arXiv subjects

Sirshendu Bhattacharyya

Publications and source records attributed to Sirshendu Bhattacharyya.

13 recordsLinked to original sources

arXiv2026

Selection Rules for Species Coexistence in a Hierarchical May-Leonard Model

One of the central challenges in evolutionary dynamics is understanding why some species combinations persist while others disappear. Although cyclic-interaction models have provided fundamental insights into biodiversity maintenance, much less is known about how hierarchical competitive interactions shape long-term community organization. Here, we investigate a hierarchical extension of the May-Leonard model, in which species interact through a directed predation chain while undergoing reproduction and mortality. Combining mean-field analysis with Monte Carlo simulations, we show that the fully coexisting state is generically unstable, causing the dynamics to evolve toward lower-dimensional coexistence states. The simulations further reveal stochastic extinctions dominating small populations with the dynamics progressively approaching the mean-field predictions as the system size increases. Rather than permitting arbitrary species combinations, the hierarchical-interaction structure dynamically constrains coexistence by selecting only specific subsets of species for long-term persistence. We show that these admissible coexistence states have a natural graph-theoretic interpretation as independent sets in the hierarchical interaction network, thereby providing general constraints on coexistence in hierarchical communities. Together, these results establish a theoretical framework linking hierarchical interactions, dynamical selection, graph topology, and biodiversity organization, extending the classical May-Leonard model beyond cyclic competition.

q-bio.PE↗

arXiv2026

On the Relation Between String Order Parameters, Entanglement, and Dynamical Quantum Phase Transitions in Topological Dynamics

Topological order is defined by topological invariants, rather than symmetries and local order parameters. Nonetheless some topological phases can be characterized by string order parameters and entanglement. In this article we study how string order parameters and entanglement spectra behave out-of-equilibrium following quenches in one dimensional topological models with $\mathbb{Z}$ invariants. Previously it has been suggested that string order parameters could serve as an experimental probe of dynamical quantum phase transitions. Despite the existence of clear zeroes in the order parameters at critical times, we show that in general there is no exact quantitative or qualitative connection with the critical times of dynamical quantum phase transitions. Another possible connection is of dynamical string order parameter zeroes and dynamical crossings at the center of entanglement spectra. Here we see that there can sometimes be a connection, but it is not typical. Again there is no general quantitative or qualitative connection. Each dynamical form of criticality behaves independently, though we do see that critical times tend to be of the same order of magnitude and give an argument for why this is the case. We also find that a string order parameter which labels one topological phase can undergo non-trivial dynamics even following a quench between \emph{other} topological phases. We elucidate where connections can be made, and where they result from a consideration of insufficiently general models. These results cast doubt on the idea of genuine dynamical phases following quenches in such models.

cond-mat.str-el↗

arXiv2024

Topological phase transition in anti-symmetric Lotka-Volterra doublet chain

We present the emergence of topological phase transition in the minimal model of two dimensional rock-paper-scissors cycle in the form of a doublet chain. The evolutionary dynamics of the doublet chain is obtained by solving the anti-symmetric Lotka-Volterra equation. We show that the mass decays exponentially towards edges and robust against small perturbation in the rate of change of mass transfer, a signature of a topological phase. For one of the configuration of our doublet chain, the mass is transferred towards both edges and the bulk is gaped. Further, we confirm this phase transition within the framework of topological band theory. For this we calculate the winding number which change from zero to one for trivial and a non-trivial topological phases respectively.

cond-mat.stat-mech↗

arXiv2024

Emergence of first-order and second-order phase transitions in a cyclic ecosystem exposed to environmental impact

A cyclically dominating three-species ecosystem, modeled within the framework of rock-paper-scissor game, is studied in presence of natural death and an effect of the environment. The environmental impact is parameterized along with the death rates in the rate equation of the species densities. Monte-Carlo simulations on this system reveal that the population density bears the signature of first-order and second-order phase transitions in different regimes of the parameters representing natural deaths of the species. The connection of this phenomena with the phase transitions is also supported by the behavior of the basin entropy calculated for the system. The density of total population evidently becomes an order parameter with respect to the change in environmental impact on the system.

cond-mat.stat-mech↗

arXiv2024

Signature of quantum phase transition manifested in quantum fidelity at finite temperature

The signature of quantum phase transition is generally wiped out at finite temperature. A few quantities that have been observed to carry this signature through a nonanalytic behavior are also limited to low temperatures only. With an aim to identify a suitable dynamical quantity at a high temperature, we have recently constructed a function from quantum fidelity, which has the potential to bear a nonanalytic signature at the quantum critical point beyond low temperature regime. In this paper, we elaborate our earlier work and demonstrate the behavior of the corresponding rate function and the robustness of the nonanalyticity for a number of many-body Hamiltonians in different dimensions. We have also shown that our rate function reduces to that used in the demonstration of the dynamical quantum phase transition (DQPT) at zero temperature. It has been further observed that, unlike DQPT, the long time limit of the rate function can faithfully detect the equilibrium quantum phase transition as well.

cond-mat.stat-mech↗

arXiv2022

Optimizing the location of the colony of foragers with Collective Learning

Animal groups collaborate with one another throughout their lives to better comprehend their surroundings. Here, we try to model, using continuous random walks, how the entire process of birth, reproduction, and death might impact the searching process. We attempt to simulate an ecosystem where the post-reproductive foragers leave their colonies to discover where the targets are while others stay and breed at the base. Actually, a group of foragers searches for a location from where they access the targets for food supply. Particularly, we have explored a hypothetical situation in which the relocation to the new position depends on the agreement level of the species as well as an additional waiting time due to this agreement level. In this backdrop, detailed numerical results reveal that searching for an optimal position at an optimal mean time can be captured for a suitable range of the agreement level. We have also shown, for a given agreement level, the optimal mean time linearly increases with the Death-to-Birth ratio.

nlin.AO↗

arXiv2022

Detection of quantum phase boundary at finite temperatures in integrable spin models

Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. Here we identify a physical quantity that shows non-analytic behaviour at finite temperatures, when an interaction parameter is quenched across the line of quantum phase transition. This quantity under consideration is the long time limit of a form of quantum fidelity. Our treatment is analytic for XY chain and 2D Kitaev model and is numerical for a 3D Hamiltonian applicable to Weyl semimetals.

cond-mat.stat-mech↗

arXiv2022

Effect of mobility in the rock-paper-scissor dynamics with high mortality

In the evolutionary dynamics of a rock-paper-scissor (RPS) model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model becomes very sensitive towards this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mortality, we perform Monte Carlo simulation on a $2$-dimensional lattice having three cyclically-competing species. The spatio-temporal dynamics has been studied along with the two-site correlation function. Spatial distribution exhibits emergence of spiral patterns in the presence of diffusion. It reveals that the joint effect of death rate and diffusion (migration) leads to new coexistence and extinction scenarios.

cond-mat.stat-mech↗

arXiv2020

Exotic signature of dynamical quantum phase transition in the time evolution of engineered initial state

Dynamical phase transition in quantum many body systems is usually studied by taking it in the ground state and then quenching a parameter to a new value. We investigate here the dynamics when one performs the time evolution of a generic state and observe that the rate function related to the Loschmidt echo shows non-analytic behavior of two types, one related, and the other unrelated, to the appearance of a quantum phase transition. Specifically, we consider a quantum Ising chain in an initial configuration which is a generic superposition of the eigenstates, and follow its dynamics under the transverse Ising Hamiltonian with constant field. Depending on the the configuration of the initial state, some singularities appear in the rate function which do not correspond to the equilibrium phase transition of the Hamiltonian. However another class of singularity is found having connection with the quantum critical point. Some features of the singularities of the rate function have been derived analytically and it is observed that the occupancy of quasiparticle eigenstates plays the key role in triggering the non-analyticities.

cond-mat.stat-mech↗

arXiv2020

Mortality makes coexistence vulnerable in evolutionary game of rock-paper-scissors

Multiple species in the ecosystem are believed to compete cyclically for survival and thus maintain balance in nature. Stochasticity has also an inevitable role in this dynamics. Considering these attributes of nature, the stochastic dynamics of the rock-paper-scissor model based on the idea of cyclic dominance becomes an effective tool to capture different aspects of ecosystem. The evolutionary dynamics of this model crucially depends on different interactions representing different natural habits. In this framework we explore the role of mortality of individual organism in the collective survival of a species. For this purpose a new parameter called `natural death' is introduced. It is meant for bringing about the decease of an individual irrespective of any intra- and interspecific interaction. We perform Monte Carlo simulation followed by the stability analysis of different fixed points of defined rate equations and observe that the natural death rate is surprisingly one of the most significant factors in deciding whether an ecosystem would come up with a coexistence or a single species survival.

q-bio.PE↗

arXiv2017

Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states having product structure in fermionic momentum-space and satisfying certain criteria, produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field $Γ$. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. At each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically with an exponent which is invariant for all such special initial states. The frequency of this oscillation varies differently with external field in ordered and disordered phases. The local magnetization after infinite time also characterizes the quantum phase transition.

cond-mat.stat-mech↗

arXiv2015

Signature of a Continuous Quantum Phase Transition in Nonequilibrium Energy Absorption: Footprints of Criticality on Highly Excited States

Understanding phase transitions in quantum matters constitutes a significant part of present day condensed matter physics. Quantum phase transitions concern ground state properties of many-body systems, and hence their signatures are expected to be pronounced in low-energy states. Here we report signature of a quantum critical point manifested in strongly out-of-equilibrium states with finite energy density with respect to the ground state and extensive (subsystem) entanglement entropy, generated by an external pulse. These non-equilibrium states are evidently completely disordered (e.g., paramagnetic in case of a magnetic ordering transition). The pulse is applied by switching a coupling of the Hamiltonian from an initial value ($λ_{I}$) to a final value ($λ_{F}$) for sufficiently long time and back again. The signature appears as non-analyticities (kinks) in the energy absorbed by the system from the pulse as a function of $λ_{F}$ at critical-points (i.e., at values of $λ_{F}$ corresponding to static critical-points of the system). As one excites higher and higher eigenstates of the final Hamiltonian $H(λ_{F})$ by increasing the pulse height ($|λ_{I} - λ_{F}|$), the non-analyticity grows stronger monotonically with it. This implies adding contributions from higher eigenstates help magnifying the non-analyticity, indicating strong imprint of the critical-point on them. Our findings are grounded on exact analytical results derived for Ising and XY chains in transverse field.

cond-mat.stat-mech↗

arXiv2012

Transverse Ising Chain under Periodic Instantaneous Quenches: Dynamical Many-Body Freezing and Emergence of Solitary Oscillation

We study the real-time dynamics of a quantum Ising chain driven periodically by instantaneous quenches of the transverse field (the transverse field varying as rectangular wave symmetric about zero). Two interesting phenomena are reported and analyzed: (1) We observe dynamical many-body freezing or DMF (Phys. Rev. B, vol. 82, 172402, 2010), i.e. strongly non-monotonic freezing of the response (transverse magnetization) with respect to the driving parameters (pulse width and height) resulting from equivocal freezing behavior of all the many-body modes. The freezing occurs due to coherent suppression of dynamics of the many-body modes. For certain combination of the pulse height and period, maximal freezing (freezing peaks) are observed. For those parameter values, a massive collapse of the entire Floquet spectrum occurs. (2) Secondly, we observe emergence of a distinct solitary oscillation with a single frequency, which can be much lower than the driving frequency. This slow oscillation, involving many high-energy modes, dominates the response remarkably in the limit of long observation time. We identify this slow oscillation as the unique survivor of destructive quantum interference between the many-body modes. The oscillation is found to decay algebraically with time to a constant value. All the key features are demonstrated analytically with numerical evaluations for specific results.

quant-ph↗