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Quantum stochastic optimization or quantum annealing is a quantum algorithm of optimizing a given... more Quantum stochastic optimization or quantum annealing is a quantum algorithm of optimizing a given cost function. This paper takes one through a journey of improving classical optimization methods to reach a quantum one. A comparative study of techniques from both parts has been done. An alternate method to imaginary time quantum monte carlo based on frctional dynamics has also been discussed.
Solar actvity is one of the widely observed phenomena since the beginning of astronomy. Theoreti... more Solar actvity is one of the widely observed phenomena since the beginning
of astronomy. Theoretical understanding of the solar activity comes for the dy-
namo models. In the initial part of we disucss basics of Magnetohydrodynamics
and kinetic dynamo model. Observations have shown that sunspot area is a better
proxy for understanding the solar activity than sunspot number. From the recently
digitized photographic images of Kodaikanal data (arXiv:1212.4776) we have ana-
lyzed the sunspot area data obtained from six solar cycles (i.e. from year 1923 to
1986). We have obtained high correlation of daily averaged sunspot area, monthly
averaged sunspot area (0.93) and yearly sunspot area(0.96) with Greenwich obser-
vatory data. Along with these regularities many irregularities exist in solar cycle.
Irregularities in solar cycle arise due to
uctuations in meridional circulation and
uctuations in Babcock Leighton mechanism. In the present paper we will discuss
one irregularity named as Waldmeier e ects (WE1 and WE2). Observations hint
on validation of high di usivity model (arXiv:1008.0824). According to high dif-
fusivity model longer cycle allows di usivity to act for a longer time which results
in low amplitude and weaker cycle.
In the given write up I shall be giving a theoretical and historical overview of classical mechan... more In the given write up I shall be giving a theoretical and historical overview of classical mechanics. After that I will be discussing about one family of one dimensional maps with their universality, similarity and apparantly randomness in order to get a glimpse of chaos in one dimensional systems. .
In this paper first of all DC glow discharge plasma is characterized by finding out plasma parame... more In this paper first of all DC glow discharge plasma is characterized by finding out plasma parameters. This involves study of Paschen curve and Langmuir probe characteristic. After that floating potential fluctuations are obtained by using Langmuir probe at different values of pressure of gas, external magnetic field and discharge voltage. The analysis of these nonlinear oscillations involves nonlinear time series analysis. Analysis is carried out by several techniques like determining correlation dimensional analysis, Fourier spectrum analysis, rescaled range analysis (for Hurst exponent), determining Largest Lyapunov exponent (by Rosenstein method), 0-1 test for chaos etc.
Conference Presentations by sourabh singh chauhan
Papers by sourabh singh chauhan
The Hohenberg-Kohn theorem and constrained search formalism of density functional theory are in ... more The Hohenberg-Kohn theorem and constrained search formalism of density functional theory
are in principle sufficient to address the question of mapping from an excited-state density of an
interacting many-electron system to the external potential. Which is also equally applicable to the
model noninteracting system. Be it the lowest (non)degenerate excited state of a given symmetry or
any other many-particle quantum states with differing symmetry and thus corresponding to arbitrary
order of excitations, the analogue of Hohenberg-Kohn theorem and constrained search formalism
can uniquely establish the one-to-one density-to-potential mapping. We have rigorously investigated
and also shown by examples that the existence of multiple effective/external potentials for excitedstates
and the seemingly contradictory results in connection to the applicability of GunnarssonLundqvist
theorem even for the lowest excited-state is not truly a failure or violation of HohenbergKohn/Gunnarsson-Lundqvist
theorem. Rather these are nothing but our limited understanding
of the subtle differences between the ground and excited-state density-functional theory. So these
are in fact no issues in the context of the foundational aspects of excited-state density-functional
formalism. Our critical analysis outlines that the multiplicity of potentials for a given density
(i.e. the symmetries of the quantum states involve) never guarantee the violation of one-to-one
correspondence between the two most valuable physical quantities of interest in modern densityfunctional
theory. By furthering the existing theories and basic principles, we have provided a firm
footing to the density -to-potential mapping for excited-states in general. We have shown that
our proposed criterions based on generalized constrained search formalism keep the excited-state
density-to-potential mapping intact.
Physica Scripta, Nov 13, 2013
Various nonlinear dynamical behaviors are experimentally observed to exist in magnetized dc glow ... more Various nonlinear dynamical behaviors are experimentally observed to exist in magnetized dc glow discharge plasma. Nonlinear plasma fluctuations are seen evolving when the initial parameters such as discharge voltage, filling pressures, etc are changed in the presence of external magnetic field. A transition pattern of chaotic to quasiperiodicity is experimentally observed when a magnetic field is applied, which is not the case in the un-magnetized one. Hence, a comparative analysis is being conducted for both the cases of magnetized and un-magnetized plasma. The nonlinear behavior of the plasma oscillations are diagnosed by different techniques namely: power spectrum, phase space plotting, correlation dimension, Liapunov exponent, fractal dimension and Hurst exponent. Furthermore, it is noticed that with increasing discharge voltage, the glow emerges from the cathode, slowly moves toward the anode and finally sinks into the anode in a ballooning manner.
Cambridge Journal of Plasma Physics, Jun 14, 2013
" Characterization of self-similarity properties of turbulence in magnetized plasma is being car... more "
Characterization of self-similarity properties of turbulence in magnetized plasma is being carried out in DC glow discharge plasma. The time series floating potential fluctuation experimental data are acquired from the plasma by Langmuir probe. Continuous wavelet transform (CWT) analysis considering db4 mother wavelet has been applied to the experimental data and self-similarity properties are detected by evaluating the Hurst exponent from the wavelet variance plotting. From the CWT spectrum, effort is made to extract a highly correlated frequency by locating the brightest spot. Accordingly, those signals are treated for finding out correlation dimension and the Liapunov exponent so that the exact frequency responsible for the chaotic behavior could be found out."
Quantum stochastic optimization or quantum annealing is a quantum algorithm of optimizing a given... more Quantum stochastic optimization or quantum annealing is a quantum algorithm of optimizing a given cost function. This paper takes one through a journey of improving classical optimization methods to reach a quantum one. A comparative study of techniques from both parts has been done. An alternate method to imaginary time quantum monte carlo based on frctional dynamics has also been discussed.
Solar actvity is one of the widely observed phenomena since the beginning of astronomy. Theoreti... more Solar actvity is one of the widely observed phenomena since the beginning
of astronomy. Theoretical understanding of the solar activity comes for the dy-
namo models. In the initial part of we disucss basics of Magnetohydrodynamics
and kinetic dynamo model. Observations have shown that sunspot area is a better
proxy for understanding the solar activity than sunspot number. From the recently
digitized photographic images of Kodaikanal data (arXiv:1212.4776) we have ana-
lyzed the sunspot area data obtained from six solar cycles (i.e. from year 1923 to
1986). We have obtained high correlation of daily averaged sunspot area, monthly
averaged sunspot area (0.93) and yearly sunspot area(0.96) with Greenwich obser-
vatory data. Along with these regularities many irregularities exist in solar cycle.
Irregularities in solar cycle arise due to
uctuations in meridional circulation and
uctuations in Babcock Leighton mechanism. In the present paper we will discuss
one irregularity named as Waldmeier e ects (WE1 and WE2). Observations hint
on validation of high di usivity model (arXiv:1008.0824). According to high dif-
fusivity model longer cycle allows di usivity to act for a longer time which results
in low amplitude and weaker cycle.
In the given write up I shall be giving a theoretical and historical overview of classical mechan... more In the given write up I shall be giving a theoretical and historical overview of classical mechanics. After that I will be discussing about one family of one dimensional maps with their universality, similarity and apparantly randomness in order to get a glimpse of chaos in one dimensional systems. .
In this paper first of all DC glow discharge plasma is characterized by finding out plasma parame... more In this paper first of all DC glow discharge plasma is characterized by finding out plasma parameters. This involves study of Paschen curve and Langmuir probe characteristic. After that floating potential fluctuations are obtained by using Langmuir probe at different values of pressure of gas, external magnetic field and discharge voltage. The analysis of these nonlinear oscillations involves nonlinear time series analysis. Analysis is carried out by several techniques like determining correlation dimensional analysis, Fourier spectrum analysis, rescaled range analysis (for Hurst exponent), determining Largest Lyapunov exponent (by Rosenstein method), 0-1 test for chaos etc.
The Hohenberg-Kohn theorem and constrained search formalism of density functional theory are in ... more The Hohenberg-Kohn theorem and constrained search formalism of density functional theory
are in principle sufficient to address the question of mapping from an excited-state density of an
interacting many-electron system to the external potential. Which is also equally applicable to the
model noninteracting system. Be it the lowest (non)degenerate excited state of a given symmetry or
any other many-particle quantum states with differing symmetry and thus corresponding to arbitrary
order of excitations, the analogue of Hohenberg-Kohn theorem and constrained search formalism
can uniquely establish the one-to-one density-to-potential mapping. We have rigorously investigated
and also shown by examples that the existence of multiple effective/external potentials for excitedstates
and the seemingly contradictory results in connection to the applicability of GunnarssonLundqvist
theorem even for the lowest excited-state is not truly a failure or violation of HohenbergKohn/Gunnarsson-Lundqvist
theorem. Rather these are nothing but our limited understanding
of the subtle differences between the ground and excited-state density-functional theory. So these
are in fact no issues in the context of the foundational aspects of excited-state density-functional
formalism. Our critical analysis outlines that the multiplicity of potentials for a given density
(i.e. the symmetries of the quantum states involve) never guarantee the violation of one-to-one
correspondence between the two most valuable physical quantities of interest in modern densityfunctional
theory. By furthering the existing theories and basic principles, we have provided a firm
footing to the density -to-potential mapping for excited-states in general. We have shown that
our proposed criterions based on generalized constrained search formalism keep the excited-state
density-to-potential mapping intact.
Physica Scripta, Nov 13, 2013
Various nonlinear dynamical behaviors are experimentally observed to exist in magnetized dc glow ... more Various nonlinear dynamical behaviors are experimentally observed to exist in magnetized dc glow discharge plasma. Nonlinear plasma fluctuations are seen evolving when the initial parameters such as discharge voltage, filling pressures, etc are changed in the presence of external magnetic field. A transition pattern of chaotic to quasiperiodicity is experimentally observed when a magnetic field is applied, which is not the case in the un-magnetized one. Hence, a comparative analysis is being conducted for both the cases of magnetized and un-magnetized plasma. The nonlinear behavior of the plasma oscillations are diagnosed by different techniques namely: power spectrum, phase space plotting, correlation dimension, Liapunov exponent, fractal dimension and Hurst exponent. Furthermore, it is noticed that with increasing discharge voltage, the glow emerges from the cathode, slowly moves toward the anode and finally sinks into the anode in a ballooning manner.
Cambridge Journal of Plasma Physics, Jun 14, 2013
" Characterization of self-similarity properties of turbulence in magnetized plasma is being car... more "
Characterization of self-similarity properties of turbulence in magnetized plasma is being carried out in DC glow discharge plasma. The time series floating potential fluctuation experimental data are acquired from the plasma by Langmuir probe. Continuous wavelet transform (CWT) analysis considering db4 mother wavelet has been applied to the experimental data and self-similarity properties are detected by evaluating the Hurst exponent from the wavelet variance plotting. From the CWT spectrum, effort is made to extract a highly correlated frequency by locating the brightest spot. Accordingly, those signals are treated for finding out correlation dimension and the Liapunov exponent so that the exact frequency responsible for the chaotic behavior could be found out."