arXiv subjects

Arjendu K. Pattanayak

Publications and source records attributed to Arjendu K. Pattanayak.

22 records · Page 2Linked to original sources

arXiv1997

Chaos and Lyapunov exponents in classical and quantal distribution dynamics

We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions $ρ(p,q)$. Of particular interest is $λ_2$, an exponent which quantifies the rate at which chaotically evolving distributions acquire structure at increasingly smaller scales and which is generally larger than the maximal Lyapunov exponent $λ$ for trajectories. The approach is trajectory-independent and is therefore applicable to both classical and quantum mechanics. In the latter case we show that the $\hbar\to 0$ limit yields the classical, fully chaotic, result for the quantum cat map.

chao-dyn↗

arXiv1996

Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of classical chaotic motion.

chao-dyn↗

arXiv1994

Gaussian Wavepacket Dynamics: semiquantal and semiclassical phase space formalism

Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an extended potential formulation. We develop Gaussian semiquantal dynamics to provide a phase space formalism and construct a propagator with desirable qualities. We qualitatively evaluate the behaviour of these semiquantal equations, and show that they reproduce the quantal behavior better than the standard Gaussian semiclassical dynamics. We also show that these semiclassical equations arise as truncations to semiquantal dynamics non-self-consistent in $\hbar$. This enables us to introduce an extended semiclassical dynamics that retains the power of the Hamiltonian phase space formulation. Finally, we show how to obtain approximate eigenvalues and eigenfunctions in this formalism, and demonstrate with an example that this works well even for a classically strongly chaotic Hamiltonian.

chao-dyn↗

arXiv1994

Semiquantal dynamics of fluctuations: Ostensible quantum chaos

The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be derived via the Ehrenfest theorem and recast as an extended classical gradient system with the fluctuation variables coupled to the average variables. An extended potential is constructed for a one-dimensional system. The semiquantal behavior is shown to be chaotic even though the system has regular classical behavior and the quantum behavior had been assumed regular.

chao-dyn↗