arXiv subjects

Nirmalendu Acharyya

Publications and source records attributed to Nirmalendu Acharyya.

At least 19 recordsLinked to original sources

arXiv2026

The fate of chiral symmetry in two-flavor matrix adjoint QC$_2$D

In the matrix model of two-flavor adjoint QC$_2$D, we study the low-lying states and their properties in the intermediate-to-strong (Yang-Mills) coupling regime. The model has a classical $SU(2)_R$ chiral symmetry and the eigenstates of the Hamiltonian can be organized in its irreps. We construct the energy eigenstates in presence of a chiral chemical potential $c$ using the variational techniques. We find that when $c=0$, the ground state is always a $SU(2)_R$ singlet, irrespective of the coupling strength $g$. However, as $g$ is tuned from intermediate to strong coupling, the system under goes a crossover from a unique to a doubly degenerate ground state. The degeneracy in the strong coupling regime spontaneously breaks the axial $\mathbb{Z}_8$, while preserving the chiral symmetry. When $c \neq 0$, we find that there can be level crossings which correspond to quantum phase transitions (QPTs). Depending on the ground state, there are three possible phases. The $SU(2)_R$ symmetry is spontaneously broken in only one of these phases, and this phase can only emerge for intermediate $g$ with moderate values of $c$. In the $g-c$ plane this phase corresponds to a narrow window, outside which $SU(2)_R$ is always preserved.

hep-th↗

arXiv2026

Quantum phases at high chemical potential in 2-flavor matrix-QC$_2$D

We investigate the matrix model of two-color two-flavor QCD (matrix-QCD$_{2,2}$) in regimes with large baryon ($μ_{_B}$), isospin ($μ_{_I}$), and/or chiral ($c$) chemical potentials. In these regimes, the Hamiltonian simplifies considerably, making it possible to investigate the ground state for intermediate and strong Yang-Mills coupling. By diagonalizing the Hamiltonian using the variational techniques, we show that in regimes where $μ_{_B}$ and $c$ (or $μ_{_B}$ and $μ_{_I}$) dominate, tuning the remaining parameters leads to quantum phase transitions (QPTs). These transitions form a complex web of phases, each of which has a ground state uniquely labelled by baryon number $B$ and isospin $I$. Several of these phases are LOFF-like, characterized by a ground state carrying non-zero spin and hence spontaneously breaking rotational symmetry. These results are consistent with older effective field theory predictions by Splittorff-Son-Stephanov \cite{Splittorff:2000mm}. The fermionic content of these LOFF-like ground states consists of spin-1 di-(anti-) quarks which are analogous to Cooper pairs. We compute the spin-fraction carried by the quarks and find that it constitutes a significant portion -- in some cases nearly the entirety -- of the total spin.

hep-th↗

arXiv2026

Localization-delocalization transition at weak coupling in two-color matrix QCD

We numerically investigate the matrix model of two-color one-flavor adjoint QCD (matrix-QCD$_{2,1}^{\text{adj}}$) in the weak coupling regime (small $g$) and in the chiral limit. The Yang-Mills potential has two distinct gauge invariant minima: one at $A_i=0$ and the other at $A_i = \frac{σ_i}{2g}$. We show that when the chiral chemical potential $c \leq \frac{3}{2}$, there is a quantum phase transition at $g_0^\ast \simeq 0.143$: for $g g_0^\ast$, the ground state is delocalized over the gauge configuration space. The transition between these two phases is singular, with the ground state at $g_0^\ast$ being distinctly different from that of $g_0^\ast \pm|ε|$. At $g_0^\ast$, we show that the square of the chromoelectric field vanishes, strongly suggesting that the system is in a ``dual superconductor" phase. Numerical evidence shows that the localization-delocalization phenomenon holds for the 1st and 2nd excited states as well, leading us to conjecture that there are an infinite number of isolated singular points $g_0^\ast> g_1^\ast>g_2^\ast> \cdots$ accumulating to $g=0$. For $c=1$, the model formally possesses $\mathcal{N}=1$ supersymmetry. We show that in the localized phase (i.e. for $g<g_0^\ast$) the supermultiplet structure is disrupted and SUSY is spontaneously broken.

hep-th↗

arXiv2024

The matrix model of two-color one-flavor QCD: The ultra-strong coupling regime

Using variational methods, we numerically investigate the matrix model for the two-color QCD coupled to a single quark (matrix-QCD$_{2,1}$) in the limit of ultra-strong Yang-Mills coupling ($g =\infty$). The spectrum of the model has superselection sectors labelled by baryon number $B$ and spin $J$. We study sectors with $B=0,1,2$ and $J=0,1$, which may be organized as mesons, (anti-)diquarks and (anti-)tetraquarks. For each of these sectors, we study the properties of the respective ground states in both chiral and heavy quark limits, and uncover a rich quantum phase transition (QPT) structure. We also investigate the division of the total spin between the glue and the quark and show that glue contribution is significant for several of these sectors. For the $(B,J)=(0,0)$ sector, we find that the dominant glue contribution to the ground state comes from reducible connections. Finally, in the presence of non-trivial baryon chemical potential $μ$, we construct the phase diagram of the model. For sufficiently large $μ$, we find that the ground state of the theory may have non-zero spin.

hep-th↗

arXiv2022

Edge states and anomalous SUSY in (2+1)-dimensional Maxwell Chern-Simons theory

In a $(2+1)$-dimensional Maxwell-Chern-Simons theory coupled with a fermion and a scalar, which has $\mathcal{N}=2$ SUSY in absence of the boundary, the insertion of a spatial boundary breaks the supersymmetry. We show that only a subset of the boundary conditions allowed by the self-adjointness of the Hamiltonian can preserve partial $\mathcal{N}=1$ supersymmetry, while for the remaining boundary conditions SUSY is completely broken. In the latter case, we demonstrate two distinct SUSY-breaking mechanisms. For some of the SUSY-breaking boundary conditions, the SUSY variation of the action does not vanish which explicitly breaks SUSY. While for certain other boundary conditions, despite the invariance of action under SUSY transformations, unpaired fermionic edge states in the domain of the Hamiltonian leads to an anomalous breaking of the supersymmetry.

hep-th↗

arXiv2021

On the Role of Non-Diagonal System-Environment Interactions in Bridge-Mediated Electron Transfer

Bridge-mediated electron transfer (ET) between a donor and an acceptor is prototypical for the description of numerous most important ET scenarios. While multi-step ET and the interplay of sequential and direct superexchange transfer pathways in the donor-bridge-acceptor (D-B-A) model is increasingly understood, the influence off-diagonal system-bath interactions on the transfer dynamics is less explored. Off-diagonal interactions account for the dependence of the ET coupling elements on nuclear coordinates (non-Condon effects) and are typically neglected. Here we numerically investigate with quasi-adiabatic propagator path integral (QUAPI) simulations the impact of off-diagonal system-environment interactions on the transfer dynamics for a wide range of scenarios in the D-B-A model. We demonstrate that off-diagonal system-environment interactions can have profound impact on the bridge-mediated ET dynamics. In the considered scenarios the dynamics itself does not allow for a rigorous assignment of the underlying transfer mechanism. Further, we demonstrate how off-diagonal system-environment interaction mediates anomalous localization by preventing long-time depopulation of the bridge B and how coherent transfer dynamics between donor D and acceptor A can be facilitated. The arising non-exponential short-time dynamics and coherent oscillations are interpreted within an equivalent Hamiltonian representation of a primary reaction coordinate model that reveals how the complex vibronic interplay of vibrational and electronic degrees of freedom underlying the non-Condon effects can impose donor-to-acceptor coherence transfer on short timescales.

physics.chem-ph↗

arXiv2021

Axial Anomaly in the $SU(N)$ Gauge Matrix Model

The $SU(N)$ Yang-Mills matrix model admits self-dual and anti-self-dual instantons. When coupled to $N_f$ flavors of massless quarks, the Euclidean Dirac equation in an instanton background has $n_+$ positive and $n_-$ negative chirality zero modes. We show that the index $(n_+ - n_-)$ is equal to a suitably defined instanton charge. Further, we show that the path integral measure is not invariant under a chiral rotation, and relate the non-invariance of the measure to the index of the Dirac operator. Axial symmetry is broken anomalously, with the residual symmetry being a finite group. For $N_f$ fundamental fermions, this residual symmetry is $\mathbb{Z}_{2N_f}$, whereas for adjoint quarks it is $\mathbb{Z}_{4N_f}$.

hep-th↗

arXiv2020

Coherent Dynamics of the Off-Diagonal Spin-Boson Model in the Ultra-Strong Coupling Regime

Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment leading to an irreversible loss of coherence. The Spin-Boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains largely unexplored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteractive effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and non-equilibrium quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel opportunities to exploit coherence as a resource in quantum devices operating in the ultra-strong coupling regime.

physics.chem-ph↗

arXiv2019

Large Q factor with very small Whispering Gallery Modes resonators

Efficient micro-resonators simultaneously require a large quality factor $Q$ and a small volume $V$. However, the former is ultimately limited by bending losses, the unavoidable radiation of energy of a wave upon changing direction of propagation. Such bending losses increase exponentially as $V$ decreases and eventually result in a drop of $Q$. Therefore, circular cavities are generally designed with radii that are much larger than the optical wavelength. The same leakage of energy by radiation limits the sharpness of bends in photonic integrated circuits. In this article, we present a way to reduce bending losses in circular micro-resonators. The proposed scheme consists of one or more external dielectric rings that are concentric with the cavity. These rings alter the field outside the cavity where radial oscillations set in, and thus control the far field radiation. As a result, the $Q$ factor can be increased by several orders of magnitude while keeping a small cavity volume.

physics.optics↗

arXiv2017

Matrix Model of QCD: Edge Localized Glue Balls and Phase Transitions

In a matrix model of pure $SU(2)$ Yang-Mills theory, boundaries emerge in the space of $\textrm{Mat}_{3}(\mathbb{R})$ and the Hamiltonian requires boundary conditions. We show the existence of edge localized glueball states which can have negative energies. These edge levels can be lifted to positive energies if the gluons acquire a London-like mass. This suggests a new phase of QCD with an incompressible bulk.

hep-th↗

arXiv2017

Multiple critical coupling and sensing in a microresonator-waveguide system

We study the optical transmission of a waveguide that is side-coupled to a high-$Q$ circular microresonator. The coupling is critical if the intrinsic resonator losses equate the coupling losses to the waveguide. When this happens, the transmittance of the waveguide displays resonance dips with maximal depth as the frequency is swept through the resonators resonances. We show that multiple configurations, parameterised by the minimal distance between the resonator and the waveguide, can lead to critical coupling. Indeed, for a sufficiently large resonator radius, the flow of power between the waveguide and the resonator can change sign several times within a single pass. This leads to an oscillatory coupling parameter as a function of the separation distance. As a result, multiple geometrical configurations can lead to critical coupling, even if the waveguide lies in the equatorial plane of the resonator. These results are explained using coupled-mode theory and full wave numerical simulations. In the vicinity of secondary or higher-order critical coupling, the depth of the transmittance dip is very sensitive to the environment. We discuss how this effect can be exploited for sensing purpose. Alternatively, by actively controlling the environment in the secondary critical configuration, the waveguide/resonator system can be driven as an optical switch.

physics.optics↗

arXiv2017

Glueball Spectra from a Matrix Model of Pure Yang-Mills Theory

We present variational estimates for the low-lying energies of a simple matrix model that approximates $SU(3)$ Yang-Mills theory on a three-sphere of radius $R$. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling $g$ as a function of $R$. This RG equation allows to estimate the masses of other glueball states, which we find to be in excellent agreement with lattice simulations.

hep-th↗

arXiv2016

Dispersion relations and bending losses of cylindrical and spherical shells, slabs, and slot waveguides

We derive formulas for Whispering Gallery Mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent waveguides. The derivation is based on a WKB treatment of Helmholtz equation and can in principle be extended to any number of concentric shells. A distinctive limit analytically arises in the analysis when two shells are brought at very close distance to one another. In that limit, the two shells act as a slot waveguide. If the two shells are sufficiently apart, we identify a structural resonance between the individual shells, which can either lead to a substantial enhancement or suppression of radiation losses.

physics.optics↗

arXiv2016

BRST Symmetry: Boundary Conditions and Edge States in QED

In manifolds with spatial boundary, BRST formalism can be used to quantize gauge theories. We show that, in a $U(1)$ gauge theory, only a subset of all the boundary conditions allowed by the self-adjointness of the Hamiltonian preserves BRST symmetry. Hence, the theory can be quantized using BRST formalism only when that subset of boundary conditions is considered. We also show that for such boundary conditions, there exist fermionic states which are localized near the boundary.

hep-th↗

arXiv2015

Supersymmetry: Boundary Conditions and Edge States

When spatial boundaries are inserted, SUSY can be broken. We show that in an $\mathcal{N}=2$ supersymmetric theory, all the boundary conditions allowed by self-adjointness of the Hamiltonian break $\mathcal{N}=2$ SUSY while only a few of these boundary conditions preserve $\mathcal{N}=1$ SUSY. We also show that for a subset of the boundary conditions compatible with $\mathcal{N}=1$ SUSY, there exist fermionic ground states which are localized near the boundary.

hep-th↗

arXiv2014

Monopoles, Dirac operator and index theory for fuzzy ${SU(3)}/({U(1)\times U(1)})$

The intersection of the 10-dimensional fuzzy conifold $Y_F^{10}$ with $S^5_F \times S^5_F$ is the compact 8-dimensional fuzzy space $X_F^8$. We show that $X_F^8$ is (the analogue of) a principal $U(1)\times U(1)$ bundle over fuzzy ${SU(3)}/({U(1) \times U(1)}) \left(\equiv\mathcal{M}^6_F\right)$. We construct $\mathcal{M}_F^6$ using the Gell-Mann matrices by adapting Schwinger's construction. The space $\mathcal{M}_F^6$ is of relevance in higher dimensional quantum Hall effect and matrix models of $D$-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of $SU(3)$ eigenvectors. We construct the Dirac operator on $\mathcal{M}_F^6$ from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

hep-th↗

arXiv2014

Quantum Entropy for the Fuzzy Sphere and its Monopoles

Using generalized bosons, we construct the fuzzy sphere $S_F^2$ and monopoles on $S_F^2$ in a reducible representation of $SU(2)$. The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent non-abelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

hep-th↗

arXiv2013

Fuzzy Conifold $Y_F^6$ and Monopoles on $S_F^2\times S_F^2$

In this article, we construct the fuzzy (finite dimensional) analogues of the conifold $Y^6$ and its base $X^5$. We show that fuzzy $X^5$ is (the analogue of) a principal U(1) bundle over fuzzy spheres $S^2_F \times S^2_F$ and explicitly construct the associated monopole bundles. In particular our construction provides an explicit discretization of the spaces $T^{κ,κ}$ and $T^{κ,0}$.

hep-th↗