arXiv subjects

Gautam Gangopadhyay

Publications and source records attributed to Gautam Gangopadhyay.

32 records · Page 2Linked to original sources

arXiv2018

Effect of Channel Noise in Synchronization and Metabolic Energy Consumption in Unidirectionally Coupled Neurons: Drug Blocking of Sodium and Potassium Channels

In this work the stochastic generalization of single Hodgkin-Huxley neuron is further extended to unidirectionally coupled neurons. Our main focus is to elucidate the role of channel noise in the kinetics and energetics of spiking of action potential and the synchronization between two coupled neurons. We have found that the size of the patch is playing the pivotal role in synchronization and metabolic energy consumption. For example, there exists three different patch size ranges in which coupled neuron system behaves in a different manner from noise enhanced phase to dead range state before reaching the deterministic limit. We have also found that the sodium and potassium channel blockers have characteristic kinetic and energetic effects on synchronization process and metabolic energy consumption rate which has been validated with the simulated data.

physics.bio-ph↗

arXiv2018

Effect Of Site Selective Ion Channel Blocking on Action Potential

In this work we have theoretically investigated how the action potential generation and its associated intrinsic properties are affected in presence of ion channel blockers by adapting Gillepie's stochastic simulation technique on a very basic neuron of Hodgkin-Huxley type. With a simple extension of the Hodgkin-Huxley Markov model we have mainly investigated three types of drug blocking mechanisms and showed that the major experimental and physiological observations such as ionic currents, spiking frequency trends, change in action potential shape and duration, altered gating dynamics etc due to the presence of ion channel blockers can be well reproduced. The nature of action potential termination process in presence of sodium and potassium channel blockers are distinct and physiologically very different from each other. Channel blockers have distinct signatures on ionic currents. In presence of only sodium channel blockers the frequency of action potential generation falls off exponentially with increasing drug affinity, whereas in contrast, for only potassium channel blockers initially an enhanced spiking activity of action potential is found followed by a gradual decrease of the spiking frequency as the drug affinity increases. In case of dual type blockers with equal sodium and potassium channel binding affinity, the spiking frequency passes through maxima and minima due to the competition between channel number fluctuation and overall sodium and potassium conductances. We have found that sodium channel blockers shorten the duration of action potential while the potassium channel blockers delay it. We have also shown how the ion channel blockers alter the gating dynamics. Some experimental results of ion channel blocking in diverse systems have been validated through our site selected binding scheme.

physics.bio-ph↗

arXiv2018

Isochronicity and limit cycle oscillation in chemical systems

Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a limit cycle around an interior stationary point. In this context Lienard equation is specifically used in the study of nonlinear dynamical properties of an open system which can be utilized to obtain the condition of limit cycle. In conjunction with the property of limit cycle oscillation, here we have shown the condition for isochronicity for different chemical oscillators with the help of renormalisation group method with multiple time scale analysis from a Lienard system. When two variable open system of equations are transformed into a Lienard system of equation the condition for limit cycle and isochronicity can be stated in a unified way. For any such nonlinear oscillator we have shown the route of a dynamical transformation of a limit cycle oscillation to a periodic orbit of centre type depending on the parameters of the system.

math.DS↗

arXiv2017

Counting triangles formula for the first Chern class of a circle bundle

We consider the problem of the combinatorial computation of the first Chern class of a circle bundle. N.Mnev found such a formula in terms of canonical shellings. It represents certain invariant of a triangulation computed by analyzing cyclic word in 3-character alphabet associated to the bundle. This curvature is a kind of discretization of Konstevich's curvature differential 2-form. We find a new expression of Mnev's curvature by counting triangles in a cyclic word. Our formula is different from that of Mnev. In particular, it is cyclically invariant by its very form. We present also some sample computations of this invariant and also provide a small Mathematica code for the computation of this invariant.

math.GT↗

arXiv2017

Physics Potential of the ICAL detector at the India-based Neutrino Observatory (INO)

The upcoming 50 kt magnetized iron calorimeter (ICAL) detector at the India-based Neutrino Observatory (INO) is designed to study the atmospheric neutrinos and antineutrinos separately over a wide range of energies and path lengths. The primary focus of this experiment is to explore the Earth matter effects by observing the energy and zenith angle dependence of the atmospheric neutrinos in the multi-GeV range. This study will be crucial to address some of the outstanding issues in neutrino oscillation physics, including the fundamental issue of neutrino mass hierarchy. In this document, we present the physics potential of the detector as obtained from realistic detector simulations. We describe the simulation framework, the neutrino interactions in the detector, and the expected response of the detector to particles traversing it. The ICAL detector can determine the energy and direction of the muons to a high precision, and in addition, its sensitivity to multi-GeV hadrons increases its physics reach substantially. Its charge identification capability, and hence its ability to distinguish neutrinos from antineutrinos, makes it an efficient detector for determining the neutrino mass hierarchy. In this report, we outline the analyses carried out for the determination of neutrino mass hierarchy and precision measurements of atmospheric neutrino mixing parameters at ICAL, and give the expected physics reach of the detector with 10 years of runtime. We also explore the potential of ICAL for probing new physics scenarios like CPT violation and the presence of magnetic monopoles.

physics.ins-det↗

arXiv2014

Comparison of Electromagnetically Induced Transparency in lambda, cascade and vee three-level systems

We discuss the Electromagnetically Induced Transparency (EIT) in lambda, cascade and vee type three-level systems where the Hamiltonian and the Lindblad term of each configuration are expressed in the $SU(3)$ representation. At steady state, the Optical Bloch Equations of each configuration are solved to obtain the dispersion and absorption profiles of the probe field along with their group velocities. When the EIT condition is achieved at resonance, the population oscillation shows which of the bare states are contributing to form the dark state. Our study reveals that the dark state for the lambda and cascade system effectively coincides with the lowest bare state of that system, while for the vee system, it is a maximally superposed state of the middle and upper bare states.

quant-ph↗

arXiv2012

Entropic estimate of cooperative binding of substrate on a single oligomeric enzyme: An index of cooperativity

Here we have systematically studied the cooperative binding of substrate molecules on the active sites of a single oligomeric enzyme in a chemiostatic condition. The average number of bound substrate and the net velocity of the enzyme catalyzed reaction are studied by the formulation of stochastic master equation for the cooperative binding classified here as spatial and temporal. We have estimated the entropy production for the cooperative binding schemes based on single trajectory analysis using a kinetic Monte Carlo technique. It is found that the total as well as the medium entropy production show the same generic diagnostic signature for detecting the cooperativity, usually characterized in terms of the net velocity of the reaction. This feature is also found to be valid for the total entropy production rate at the nonequilibrium steady state. We have introduced an index of cooperativity, C, defined in terms of the ratio of the surprisals or equivalently, the stochastic system entropy associated with the fully bound state of the cooperative and non-cooperative cases. The criteria of cooperativity in terms of C is compared with that of the Hill coefficient and gives a microscopic insight on the cooperative binding of substrate on a single oligomeric enzyme which is usually characterized by macroscopic reaction rate.

physics.bio-ph↗

arXiv2012

Bloch space structure, the qutrit wave function and atom-field entanglement in three-level systems

We have given a novel formulation of the exact solutions for the lambda, vee and cascade three-level systems where the Hamiltonian of each configuration is expressed in the SU(3) basis. The solutions are discussed from the perspective of the Bloch equation and the atom-field entanglement scenario. For the semiclassical systems, the Bloch space structure of each configuration is studied by solving the corresponding Bloch equation and it is shown that at resonance, the eight-dimensional Bloch sphere is broken up into two distinct subspaces due to the existence of a pair of quadratic constants. Because of the different structure of the Hamiltonian in the SU(3) basis, the non-linear constants are found to be distinct for different configurations. We propose a possible representation of the qutrit wave function and show its equivalence with the three-level system. Taking the bichromatic cavity modes to be in the coherent state, the amplitudes of all three quantized systems are calculated by developing an Euler angle based dressed state scheme. Finally following the Phoenix-Knight formalism, the interrelation between the atom-field entanglement and population inversion for all configurations is studied and the existence of collapses and revivals of two different types is pointed out for the equidistant cascade system in particular.

quant-ph↗

arXiv2010

Bloch space structure of cascade, lambda and vee type of three-level systems and qutrit wave function

The cascade, lambda and vee type of three-level systems are shown to be described by three different Hamiltonians in the SU(3) basis. We investigate the Bloch space structure of each configuration by solving the corresponding Bloch equation and show that at resonance, the seven-dimensional Bloch sphere ${\mathcal S}^7$ is broken into two distinct subspaces ${\mathcal S}^2{\times}{\mathcal S}^4$ due to the existence of a pair of quadratic constants. We also give a possible representation of the qutrit wave function and discuss its equivalence with the three-level system.

quant-ph↗

arXiv2008

Dynamical symmetry breaking of lambda and vee-type three-level systems on quantization of the field modes

We develop a scheme to construct the Hamiltonians of the lambda, vee and cascade type of three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well defined selection rule to give different Hamitonians for each configurations. The lambda and vee type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields . For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when the field modes are both in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.

quant-ph↗

arXiv2008

Effect of field quantization on Rabi oscillation of equidistant cascade four-level system

We have exactly solved a model of equidistant cascade four-level system interacting with a single-mode radiation field both semiclassically and quantum mechanically by exploiting its similarity with Jaynes-Cummings model. For the classical field, it is shown that the Rabi oscillation of the system initially in the first level (second level) is similar to that of the system when it is initially in the fourth level (third level). We then proceed to solve the quantized version of the model where the dressed state is constructed by using a six parameter four-dimensional matrix and show that the symmetry exhibited in the Rabi oscillation of the system for the semiclassical model is completely destroyed on the quantization of the cavity field. Finally we have studied the collapse and revival of the system for the cavity field-mode in a coherent state to discuss the restoration of symmetry and its implication is discussed.

quant-ph↗

arXiv2008

On the microscopic basis of Newton's law of cooling and beyond

The microscopic basis of Newton's law of cooling and its modification when the difference in temperature between the system and the surroundings is very large is discussed. When the system of interest is interacting with a small bath, the effect of the dynamical evolution of the bath variables is important to find out its dynamical feedback on the system. As in the usual system-bath approach, however, the bath is finally considered to be in thermal equilibrium and thereby provides an effective generalization of the Born-Markov master equation. It is shown that the cooling at early time is faster than that predicted by Newton's law due to the dynamical feedback of the bath.

quant-ph↗

arXiv2007

Dynamics of cascade three-level system interacting with the classical and quantized field

We study the exact solutions of the cascade three-level atom interacting with a single mode classical and quantized field with different initial conditions of the atom. For the semiclassical model, it is found that if the atom is initially in the middle level, the time dependent populations of the upper and lower levels are always equal. This dynamical symmetry exhibited by the classical field is spoiled on quantization of the field mode. To reveal this nonclassical effect an Euler matrix formalism is developed to solve the dressed states of the cascade Jaynes-Cummings model (JCM). Possible modification of such effect on the collapse and revival phenomenon is also discussed by taking the quantized field in a coherent state.

quant-ph↗

arXiv1998

Theory of non-stationary activated rate processes : nonexponential relaxation kinetics

We have explored a simple microscopic model to simulate a thermally activated rate process where the associated bath which comprises a set of relaxing modes is not in an equilibrium state. The model captures some of the essential features of non-Markovian Langevin dynamics with a fluctuating barrier. Making use of the Fokker-Planck description we calculate the barrier dynamics in the steady state and non-stationary regimes. The Kramers-Grote-Hynes reactive frequency has been computed in closed form in the steady state to illustrate the strong dependence of the dynamic coupling of the system with the relaxing modes. The influence of nonequilibrium excitation of the bath modes and its relaxation on the kinetics of activation of the system mode is demonstrated. We derive the dressed time-dependent Kramers rate in the nonstationary regime in closed analytical form which exhibits strong non-exponential relaxation kinetics of the reaction co-ordinate. The feature can be identified as a typical non-Markovian dynamical effect.

cond-mat.stat-mech↗