Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum to classical transition in a system with a mixed classical dynamics
96
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study how decoherence rules the quantum-classical transition of the Kicked Harmonic Oscillator (KHO). When the amplitude of the kick is changed the system presents a classical dynamics that range from regular to a strong chaotic behavior. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and the quantum phase space distributions is proportional to a single parameter $chiequiv Khbar_{rm eff}^2/4D^{3/2}$ which relates the effective Planck constant $hbar_{rm eff}$, the kick amplitude $K$ and the diffusion constant $D$. This is valid when $chi < 1$, a case that is always attainable in the semiclassical regime independently of the value of the strength of noise given by $D$. Our results extend a recent study performed in the chaotic regime.
rate research
Read More
We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Plancks constant $hbar_{eff}equivbeta$ and coupling to the environment, $Gamma$. 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 $beta$ 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.
We study the quantum to classical transition in a chaotic system surrounded by a diffusive environment. The emergence of classicality is monitored by the Renyi entropy, a measure of the entanglement of a system with its environment. We show that the Renyi entropy has a transition from quantum to classical behavior that scales with $hbar^2_{rm eff}/D$, where $hbar_{rm eff}$ is the effective Planck constant and $D$ is the strength of the noise. However, it was recently shown that a different scaling law controls the quantum to classical transition when it is measured comparing the corresponding phase space distributions. We discuss here the meaning of both scalings in the precise definition of a frontier between the classical and quantum behavior. We also show that there are quantum coherences that the Renyi entropy is unable to detect which questions its use in the studies of decoherence.
The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuations theorems. Here we develop a semiclassical approximation to the work distribution for a quench process in chaotic systems. The approach is based on the dephasing representation of the quantum Loschmidt echo and on the quantum ergodic conjecture, which states that the Wigner function of a typical eigenstate of a classically chaotic Hamiltonian is equidistributed on the energy shell. We show that our semiclassical approximation is accurate in describing the quantum distribution as we increase the temperature. Moreover, we also show that this semiclassical approximation provides a link between the quantum and classical work distributions.
We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough that quantum backaction noise is negligible. We investigate the conditions under which classical dynamics emerges, via continuous position measurement, for a particle moving in a harmonic well with its position coupled to internal spin. As a consequence of this coupling we find that classical dynamics emerges only when the position and spin actions are both large compared to $hbar$. These conditions are quantified by placing bounds on the size of the covariance matrix which describes the delocalized quantum coherence over extended regions of phase space. From this result it follows that a mixed quantum-classical regime (where one subsystem can be treated classically and the other not) does not exist for a continuously observed spin 1/2 particle. When the conditions for classicallity are satisfied (in the large-spin limit), the quantum trajectories reproduce both the classical periodic orbits as well as the classically chaotic phase space regions. As a quantitative test of this convergence we compute the largest Lyapunov exponent directly from the measured quantum trajectories and show that it agrees with the classical value.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
