1} \otimes \mathscr H_{\kappa_2}}/[p]$ is equivalent to that of the module tensor product $\mathscr H_{\kappa_1} \otimes_{\mathbb C[z]} \mathscr H_{\kappa_2}$ of $\mathbb T$-invariant Hilbert modules $\mathscr H_{\kappa_1}$ and $\mathscr H_{\kappa_2}$, a problem first considered by N. Salinas. In addition to general structural results on principal homogeneous submodules $[p]$ of $\mathscr H$, we prove that if $\mathscr H/[p]$ is subnormal, then $p$ must be square-free. Furthermore, when $\mathscr H$ is either $H^2(\mathbb D^d)$ or $H^2(\mathbb B^d),$ $d \ge 1,$ the subnormality of the quotient module $\mathscr H/[p]$ implies that $\mathrm{deg}\,p \le 1.$ We further show that $H^2(\mathbb D^2)/[p]$ (resp. $H^2(\mathbb B^2)/[p]$) is subnormal if and only if $\mathrm{deg} \,p \le 1.$ If $H^2_d$ denotes the Drury-Arveson module in $d$ dimensions, then $H^2_2/[p]$ is subnormal if and only if $p$ is nonzero and $\mathrm{deg} \,p \le 1$. This is surprising, especially since $H^2_d$ is not a subnormal Hilbert module for $d \ge 2.$ Moreover, the phenomenon above does not occur for the Dirichlet module $D_2(\mathbb B^2)$. Finally, we present an example demonstrating that a $\mathcal U_d$-invariant subnormal Hilbert module $\mathscr H$ may have a subnormal quotient module $\mathscr H/[p]$ even when $\mathrm{deg}\, p = 2.$

math.FA↗

arXiv2019

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases -- due to their repulsion -- the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the $N$-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For $N$ interacting bosons, a splitting into an $N$-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that the splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

cond-mat.quant-gas↗

arXiv2019

Relaxation of Shannon entropy for trapped interacting bosons with dipolar interactions

We study the dynamics of dipolar bosons in an external harmonic trap. We monitor the time evolution of the occupation in the natural orbitals and normalized first- and second-order Glauber's correlation functions. We focus in particular on the relaxation dynamics of the Shannon entropy. Comparison with the corresponding results for contact interactions is presented. We observe significant effects coming from the presence of the non-local repulsive part of the interaction. The relaxation process is very fast for dipolar bosons with a clear signature of a truly saturated maximum entropy state. We also discuss the connection between the entropy production and the occurrence of correlations and loss of coherence in the system. We identify the long-time relaxed state as a many-body state retaining only diagonal correlations in the first-order correlation function and building up anti-bunching effect in the second-order correlation function.

cond-mat.quant-gas↗

arXiv2019

Survival probability in Generalized Rosenzweig-Porter random matrix ensemble

We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability $R(t)$, the probability of finding the initial state after time $t$. In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that $R(t)$ can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of $R(t)$ with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of $R(t\to\infty)=k$, finite in the thermodynamic limit $N\rightarrow\infty$, which approaches $k=R(t\to 0)$ in this limit.

cond-mat.dis-nn↗

arXiv2018

Quench dynamics of 1D Bose gas in an optical lattice: does the system relax?

Understanding the relaxation process is the most important unsolved problem in non-equilibrium quantum physics. Current understanding primarily concerns on if and how an isolated quantum many-body system thermalize. However, there is no clear understanding of what conditions and on which time-scale do thermalization occurs. In this article, we simulate the quench dynamics of one-dimensional Bose gas in an optical lattice from an{\it {ab initio}} perspective by solving the time-dependent many-boson Schrödinger equation using the multi-configurational time-dependent Hartree method for bosons (MCTDHB). We direct a superfluid (SF) to Mott-insulator (MI) transition by performing two independent quenches: an interaction quench when the interaction strength is changed instantaneously, and a lattice depth quench where the depth of the lattice is altered suddenly. We show that although the Bose-Hubbard model predicts identical physics, the general many-body treatment shows significant differences between the two cases. We observe that lattice depth quench exhibits a large time-scale to reach the MI state and shows an oscillatory phase collapse-revival dynamics and a complete absence of thermalization that reveals through the analysis of the time-evolution of the reduced one-body density matrix, two-body density, and entropy production. In contrast, the interaction quench shows a swift transition to the MI state and shows a clear signature of thermalization for strong quench values. We provide a physical explanation for these differences and prescribe an analytical fitting formula for the time required for thermalization.

cond-mat.quant-gas↗

arXiv2016

Piezoelectric Domains in the AlGaN Hexagonal Microrods: Effect of Crystal Orientations

Presently, the piezoelectric materials are finding tremendous applications in the micro-mechanical actuators, sensors and self-powered devices. In this context, the studies pertaining to piezoelectric properties of materials in the different size ranges are very important for the scientific community. The III-nitrides are exceptionally important, not only for optoelectronic but also for their piezoelectric applications. In the present study, we synthesized AlGaN via self catalytic vapor-solid mechanism by atmospheric pressure chemical vapor deposition technique on AlN base layer over intrinsic Si(100) substrate. The growth process is substantiated using X-ray diffraction and X-ray photoelectron spectroscopy. The Raman and photoluminescence study reveal the formation of AlGaN microrods in the wurtzite phase and ensures the high optical quality of the crystalline material. The single crystalline, direct wide band gap and hexagonally shaped AlGaN microrods are studied for understanding the behavior of the crystallites under the application of constant external electric field using the piezoresponse force microscopy. The present study is mainly focused on understanding the behavior of induced polarization for the determination of piezoelectric coefficient of AlGaN microrod along the c-axis and imaging of piezoelectric domains in the sample originating because of the angular inclination of AlGaN microrods with respect to its AlN base layers.

cond-mat.mtrl-sci↗

arXiv2015

Direct Evidence of Mg Incorporation Pathway in Vapor-Liquid-Solid Grown p-type Nonpolar GaN Nanowires

Doping of III-nitride based compound semiconductor nanowires is still a challenging issue to have a control over the dopant distribution in precise locations of the nanowire optoelectronic devices. Knowledge of the dopant incorporation and its pathways in nanowires for such devices is limited by the growth methods. We report the direct evidence of incorporation pathway for Mg dopants in p-type nonpolar GaN nanowires grown via vapour-liquid-solid (VLS) method in a chemical vapour deposition technique for the first time. Mg incorporation is confirmed using X-ray photoelectron (XPS) and electron energy loss spectroscopic (EELS) measurements. Energy filtered transmission electron microscopic (EFTEM) studies are used for finding the Mg incorporation pathway in the GaN nanowire. Photoluminescence studies on Mg doped GaN nanowires along with the electrical characterization on heterojunction formed between nanowires and n-Si confirm the activation of Mg atoms as p-type dopants in nonpolar GaN nanowires.

cond-mat.mtrl-sci↗

arXiv2015

On some characterizations of strong power graphs of finite groups

Let $ G $ be a finite group of order $ n$. The strong power graph $\mathcal{P}_s(G) $ of $G$ is the undirected graph whose vertices are the elements of $G$ such that two distinct vertices $a$ and $b$ are adjacent if $a^{{m}_1}$=$b^{{m}_2}$ for some positive integers ${m}_1 ,{m}_2 < n$. In this article we classify all groups $G$ for which $\mathcal{P}_s(G)$ is line graph and Caley graph. Spectrum and permanent of the Laplacian matrix of the strong power graph $\mathcal{P}_s(G)$ are found for any finite group $G$.

math.CO↗

arXiv2014

Density of states in graphene with vacancies: midgap power law and frozen multifractality

The density of states (DoS), $\varrho(E)$, of graphene is investigated numerically and within the self-consistent T-matrix approximation (SCTMA) in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies, $n_\text{A}$ and $n_\text{B}$, in both sub-lattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The prediction of the non-linear sigma-model for this class is a Gade-type singularity $\varrho(E) \sim |E|^{-1}\exp(-|\log(E)|^{-1/x})$. Our numerical data is compatible with this result in a preasymptotic regime that gives way, however, at even lower energies to $\varrho(E)\sim E^{-1}|\log(E)|^{-\mathfrak{x}}$, $1\leq \mathfrak{x} < 2$. We take this finding as an evidence that similar to the case of dirty d-wave superconductors, also generic bipartite random hopping models may exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems.

cond-mat.mes-hall↗

arXiv2011

Quantum Size Effects in the Atomistic Structure of Armchair-Nanoribbons

Quantum size effects in armchair graphene nano-ribbons (AGNR) with hydrogen termination are investigated via density functional theory (DFT) in Kohn-Sham formulation. "Selection rules" will be formulated, that allow to extract (approximately) the electronic structure of the AGNR bands starting from the four graphene dispersion sheets. In analogy with the case of carbon nanotubes, a threefold periodicity of the excitation gap with the ribbon width (N, number of carbon atoms per carbon slice) is predicted that is confirmed by ab initio results. While traditionally such a periodicity would be observed in electronic response experiments, the DFT analysis presented here shows that it can also be seen in the ribbon geometry: the length of a ribbon with L slices approaches the limiting value for a very large width 1 << N (keeping the aspect ratio small N << L) with 1/N-oscillations that display the electronic selection rules. The oscillation amplitude is so strong, that the asymptotic behavior is non-monotonous, i.e., wider ribbons exhibit a stronger elongation than more narrow ones.

cond-mat.mes-hall↗

arXiv2010

Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions

We analyze the critical behavior of the dephasing rate induced by short-range electron-electron interaction near an Anderson transition of metal-insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in $2+ε$ dimensions) with numerical simulations on the Chalker-Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.

cond-mat.mes-hall↗

arXiv2010

Diffusion and criticality in undoped graphene with resonant scatterers

A general theory is developed to describe graphene with arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the minimal conductivity of graphene with resonant scatterers. In the case of smooth resonant impurities conductivity grows logarithmically with increasing impurity concentration, in agreement with renormalization group analysis for the symmetry class DIII. For vacancies (or strong on-site potential impurities) the conductivity saturates at a constant value that depends on the vacancy distribution among two sublattices as expected for the symmetry class BDI.

cond-mat.mes-hall↗

arXiv2010

Elastic properties of graphene flakes: boundary effects and lattice vibrations

We present a calculation of the free energy, the surface free energy and the elastic constants ("Lam'e parameters" i.e, Poisson ratio, Young's modulus) of graphene flakes on the level of the density functional theory employing different standard functionals. We observe that the Lam'e parameters in small flakes can differ from the bulk values by 30% for hydrogenated zig-zag edges. The change results from the edge of the flake that compresses the interior. When including the vibrational zero point motion, we detect a decrease in the bending rigidity by ~26%. This correction is depending on the flake size, N, because the vibrational frequencies flow with growing N due to the release of the edge induced compression. We calculate Grueneisen parameters and find good agreement with previous authors.

cond-mat.mes-hall↗

arXiv2005

Ion-beam induced 1D to 3D periodic transformation in nanostructured multilayers

Ion-irradiation-induced modifications of a periodic Pt/C multilayer system containing Fe impurity have been analyzed by transmission electron microscopy (TEM). The multilayer stack with 16 Pt/C layer pairs (period 4.23 nm) was fabricated on a glass substrate. A 2 MeV Au$^{2+}$ ion beam was rastered on the sample to obtain uniformly irradiated strips with fluences from 1$\times10^{14}$ to 1$\times10^{15}$ $ions/cm^2$. Ion-irradiation has been found to cause preferential migration of Fe towards Pt layers [Nucl. Instr. Methods Phys. Res. B212 (2003) 530]. Cross-sectional transmission electron microscopy (XTEM) shows considerable atomic redistribution for irradiation at the highest ion fluence (1$\times10^{15}$ $ions/cm^2$). Individual entities in this structure is like a cluster. Periodic multilayers have periodicity only in the direction normal to the multilayer surface. However, Fourier transform of the XTEM images of the sample irradiated at the highest-fluence shows new off-normal Fourier components of superlattice periodicities arising due to ion irradiation. With a proper understanding of this phenomenon it may be possible to fabricate three dimensional periodic structures of nanoclusters.

cond-mat.mtrl-sci↗