arXiv subjects

Gautam Gangopadhyay

Publications and source records attributed to Gautam Gangopadhyay.

At least 19 recordsLinked to original sources

arXiv2025

Current and quantum transport factor of fermionic system in fermionic bath

This paper explores the dynamics of current and the quantum transport factor in a fermionic system with a central oscillator interacting with two fermionic reservoirs at different temperatures. We derive the master equation for the system density matrix, accounting for energy exchange between the system and the reservoirs. The current is analyzed in relation to system parameters and reservoir temperatures, revealing that the quantum transport factor differs from classical systems, approaching Carnot efficiency at high temperatures but being different at low temperatures. We also examine the power spectrum of the current, providing insights into current fluctuations and their temperature dependence. Furthermore, we derive the Fokker-Planck equation and the Glauber-Sudarshan P-representation, where the steady-state probability distribution takes a Gaussian form, confirming the system behaves like a harmonic oscillator. This work advances the understanding of quantum transport in fermionic systems and provides a foundation for future research in quantum thermodynamics.

quant-ph↗

arXiv2025

Current, quantum transport and entropic force of bosonic systems interacting with two thermal reservoirs

This paper investigates the dynamics of current and quantum transport factor in a bosonic system consisting of a central system interacting with two reservoirs at different temperatures. We derive a master equation describing the time evolution of the density matrix of the system, accounting for the interactions and energy transfer between the components. We quantify the current, representing the flow of bosons through the system and analyse its dependence on the system's parameters and temperatures of the thermal reservoirs. In the steady state regime, we derived an expression for the quantum transport factor of the energy transfer process. Our analysis show that quantum effects, such as the dependence on temperature can significantly impact this factor. In particular, we observe that the transport factor of the quantum system is greater than the corresponding factor when the temperature goes to infinity, where the factor has an identical form with the Carnot efficiency of an ideal heat engine. We then derived the Fokker-Planck equation to find out the Glauber-Sudarsan $P$-representation. In the steady state of the equation, the probability distribution comes out to be in Gaussian form. We then calculated the entropic force for this probability distribution which gives the Hooke's law in the steady state, in agreement with the fact that our system is a harmonic oscillator.

quant-ph↗

arXiv2023

Effect of neighbouring molecules on ground-state properties of many-body polar linear rotor systems

A path integral ground state approach has been used to estimate the ground-state energy and structural properties of hydrogen fluoride molecules pinned to a one-dimensional lattice. In the simulations, the molecules are assumed to be rigid, and only the continuous rotational degrees of freedom are considered. The constituents of a many-body system interact through the dipole-dipole interaction because the molecules have a permanent dipole moment. The workability of our approach has been demonstrated by estimating the ground-state energy, order parameter and nearest neighbour correlation for the systems of 2 and 3 HF molecules using quantum Monte Carlo simulations based on the path integral ground state methodology. The results agree satisfactorily with those obtained from exact Hamiltonian matrix diagonalization. In addition, the effect of neighbours on the ground state properties has been investigated for larger systems. The converged ground-state energy per neighbour as a function of inter-nuclear separation is considered to be the equation of state for the system. The chemical potential of the rotor chains also supports the convergence test.

physics.chem-ph↗

arXiv2023

Nonequilibrium thermodynamic signatures of collective dynamical states around chimera in a chemical reaction network

Different dynamical states ranging from coherent, incoherent to chimera, multichimera, and related transitions are addressed in a globally coupled nonlinear continuum chemical oscillator system by implementing a modified complex Ginzburg-Landau equation. Besides dynamical identifications of observed states using standard qualitative metrics, we systematically acquire nonequilibrium thermodynamic characterizations of these states obtained via coupling parameters. The nonconservative work profiles in collective dynamics qualitatively reflect the time-integrated concentration of the activator, and the majority of the nonconservative work contributes to the entropy production over the spatial dimension. It is illustrated that the evolution of spatial entropy production and semigrand Gibbs free energy profiles associated with each state are connected yet completely out of phase, and these thermodynamic signatures are extensively elaborated to shed light on the exclusiveness and similarities of these states. Moreover, a relationship between the proper nonequilibrium thermodynamic potential and the variance of activator concentration is established by exhibiting both quantitative and qualitative similarities between a Fano factor-like entity, derived from the activator concentration, and the Kullback-Leibler divergence associated with the transition from a nonequilibrium homogeneous state to an inhomogeneous state. Quantifying the thermodynamic costs for collective dynamical states would aid in efficiently controlling, manipulating, and sustaining such states to explore the real-world relevance and applications of these states.

cond-mat.stat-mech↗

arXiv2023

Entropic force for quantum particles

Entropic force has been drawing the attention of theoretical physicists following E. Verlinde's work in 2011 to derive Newton's second law and Einstein's field equations of general relativity. In this paper, we extend the idea of entropic force to the distribution of quantum particles. Starting from the definition of Shannon entropy for continuous variables, here we have derived quantum osmotic pressure as well as the consequent entropic forces for bosonic and fermionic particles. The entropic force is computed explicitly for a pair of bosons and fermions. The low temperature limit of this result show that the entropic force for bosons is similar to Hooke's law of elasticity revealing the importance of this idea in the formation of a Bose-Einstein condensate. For fermions, the low temperature limit boils down to the well known Neumann's radial force and also reveals the Pauli's exclusion principle. The classical limit of the entropic force between quantum particles is then discussed. As a further example, the entropic force for quantum particles in noncommutative space is also computed. The result reveals a violation of the Pauli exclusion principle for fermions in noncommutative space.

quant-ph↗

arXiv2022

Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions

An inhomogeneous profile of chemostatted species generates a rich variety of patterns in glycolytic waves depicted in a Selkov reaction-diffusion framework here. A key role played by diffusion amplitude and symmetry in the chemostatted species profile in dictating the fate of local spatial dynamics involving periodic, quasiperiodic, and chaotic patterns and transitions among them are investigated systematically. More importantly, various dynamic transitions, including wave propagation direction changes, are illustrated in interesting situations. Besides numerical results, our analytical formulation of the amplitude equation connecting complex Ginzburg-Landau and Lambda-omega representation shed light on the phase dynamics of the system. This systematic study of the glycolytic reaction-diffusion wave is in line with previous experimental results in the open spatial reactors and will provide knowledge about the dynamics that shape and control biological information processing and related phenomena.

nlin.AO↗

arXiv2022

Nonequilibrium thermodynamic characterization of chimeras in a continuum chemical oscillator system

The emergence of the chimera state as counterintuitive spatial coexistence of synchronous and asynchronous regimes is addressed here in a continuum chemical oscillator system by implementing a relevant complex Ginzburg-Landau equation with global coupling. This study systematically acquires and characterizes the evolution of nonequilibrium thermodynamic entities corresponding to the chimera state. The temporal evolution of the entropy production rate exhibits a beat pattern with a series of equidistant spectral lines in the frequency domain. Symmetric profiles associated with the incoherence regime appear in descriptions of the dynamics and thermodynamics of the chimera. It is shown that identifying the semigrand Gibbs free energy of the state as the Gabor elementary function can unveil the guiding role of the information uncertainty principle in shaping the chimera energetics.

nlin.AO↗

arXiv2021

Interplay of energy, dissipation, and error in kinetic proofreading: Control via concentration and binding energy

Kinetic proofreading mechanisms explain the extraordinary accuracy observed in central biological events in terms of the enhanced specificity of substrate selection networks under a nonequilibrium environment. The nonequilibrium steady state theory incorporated with a chemical thermodynamic framework is implemented to execute a systematic investigation of dynamic and thermodynamic features of the proofreading network under continuous fuel consumption. We have identified that the dissipation-error trade-off domain of the network has a one-to-one correspondence with the deeper portion of the basin-like error rate profile depicted here. Further, quantifying the energy cost through concentration control of the chemical fuel aids in unveiling the association of the energy and chemical work with the optimal operating region of the biological error-correcting mechanism. It is shown that the proper energy content of the system, the semigrand Gibbs free energy, approaches a nominal value in the trade-off regime, whereas it gets considerably minimized in the domain with a lack of trade-off. We have also introduced a performance measuring entity corresponding to different energetic discrimination magnitudes as a product of average dissipation and coefficient of variation for the whole range of chemical fuel. Besides invoking a different perspective to the experimental and theoretical assessment of biological processes like DNA replication or protein synthesis, our findings can be advantageous in designing more efficient synthetic biological architectures.

nlin.AO↗

arXiv2021

Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability

Evolution of the nonequilibrium thermodynamic entities corresponding to dynamics of the Hopf instabilities and traveling waves at a nonequilibrium steady state of a spatially extended glycolysis model is assessed here by implementing an analytically tractable scheme incorporating a complex Ginzburg-Landau equation (CGLE). In the presence of self and cross diffusion, a more general amplitude equation exploiting the multiscale Krylov-Bogoliubov averaging method serves as an essential tool to reveal the various dynamical instability criteria, especially Benjamin-Feir (BF) instability, to estimate the corresponding nonlinear dispersion relation of the traveling wave pattern. The critical control parameter, wave-number selection criteria, and magnitude of the complex amplitude for traveling waves are modified by self- and cross-diffusion coefficients within the oscillatory regime, and their variabilities are exhibited against the amplitude equation. Unlike the traveling waves, a low-amplitude broad region appears for the Hopf instability in the concentration dynamics as the system phase passes through minima during its variation with the control parameter. The total entropy production rate of the uniform Hopf oscillation and glycolysis wave not only qualitatively reflects the global dynamics of concentrations of intermediate species but almost quantitatively. Despite the crucial role of diffusion in generating and shaping the traveling waves, the diffusive part of the entropy production rate has a negligible contribution to the system's total entropy production rate. The Hopf instability shows a more complex and colossal change in the energy profile of the open nonlinear system than in the traveling waves. A detailed analysis of BF instability shows a contrary nature of the semigrand Gibbs free energy with discrete and continuous wave numbers for the traveling wave.

nlin.AO↗

arXiv2021

Energetic and entropic cost due to overlapping of Turing-Hopf instabilities in presence of Cross Diffusion

A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities is considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability in presence of cross diffusion can be best viewed in terms of the critical control parameter and wave number containing both the self and cross diffusion coefficients. Our main focus is on the entropic and energetic cost of Turing-Hopf interplay in stationary pattern formation. Depending on the relative dispositions of Turing-Hopf codimensional instabilities from the reaction-diffusion equation it clarifies two aspects: energy cost of pattern formation, especially how Hopf instability can be utilized to dictate a stationary concentration profile, and the possibility of revealing nonequilibrium phase transition. In the Brusselator model to understand these phenomena, we have analyzed through the relevant complex Ginzberg-Landau equation using the multiscale Krylov-Bogoiubov averaging method. Due to Hopf instability, it is observed that the cross diffusion parameters can be a source of huge change in free energy and concentration profiles.

nlin.AO↗

arXiv2021

Limit Cycle Analysis of 3-D Nonlinear systems

Considering Limit Cycles as one of the limits of Lienard equation, an analyis analogous to centre manifold analysis has been done for a $3-D$ nonlinear system exhibiting Limit Cycle. A rigorous study on radius of the Limit Cycle orbit has been done by considering $λ-ω$ equations for the particular system and subsequently converting the system equations from cartesian to polar form. It has been shown through an analysis analogous to Centre Manifold Analysis and reduction of the system dynamics on a lower dimensional space, the Limit cycle radius undergoes an increment change. One example is provided to support the theoretical predictions.

math.DS↗

arXiv2021

Where the Liénard--Levinson--Smith (LLS) theorem cannot be applied for a generalised Liénard system

We have examined a class of Liénard--Levinson--Smith (LLS) system having a stable limit cycle which demonstrates the case where the LLS theorem cannot be applied. The problem has been partly raised in a recent communication by Saha et al., CNSNS 85, 105234 (2020) (last para of sec 4.2.2). Here we have provided a physical approach to address this problem using the concept of energy consumption per cycle. We have elaborated the idea through proper demonstration by considering a generalized model system. Such issues have potential utility in nonlinear vibration control.

nlin.AO↗

arXiv2020

Centre Manifold Analysis of 3-D nonlinear system and Kinetic stability of Protein Assembly

Centre Manifold analysis of a 3-D nonlinear system with general second order nonlinearities have been worked out. The system is shown to possess two fixed points on the reduced 2-D centre manifold. By introducing a 2-D centre manifold one can show how an oscillatory dynamics may be generated in the system. We also state and prove a theorem to find the stability of the resultant centre manifold equation apriori from the parity of the nonlinear terms in the original equations. For a 2-D nonlinear model with the example picked up from biochemistry, the protein molecules in assembly, kinetic stability analysis is provided for the chosen example and establish herewith the validity of the theorem for our chosen example.

math.DS↗

arXiv2020

Parametric excitation and Hopf bifurcation analysis of a time delayed nonlinear feedback oscillator

In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is considered with nonlinear feedback oscillator defined in terms of Liénard oscillator description which can give rise to any one of the periodic orbits stated above. We have characterized the resonance and antiresonance behaviour for arbitrary nonlinear system from their stability and bifurcation analyses in reference to the standard delayed van der Pol system. An approximate analytical solution using Krylov--Bogoliubov (K-B) averaging method is utilised to recognize the sub-harmonic resonance and antiresonance, and average energy consumption per cycle. Direction of Hopf bifurcation and stability of the periodic solution bifurcating from the trivial fixed point are carried out using normal form and center manifold theory. The parametric excitation is also thoroughly investigated via bifurcation analysis to find the role of the control parameters like time delay, damping and nonlinear terms.

nlin.CD↗

arXiv2020

Suppressing birhythmicity by parametrically modulating nonlinearity in limit cycle oscillators

Multirhythmicity, a form of multistability, in an oscillator is an intriguing phenomenon found across many branches of science. From an application point of view, while the multirhythmicity is sometimes desirable as it presents us with many possible coexisting stable oscillatory states to tap into, it can also be a nuisance because a random perturbation may make the system settle onto an unwanted stable state. Consequently, it is not surprising that there are many natural and artificial mechanisms available that can control the multirhythmicity. We propose in this paper the idea of incorporating parametric (periodic) modulation of the nonlinear damping in the limit cycle oscillators with a view to exciting resonance and antiresonance responses at particular angular driving frequencies, and controlling the resulting birhythmicity by changing the amplitude of the modulation. To this end, we employ analytical (perturbative) and numerical techniques on the van der Pol oscillator---a paradigmatic limit cycle system---having additional position dependent time delay term and its modified autonomous birhythmic version. We also bring the fact to the fore that introduction of delay---a commonly adopted method of controlling multirhythmicity---in such a system can sometimes bring forth unwanted birhythmicity; and interestingly, our method of controlling birhythmicity through periodic modulation can suppress such a delay induced birhythmic response.

nlin.AO↗

arXiv2020

Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators

Van der Pol and Rayleigh oscillators are two traditional paradigms of nonlinear dynamics. They can be subsumed into a general form of Liénard--Levinson--Smith(LLS) system. Based on a recipe for finding out maximum number of limit cycles possible for a class of LLS oscillator, we propose here a scheme for systematic designing of generalised Rayleigh and Van der Pol families of oscillators with a desired number of multiple limit cycles. Numerical simulations are explicitly carried out for systematic search of the parameter space for bi-rhythmic and tri-rhythmic systems and their higher order variants.

nlin.AO↗

arXiv2019

Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles

We have presented an unified scheme to express a class of system of equations in two variables into a Liénard-Levinson-Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Liénard systems for arbitrary polynomial functions of damping and restoring force. Krylov-Boguliubov (K-B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases.

math.DS↗

arXiv2018

When an oscillating center in an open system undergoes power law decay

We have probed the condition of periodic oscillation in a class of two variable nonlinear dynamical open systems modeled with Lienard-Levinson-Smith(LLS) equation which can be a limit cycle, center or a very slowly decaying center type oscillation. Using a variety of examples of open systems like Glycolytic oscillator, Lotka-Volterra(L-V) model, a generalised van der Pol oscillator and a time delayed nonlinear feedback oscillation as a non-autonomous system, each of which contains a family of periodic orbits, we have solved LLS systems in terms of a multi-scale perturbation theory using Krylov-Bogoliubov(K-B) method and it is utilised to characterise the size and shape of the limit cycle and center as well as the approach to their steady state dynamics. We have shown the condition when the average scaled radius of a center undergoes a power law decay with exponent 1/2.

nlin.CD↗