arXiv subjects

Abhishek Mukherjee

Publications and source records attributed to Abhishek Mukherjee.

At least 19 recordsLinked to original sources

arXiv2026

Trace Coordinates and Local Fenchel--Nielsen Parameters in Real Hyperbolic 5-Space

We study representations of fundamental groups of closed orientable surfaces into $\mathrm{SL}(2,\mathbb{H})$, whose projectivization $\mathrm{PSL}(2,\mathbb{H})$ is the group of orientation-preserving isometries of real hyperbolic $5$-space, with the aim of developing a quaternionic analogue of Fenchel--Nielsen theory. We give a normal form for pairs of regular loxodromic elements with disjoint fixed point sets and show that, on an open dense generic locus, the corresponding moduli space is $15$-dimensional. We also associate fifteen word traces whose differentials are linearly independent on an open dense subset and hence give local real-analytic coordinates there. For a pair of pants with prescribed regular loxodromic boundary conjugacy classes, we show that the relative deformation space is locally $6$-dimensional. Combining this internal pants data with the three-dimensional boundary conjugacy data and the three-dimensional centralizer gluing freedom gives a local parameter decomposition for closed surface group representations. For a closed surface of genus $g$, this yields $30g-30$ real parameters.

math.GT↗

arXiv2026

Large Transverse Thermoelectric Effect in Weyl Semimetal TaIrTe$_4$ Engineered for Photodetection

Anomalous local photocurrent generation via second-order nonlinear and thermoelectric responses is a signature of many topological semimetals. The emergence of these photocurrents is inherently linked to symmetry breaking and anisotropy of their crystal lattices. Studies of type-II Weyl semimetals of group C$_{2v}$ (WTe$_2$, MoTe$_2$, TaIrTe$_4$) have reported anomalous, nonlocal photocurrents localized to crystals edges or far from electrodes, which are highly dependent on the geometry of the material sample. While originally attributed to a nonlinear charge current response, it was recently shown that these currents could instead be attributed to the anisotropic Seebeck coefficients of the materials. Here, we confirm that anomalous photocurrents observed in TaIrTe$_4$ under either visible or far-infrared far-field illumination originate from the large transverse thermoelectric effect. We engineer the mutual orientation of crystal edges and electrodes as well as the thermal environment of TaIrTe$_4$ to control and amplify its spatial photocurrent response. We show that substrate engineering can locally enhance photocurrent. This framework of thermal device engineering can enable broadband photo detection schemes by leveraging spectral and spatial dependence of photocurrents for applications like wavefront sensing, beam positioning, and edge detection.

cond-mat.mtrl-sci↗

arXiv2026

Algebraic characterization of reversibility in the quaternionic Möbius group

An element of a group is called \emph{reversible} if it is conjugate to its inverse. While reversibility in the quaternionic Möbius group $\mathrm{PSL}(2,\mathbb{H})$ has traditionally been studied using geometric and dynamical methods, we develop a purely algebraic approach. We obtain an explicit, computable criterion for the reversibility of a quaternionic Möbius transformation, expressed solely in terms of the entries of a matrix representative. More precisely, we prove that \[ [A]\in \mathrm{PSL}(2,\mathbb{H}) \text{ is reversible} \quad \Longleftrightarrow \quad β_A^{2}=δ_A^{2}, \] where $β_A$ and $δ_A$ are real conjugacy invariants associated with a lift $A\in \mathrm{SL}(2,\mathbb{H})$. Furthermore, we give a complete characterization of reversing symmetries of reversible elements in $\mathrm{SL}(2,\mathbb{H})$ and $\mathrm{PSL}(2,\mathbb{H})$.

math.GT↗

arXiv2025

Thermal and dimensional stability of photocatalytic material ZnPS$_3$ under extreme environmental conditions

Zinc phosphorus trisulfide (ZnPS$_3$), a promising material for photocatalysis and energy storage, is shown in this study to exhibit remarkable stability under extreme conditions. We explore its optical and structural properties under high pressure and cryogenic temperatures using photoluminescence (PL) spectroscopy, Raman scattering, and density functional theory (DFT). Our results identify a pressure-induced phase transition starting at 6.75 GPa and stabilizing by 12.5 GPa, after which ZnPS$_3$ demonstrates robust stability across a broad pressure range of 15 to 100 GPa. DFT calculations predict a semiconductor-to-semimetal transition at 100 GPa, while PL measurements reveal defect-assisted emissions that quench under pressure due to enhanced non-radiative recombination. At cryogenic temperatures, PL quenching intensifies as non-radiative processes dominate, driven by a rising Grüneisen parameter and reduced phonon population. Cryogenic X-ray diffraction (XRD) also reveals a high mean thermal expansion coefficient (TEC) of (4.369 $\pm$ 0.393) $\times$ 10$^{-5}$ K$^{-1}$, among the highest reported for 2D materials. This unique combination of tunable electronic properties under low pressure and high thermal sensitivity makes ZnPS$_3$ a strong candidate for sensing applications in extreme environments.

cond-mat.mtrl-sci↗

arXiv2024

Defect-Induced Strain-Tunable Photoluminescence in AgScP$_2$S$_6$

Metal thiophosphates (MTPs) are a large family of 2D materials that exhibit large structural and chemical diversity. They also show promise for applications in energy harvesting and photodetection. Strain and defect engineering have previously been demonstrated as useful mechanisms to tune several properties of MTPs such as resistivity, magnetic state, and electronic band gap. However, the effect of these stimuli on engineering tunable light emission in MTPs remains unexplored. Here, we show experimentally that structural defects in metal thiophosphate AgScP$_2$S$_6$ are prominent in exhibiting photoluminescence, which is likely driven by the defect-state-to-conduction-band transitions and can be further tuned by temperature-induced strain gradients.

physics.optics↗

arXiv2022

Forest density is more effective than tree rigidity at reducing the onshore energy flux of tsunamis: Evidence from Large Eddy Simulations with Fluid-Structure Interactions

Communities around the world are increasingly interested in nature-based solutions to mitigation of coastal risks like coastal forests, but it remains unclear how much protective benefits vegetation provides, particularly in the limit of highly energetic flows after tsunami impact. The current study, using a three-dimensional incompressible computational fluid dynamics model with a fluid-structure interaction approach, aims to quantify how energy reflection and dissipation vary with different degrees of rigidity and vegetation density of a coastal forest. We represent tree trunks as cylinders and use the elastic modulus of hardwood trees such as pine or oak to characterize the rigidity of these cylinders. The numerical results show that energy reflection increases with rigidity only for a single cylinder. In the presence of multiple cylinders, the difference in energy reflection created by varying rigidity diminishes as the number of cylinders increases. Instead of rigidity, we find that the blockage area created by the presence of multiple tree trunks dominates energy reflection. As tree trunks are deformed by the hydrodynamic forces, they alter the flow field around them, causing turbulent kinetic energy generation in the wake region. As a consequence, trees dissipate flow energy, highlighting coastal forests reducing the onshore energy flux of tsunamis by means of both reflection and dissipation.

physics.flu-dyn↗

arXiv2021

Discreteness Of Hyperbolic Isometries by Test Maps

Let $\mathbb F=\mathbb R$, $\mathbb C$ or $\mathbb H$. Let ${\bf H}_{\mathbb F}^n$ denote the $n$-dimensional $\mathbb F$-hyperbolic space. Let ${\rm U}(n,1; \mathbb F)$ be the linear group that acts by the isometries. A subgroup $G$ of ${\rm U}(n,1; \mathbb F)$ is called \emph{Zariski dense} if it does not fix a point on the closure of the $\mathbb F$-hyperbolic space, and neither it preserves a totally geodesic subspace of it. We prove that a Zariski dense subgroup $G$ of ${\rm U}(n,1; \mathbb F)$ is discrete if for every loxodromic element $g \in G$, the two generator subgroup $\langle f, g \rangle$ is discrete, where $f \in {\rm U}(n,1; \mathbb F)$ is a test map not necessarily from $G$.

math.GT↗

arXiv2018

Test map and Discreteness in SL(2, $\mathbb H$)

Let SL(2, $\mathbb H$) be the group of $2 \times 2$ quaternionic matrices $A=\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ with quaternionic determinant $\det A=|ad-aca^{-1} b|=1$. This group acts by the orientation-preserving isometries of the five dimensional (real) hyperbolic space. We obtain discreteness criteria for Zariski-dense subgroups of SL(2, $\mathbb H$) using test maps.

math.GT↗

arXiv2015

Extremality of Quaternionic Jørgensen Inequality

Let ${\rm SL(2, \mathbb H)}$ be the group of $2 \times 2$ quaternionic matrices with Dieudonné determinant $1$. The group ${\rm SL(2, \mathbb H)}$ acts on the five dimensional hyperbolic space by isometries. We investigate extremality of Jørgensen type inequalities in ${\rm SL(2, \mathbb H)}$. Along the way, we derive Jørgensen type inequalities for quaternionic Möbius transformations which extend earlier inequalities obtained by Waterman and Kellerhals.

math.CV↗

arXiv2015

Constraining the nuclear energy density functional with quantum Monte Carlo calculations

We study the problem of an impurity in fully polarized (spin-up) low density neutron matter with the help of an accurate quantum Monte Carlo method in conjunction with a realistic nucleon-nucleon interaction derived from chiral effective field theory at next-to-next-to-leading-order. Our calculations show that the behavior of the proton spin-down impurity is very similar to that of a polaron in a fully polarized unitary Fermi gas. We show that our results can be used to put tight constraints on the time-odd parts of the energy density functional, independent of the time-even parts, in the density regime relevant to neutron-rich nuclei and compact astrophysical objects such as neutron stars and supernovae.

nucl-th↗

arXiv2014

Lefschetz thimble Monte Carlo for many body theories: application to the repulsive Hubbard model away from half filling

Recently, a new method, based on stochastic integration on the surfaces of steepest descent of the action, was introduced to tackle the sign problem in quantum field theories. We show how this method can be used in many body theories to perform fully non-perturbative calculations of quantum corrections about mean field solutions. We discuss an explicit algorithm for implementing our method, and present results for the repulsive Hubbard model away from half-filling at intermediate temperatures. Our results are consistent with those from the recent state of the art cluster dynamical mean field theory calculations.

cond-mat.str-el↗

arXiv2014

Quantum Monte Carlo calculations of neutron matter with non-local chiral interactions

We present fully non-perturbative quantum Monte Carlo calculations with non-local chiral effective field theory (EFT) interactions for the ground state properties of neutron matter. The equation of state, the nucleon chemical potentials and the momentum distribution in pure neutron matter up to one and a half times the nuclear saturation density are computed with a newly optimized chiral EFT interaction at next-to-next-to-leading order. This work opens the way to systematic order by order benchmarking of chiral EFT interactions, and \emph{ab initio} prediction of nuclear properties while respecting the symmetries of quantum chromodynamics.

nucl-th↗

arXiv2013

Monte Carlo simulations on the Lefschetz thimble: taming the sign problem

We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo calculations of models with complex actions can be softened significantly by changing the domain of integration to the Lefschetz thimble or approximations thereof. We study the interacting complex scalar field theory (relativistic Bose gas) in lattices of size up to 8^4 using a computationally inexpensive approximation of the Lefschetz thimble. Our results are in excellent agreement with known results. We show that - at least in the case of the relativistic Bose gas - the thimble can be systematically approached and the remaining residual phase leads to a much more tractable sign problem (if at all) than the original formulation. This is especially encouraging in view of the wide applicability - in principle - of our method to quantum field theories with a sign problem. We believe that this opens up new possibilities for accurate Monte Carlo calculations in strongly interacting systems of sizes much larger that previously possible.

hep-lat↗

arXiv2013

Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model

We propose a new algorithm based on the Metropolis sampling method to perform Monte Carlo integration for path integrals in the recently proposed formulation of quantum field theories on the Lefschetz thimble. The algorithm is based on a mapping between the curved manifold defined by the Lefschetz thimble of the full action and the flat manifold associated with the corresponding quadratic action. We discuss an explicit method to calculate the residual phase due to the curvature of the Lefschetz thimble. Finally, we apply this new algorithm to a simple one-plaquette model where our results are in perfect agreement with the analytic integration. We also show that for this system the residual phase does not represent a sign problem.

physics.comp-ph↗

arXiv2013

Quantum Monte Carlo with Coupled-Cluster wave functions

We introduce a novel many body method which combines two powerful many body techniques, viz., quantum Monte Carlo and coupled cluster theory. Coupled cluster wave functions are introduced as importance functions in a Monte Carlo method designed for the configuration interaction framework to provide rigorous upper bounds to the ground state energy. We benchmark our method on the homogeneous electron gas in momentum space. The importance function used is the coupled cluster doubles wave function. We show that the computational resources required in our method scale polynomially with system size. Our energy upper bounds are in very good agreement with previous calculations of similar accuracy, and they can be systematically improved by including higher order excitations in the coupled cluster wave function.

nucl-th↗

arXiv2013

Level densities of nickel isotopes: microscopic theory versus experiment

We apply a spin-projection method to calculate microscopically the level densities of a family of nickel isotopes $^{59-64}$Ni using the shell model Monte Carlo approach in the complete $pfg_{9/2}$ shell. Accurate ground-state energies of the odd-mass nickel isotopes, required for the determination of excitation energies, are determined using the Green's function method recently introduced to circumvent the odd particle-number sign problem. Our results are in excellent agreement with recent measurements based on proton evaporation spectra and with level counting data at low excitation energies. We also compare our results with neutron resonance data, assuming equilibration of parity and a spin-cutoff model for the spin distribution at the neutron binding energy, and find good agreement with the exception of $^{63}$Ni.

nucl-th↗

arXiv2013

Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas

We develop a quantum Monte Carlo method to estimate the ground-state energy of a fermionic many-particle system in the configuration-interaction shell model approach. The fermionic sign problem is circumvented by using a guiding wave function in Fock space. The method provides an upper bound on the ground-state energy whose tightness depends on the choice of the guiding wave function. We argue that the antisymmetric geminal product class of wave functions is a good choice for guiding wave functions. We demonstrate our method for the trapped two-species fermionic cold atom system in the unitary regime of infinite scattering length using the particle-number projected Hartree-Fock-Bogoliubov wave function as the guiding wave function. We estimate the ground-state energy and energy-staggering pairing gap as a function of the number of particles. Our results compare favorably with exact numerical diagonalization results and with previous coordinate-space Monte Carlo calculations.

nucl-th↗

arXiv2012

Odd-particle systems in the shell model Monte Carlo: circumventing a sign problem

We introduce a novel method within the shell model Monte Carlo approach to calculate the ground-state energy of a finite-size system with an odd number of particles by using the asymptotic behavior of the imaginary-time single-particle Green's functions. The method circumvents the sign problem that originates from the projection on an odd number of particles and has hampered direct application of the shell model Monte Carlo method to odd-particle systems. We apply this method to calculate pairing gaps of nuclei in the iron region. Our results are in good agreement with experimental pairing gaps.

nucl-th↗