Related papers: An analytical relation between entropy production …
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
We present a detailed analysis of the convergence properties of Lyapunov control for finite-dimensional quantum systems based on the application of the LaSalle invariance principle and stability analysis from dynamical systems and control…
Despite the rapid development of quantum science and technology, errors are inevitable and play a crucial role in quantum simulation and quantum computation. In quantum chaotic systems, coherent errors arising from imperfect Hamiltonian…
In macroscopic systems behavior is usually reproducible and fluctuations, which are deviations from the typically observed mean values, are small. But almost all inverse problems in the physical and biological sciences are ill-posed and…
We examine an exactly solvable model of decoherence -- a spin-system interacting with a collection of environment spins. We show that in this simple model (introduced some time ago to illustrate environment--induced superselection) generic…
A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order-correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs…
We calculate the Lyapunov exponents describing spatial clustering of particles advected in one- and two-dimensional random velocity fields at finite Kubo numbers Ku (a dimensionless parameter characterising the correlation time of the…
The work done when a system at thermal equilibrium is externally driven by a unitary control parameter leads to irreversible entropy production. The entropy produced can be thought of as a combination of coherence generation and a…
We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the…
We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abstract decay result underpinning a form of inhomogeneous…
Bochi-Katok-Rodriguez Hertz proposed in [BKH21] a program on the flexibility of Lyapunov exponents for conservative Anosov diffeomorphisms, and obtained partial results in this direction. For conservative Anosov diffeomorphisms with strong…
In the framework of the Lindblad theory for open quantum systems, expressions for the density operator, von Neumann entropy and effective temperature of the damped harmonic oscillator are obtained. The entropy for a state characterized by a…
We have systematically studied both classical and quantum chaotic behaviors of two colliding harmonic oscillators. The classical case falls in Kolmogorov-Arnold-Moser class. It is shown that there exists an energy threshold, above which the…
This study establishes a universal mechanism for entropy production in isolated quantum systems governed by interactions that induce random-phase fluctuations. By developing a resolvent-based framework, we demonstrate that steady-state…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…
In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear…
We show that the effect of a Gaussian Bosonic environment linearly coupled to a quantum system can be simulated by a stochastic Lindblad master equation characterized by a set of ancillary Bosonic modes initially at zero temperature and…
We propose a generalized parity-time ($\mathcal{PT}$) -symmetric Li\'enard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
We propose an efficient method to compute Lyapunov exponents and Lyapunov eigenvectors of long-range interacting many-particle systems, whose dynamics is described by the Vlasov equation. We show that an expansion of a distribution function…