arXiv subjects

Bala Sundaram

Publications and source records attributed to Bala Sundaram.

24 records · Page 2Linked to original sources

arXiv2005

The Semiclassical Regime of the Chaotic Quantum-Classical Transition

An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress the development of fine structure in classical phase space and damp nonlocal contributions to the semiclassical Wigner function which would otherwise invalidate the approximation. This dual regularization of the singular nature of the semiclassical limit is demonstrated by a numerical investigation of the chaotic Duffing oscillator.

quant-ph↗

arXiv2002

Parameter scaling in the decoherent quantum-classical transition for chaotic systems

The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hbar$, a measure of the coupling between a system and its environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $λ$. We propose computing a measure, reflecting the proximity of quantum and classical evolutions, as a multivariate function of $(\hbar,λ,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $ζ= \hbar^αλ^βD^γ$. We report results for the quantum Cat Map, showing extremely accurate scaling behavior over a wide range of parameters and suggest that, in general, the technique may be effective in constructing universality classes in this transition.

quant-ph↗

arXiv2000

The Quantum-Classical Transition in Nonlinear Dynamical Systems

Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical transition. In particular, the late-time Wigner function can become positive without any corresponding approach to classical dynamics. In the light of these results, we emphasize key issues relevant for experiments studying the quantum-classical transition.

quant-ph↗

arXiv1999

Quantized Orbits and Resonant Transport

A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples of $π/2$. Commensurability relations between the orbit frequencies are shown to correlate with the emergence of accelerator modes in the classical phase space of the original kicked problem. The signature of this resonant transport is seen in both classical and quantum behavior. An important feature of our analysis is the emergence of a natural scaling relating classical and quantum couplings which is necessary for establishing correspondence.

chao-dyn↗

arXiv1999

Localization and Fluctuations in Quantum Kicked Rotors

We address the issue of fluctuations, about an exponential lineshape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical localization. An exact renormalization scheme establishes the fractal character of the fluctuations and provides a new method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuations are independent of the kicking parameter $k$ and exhibit self-similarity for certain values of the quasienergy. For given $k$, the asymptotic localization length is a good characteristic of the localized lineshapes for all quasienergies. This is in stark contrast to the quadratic rotor, where the fluctuations depend upon the strength of the kicking and exhibit local "resonances". These resonances result in strong deviations of the localization length from the asymptotic value. The consequences are particularly pronounced when considering the time evolution of a packet made up of several quasienergy states.

chao-dyn↗

arXiv1999

Anomalous transport and quantum-classical correspondence

We present evidence that anomalous transport in the classical standard map results in strong enhancement of fluctuations in the localization length of quasienergy states in the corresponding quantum dynamics. This generic effect occurs even far from the semiclassical limit and reflects the interplay of local and global quantum suppression mechanisms of classically chaotic dynamics. Possible experimental scenarios are also discussed.

chao-dyn↗