Related papers: Measuring the Lyapunov exponent using quantum mech…
We show that the rate of increase of von Neumann entropy computed from the reduced density matrix of an open quantum system is an excellent indicator of the dynamical behavior of its classical hamiltonian counterpart. In decohering quantum…
Hamiltonian trajectories are strictly time-reversible. Any time series of Hamiltonian coordinates {q} satisfying Hamilton's motion equations will likewise satisfy them when played "backwards", with the corresponding momenta changing signs :…
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
By analyzing a paradigmatic example of the theory of dissipative systems -- the classical and quantum dissipative standard map -- we are able to explain the main features of the decay to the quantum equilibrium state. The classical…
One of the main methods for protecting quantum information against decoherence is to encode information in the ground subspace (or the low energy sector) of a Hamiltonian with a large energy gap which penalizes errors from environment. The…
Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large…
The dependence of the Lyapunov exponent on the closeness parameter, $\epsilon$, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we…
The relation between the onset of chaos and critical phenomena, like Quantum Phase Transitions (QPT) and Excited-State Quantum Phase transitions (ESQPT), is analyzed for atom-field systems. While it has been speculated that the onset of…
We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…
The mean Poincarr\'e recurrence time as well as the Lyapunov time are measured for the Fermi-Ulam model. We confirm the mean recurrence time is dependent on the size of the window chosen in the phase space to where particles are allowed to…
We study the behavior of an open quantum system, with an $N$--dimensional space of states, whose density matrix evolves according to a non--unitary map defined in two steps: A unitary step, where the system evolves with an evolution…
Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix $\rho_1$, obtained by…
We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward…
We present a Gedankenexperiment that leads to a violation of detailed balance if quantum mechanical transition probabilities are treated in the usual way by applying Fermi's "golden rule". This Gedankenexperiment introduces a collection of…
A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of…