The quantum theory of motion and signatures of chaos in the quantum behaviour of a classically chaotic system

Sengupta, S.; Chattaraj, Pratim Kumar

doi:10.1016/0375-9601(96)00240-x

Cited by 59 publications

(36 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because of the presence of nonlinearity and also the "classical language", these theories have been found [57][58][59][81][82][83][84][85] to be helpful in understanding the quantum domain behavior of classically chaotic systems which is described as quantum chaology by Berry [86].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Initial momentum of the particle is taken as zero in all cases. We study the time evolution of phase space distance (D) for the corresponding quantum trajectories defined as [56,59,82,83] [ ]…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Depending on the frequency and the field intensity, hydrogen [54,55] atoms in the presence of an external field have been shown to exhibit regular / chaotic dynamics. Both quantum fluid dynamics (QFD) [56,57] and quantum theory of motion (QTM) [58,59] have provided quantum signatures of chaos in hydrogen atoms. In QFD [56] the overall motion of the system under consideration is mapped onto that of a "probability fluid" having density ( ) are respectively obtained [55][56][57][58][59] from the amplitude and the phase of the wave function.…”

Section: Introductionmentioning

confidence: 99%

“…Both quantum fluid dynamics (QFD) [56,57] and quantum theory of motion (QTM) [58,59] have provided quantum signatures of chaos in hydrogen atoms. In QFD [56] the overall motion of the system under consideration is mapped onto that of a "probability fluid" having density ( ) are respectively obtained [55][56][57][58][59] from the amplitude and the phase of the wave function. In QTM [58], the wave motion is governed by the solution to the time dependent Schrödinger equation (TDSE) and the particle motion is followed by solving the pertinent Newton's equation of motion with forces originating from both classical and quantum potentials.…”

Section: Introductionmentioning

confidence: 99%

“…Important insight into the chaotic dynamics has been obtained [57] through ρ vs χ − plots which can be considered to be "canonically conjugate". In QTM it is obtained [59] in terms of the distance between two initially close Bohmian trajectories and the associated Kolmogorov -Sinai entropy.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Chemical Reactivity Dynamics and Quantum Chaos in Highly Excited Hydrogen Atoms in an External Field: A Quantum Potential Approach

Chattaraj

Maiti

2002

IJMS

View full text Add to dashboard Cite

Dynamical behavior of chemical reactivity indices like electronegativity, hardness, polarizability, electrophilicity and nucleophilicity indices is studied within a quantum fluid density functional framework for the interactions of a hydrogen atom in its ground electronic state (n = 1) and an excited electronic state (n = 20) with monochromatic and bichromatic laser pulses. Time dependent analogues of various electronic structure principles like the principles of electronegativity equalization, maximum hardness, minimum polarizability and maximum entropy have been found to be operative. Insights into the variation of intensities of the generated higher order harmonics on the color of the external laser field are obtained. The quantum signature of chaos in hydrogen atom has been studied using a quantum theory of motion and quantum fluid dynamics. A hydrogen atom in the electronic ground state (n = 1) and in an excited electronic state ( n = 20) behaves differently when placed in external oscillating monochromatic and bichromatic electric fields. Temporal evolutions of Shannon entropy, quantum Lyapunov exponent and Kolmogorov -Sinai entropy defined in terms of the distance between two initially close Bohmian trajectories for these two cases show marked differences. It appears that a larger uncertainty product and a smaller hardness value signal a chaotic behavior.

show abstract

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Chemical Reactivity Dynamics and Quantum Chaos in Highly Excited Hydrogen Atoms in an External Field: A Quantum Potential Approach

Chattaraj

Maiti

2002

IJMS

View full text Add to dashboard Cite

show abstract

Quantum fluid density functional theory of time-dependent processes

Chattaraj

Sengupta

Poddar

1998

Int. J. Quant. Chem.

View full text Add to dashboard Cite

ABSTRACT:A quantum fluid density functional theory has been developed through an amalgamation of the quantum fluid dynamics and the time-dependent density functional theory. It is used in studying typical time-dependent processes like ion᎐atom collisions and atom᎐field interaction. Temporal evolution of chemical reactivity parameters as electronegativity, hardness, entropy, and polarizability is monitored for a He atom in its ground and excited states interacting with an external electric field and an incoming proton. It is observed that these reactivity parameters either remain static or oscillate with the external field in the atom᎐field interaction case, whereas during the collision process, hardness and entropy maximize and polarizability minimizes for both the electronic states of the atom. The possibility of a quantum theory of motion within the purview of this quantum fluid density functional framework is also explored.

show abstract

Net reactivity index (Δω)

Chakraborty

Das

Giri

et al. 2011

J of Physical Organic Chem

View full text Add to dashboard Cite

A Hammett‐type relationship has been obtained for a set of substituted benzoic acids, in terms of the net electrophilicity index. A new multiphilic descriptor, the net reactivity index (NRI) has been proposed. It can properly describe whether a Diels–Alder type reaction would follow a polar‐stepwise pathway or a non‐polar‐concerted mechanism. It can also clearly delineate whether a reaction is of normal or inverse electron demand type, in case the minimum ionization potential and the maximum electron affinity values do not belong to the same molecule in a diene–dienophile pair. Copyright © 2011 John Wiley & Sons, Ltd.

show abstract

The quantum theory of motion and signatures of chaos in the quantum behaviour of a classically chaotic system

Cited by 59 publications

References 43 publications

Chemical Reactivity Dynamics and Quantum Chaos in Highly Excited Hydrogen Atoms in an External Field: A Quantum Potential Approach

Chemical Reactivity Dynamics and Quantum Chaos in Highly Excited Hydrogen Atoms in an External Field: A Quantum Potential Approach

Quantum fluid density functional theory of time-dependent processes

Net reactivity index (Δω)

Contact Info

Product

Resources

About