arXiv subjects

Arjendu K. Pattanayak

Publications and source records attributed to Arjendu K. Pattanayak.

At least 19 recordsLinked to original sources

arXiv2023

Parametric hypersensitivity in many-body bath-mediated transport: The quantum Rabi model

We demonstrate that non-equilibrium steady states of the dissipative Rabi model show dramatic spikes in transport rates over narrow parameter ranges. Similar results are found for the Holstein and Dicke models. This is found to be due to avoided energy level crossings in the corresponding closed systems, and correlates with spikes in the entanglement entropy of key eigenstates, a signature of strong mixing and resonance among system degrees of freedom. Further, contrasting the Rabi model with the Jaynes-Cummings model reveals this behavior as being related to quantum integrability.

quant-ph↗

arXiv2020

Ordinal Patterns in the Duffing Oscillator: Analyzing Powers of Characterization

Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the Lyapunov exponent. However ordinal patterns store strictly more information than Permutation Entropy or Lyapunov exponents. We present results working with the Duffing oscillator showing that ordinal patterns reflect changes in dynamical symmetry invisible to other measures, even Permutation Entropy. We find that these changes in symmetry at given parameter values are correlated with a change in stability at neighboring parameters which suggests a novel predictive capability for this analysis technique.

nlin.AO↗

arXiv2020

Chaos in the quantum Duffing oscillator in the semiclassical regime under parametrized dissipation

We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial (based on Kullback-Leibler distances between phase-space attractors) and temporal (Lyapunov exponent-based) complexity metrics, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. Remarkably, we find that a parametrically invariant meta-attractor emerges at a specific length scale and noise-added classical models deviate strongly from quantum dynamics below this scale. Our findings also generalize the previous surprising result that classically regular orbits can have the greatest quantum-classical differences in the semiclassical regime. In particular, we show that the dynamical growth of quantum-classical differences is not determined by the degree of classical chaos.

quant-ph↗

arXiv2017

Entanglement and its relationship to classical dynamics

We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement $S_Q$ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of $S_Q$ even for the extreme case of two spin-$1/2$ qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum initial-condition dependence are both organized around the symmetry points of the Hamiltonian. We also show clear (quasi-)periodicity in entanglement as a function of number of kicks and of kick strength.

quant-ph↗

arXiv2016

Dynamical complexity in the quantum to classical transition

We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Planck's constant $\hbar_{eff}\equivβ$ and coupling to the environment, $Γ$. We study this using stochastic Schrodinger equations, semiclassical equations, and the classical limit equation. We show that (i) the dynamical complexity initially increases with effective Hilbert space size (as $β$ decreases) such that the most quantum systems are the least dynamically complex. (ii) If the classical limit is chaotic, that is the most dynamically complex (iii) if the classical limit is regular, there is always a quantum system more dynamically complex than the classical system. There are several parameter regimes where the quantum system is chaotic even though the classical limit is not. While some of the quantum chaotic attractors are of the same family as the classical limiting attractors, we also find a quantum attractor with no classical counterpart. These phenomena occur in experimentally accessible regimes.

quant-ph↗

arXiv2012

Dynamics of Non-classicality Measures in the Decohering Harmonic Oscillator

We show that eigenstates |n> of the harmonic oscillator coupled to a linear Markovian bath demonstrate a non-trivial behavior in the dynamics of measures of non-classicality. Specifically, as the system undergoes decoherence, a time-dependent peak in non-classicality as a function of n emerges. We find this effect studying the dynamics of several non-classicality measures previously presented in the literature which compare quantum states to the set of all classical states. In studying these measures we introduce a novel set of classical states for the purpose of calculations which improve upon the results obtainable using these measures. In addition, following in the footsteps of Kenfack and Źyczkowski, we show that the negative volume of the Wigner function agrees well with all the non-classicality measures while being otherwise calculationally significantly more tractable. Finally, we explore the dynamics of non-classicality of several other states.

quant-ph↗

arXiv2012

Experimental signatures of the quantum-classical transition in a nanomechanical oscillator modeled as a damped driven double-well problem

We demonstrate robust and reliable signatures for the transition from quantum to classical behavior in the position probability distribution of a damped double-well system using the Qunatum State Diffusion approach to open quantum systems. We argue that these signatures are within experimental reach, for example in a doubly-clamped nanomechanical beam.

quant-ph↗

arXiv2010

Decoherence of Fock States Leads to a Maximally Quantum State

We consider the Wigner function evolution of Fock states $|n\rangle$ linearly coupled to a Markovian bath of oscillators. In the absence of environmental coupling, apparent ``quantumness'' increases with $n$, but the presence of any environmental interaction causes high-$n$ states to lose their quantum features more rapidly than low-$n$ states. Using the negative volume of the Wigner function as a metric \cite{kenfack04}, we observe a time-dependent quantumness peak across the eigenstates.

quant-ph↗

arXiv2009

Parameter scaling in a novel measure of quantum-classical difference for decohering chaotic systems

In this paper we introduce a diagnostic for measuring the quantum-classical difference for open quantum systems, which is the normalized size of the quantum terms in the Master equation for Wigner function evolution. For a driven Duffing oscillator, this measure shows remarkably precise scaling over long time-scales with the parameter $ζ_0=\hbar^2/D$. We also see that, independent of $ζ_0$ the dynamics follows a similar pattern. For small $ζ_0$ all of our curves collapses to essentially a single curve when scaled by the maximum value of the quantum-classical difference. In both limits of large and small $ζ_0$ we see a saturation effect in the size of the quantum-classical difference; that is, the instantaneous difference between quantum and classical evolutions cannot be either too small or too large.

quant-ph↗

arXiv2008

Negativity of the Coarse Grained Wigner Function as a Measure of Quantal Behavior

The negativity of a given state's Wigner function has been proposed as a measure of quantumness of that state in a unipartite system. This otherwise physically intuitive and useful phase-space measure however does not yield the right correspondence principle limit, and also turns out to yield infinite values for the infinite square well. We show that both these issues can be sensibly resolved using coarse-graining of the Wigner function.

quant-ph↗

arXiv2007

Controlling the Ratchet Effect for Cold Atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.

quant-ph↗

arXiv2007

Non-monotonicity in the quantum-classical transition: Chaos induced by quantum effects

The transition from classical to quantum behavior for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative size of $\hbar$ is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the double-well Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective $\hbar$ is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantum-classical transition in this case is non-monotonic in $\hbar$.

quant-ph↗

arXiv2007

Quantum entropy dynamics for chaotic systems beyond the classical limit

The entropy production rate for an open quantum system with a classically chaotic limit has been previously argued to be independent of $\hbar$ and $D$, the parameter denoting coupling to the environment, and to be equal to the sum of generalized Lyapunov exponents, with these results applying in the near-classical regime. We present results for a specific system going well beyond earlier work, considering how these dynamics are altered for the Duffing problem by changing $\hbar,D$ and show that the entropy dynamics have a transition from classical to quantum behavior that scales, at least for a finite time, as a function of $\hbar^2/D$.

quant-ph↗

arXiv2006

Bifurcations and sudden current change in ensembles of classically chaotic ratchets

In \prl 84, 258 (2000), Mateos conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes. This is based on the comparison of the current and the bifurcation diagram as a function of a given parameter for a periodic asymmetric potential. Barbi and Salerno, in \pre 62, 1988 (2000), have further investigated this claim and argue that, contrary to Mateos' claim, current reversals can occur also in the absence of bifurcations. Barbi and Salerno's studies are based on the dynamics of one particle rather than the statistical mechanics of an ensemble of particles moving in the chaotic system. The behavior of ensembles can be quite different, depending upon their characteristics, which leaves their results open to question. In this paper we present results from studies showing how the current depends on the details of the ensemble used to generate it, as well as conditions for convergent behavior (that is, independent of the details of the ensemble). We are then able to present the converged current as a function of parameters, in the same system as Mateos as well as Barbi and Salerno. We show evidence for current reversal without bifurcation, as well as bifurcation without current reversal. We conjecture that it is appropriate to correlate abrupt changes in the current with bifurcation, rather than current reversals, and show numerical evidence for our claims.

nlin.CD↗

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

Stabilizing an Attractive Bose-Einstein Condensate by Driving a Surface Collective Mode

Bose-Einstein condensates of $^7$Li have been limited in number due to attractive interatomic interactions. Beyond this number, the condensate undergoes collective collapse. We study theoretically the effect of driving low-lying collective modes of the condensate by a weak asymmetric sinusoidally time-dependent field. We find that driving the radial breathing mode further destabilizes the condensate, while excitation of the quadrupolar surface mode causes the condensate to become more stable by imparting quasi-angular momentum to it. We show that a significantly larger number of atoms may occupy the condensate, which can then be sustained almost indefinitely. All effects are predicted to be clearly visible in experiments and efforts are under way for their experimental realization.

cond-mat↗

arXiv1999

Lyapunov exponents, entropy production and decoherence

We establish that the entropy production rate of a classically chaotic Hamiltonian system coupled to the environment settles, after a transient, to a meta-stable value given by the sum of positive generalized Lyapunov exponents. A meta-stable steady state is generated in this process. This behavior also occurs in quantum systems close to the classical limit where it leads to the restoration of quantum-classical correspondence in chaotic systems coupled to the environment.

chao-dyn↗

arXiv1997

Exponentially rapid decoherence of quantum chaotic systems

We use a recent result to show that the rate of loss of coherence of a quantum system increases with increasing system phase space structure and that a chaotic quantal system in the semiclassical limit decoheres exponentially with rate $2 λ_2$, where $λ_2$ is a generalized Lyapunov exponent. As a result, for example, the dephasing time for classically chaotic systems goes to infinity logarithmically with the temperature, in accord with recent experimental results.

chao-dyn↗