Open system control of dynamical transitions under the generalized Kruskal-Neishtadt-Henrard theorem.

Useful dynamical processes often begin through barrier-crossing dynamical transitions; engineering system dynamics in order to make such transitions reliable is therefore an important task for biological or artificial microscopic machinery. Here, we first show by example that adding even a small amount of back-reaction to a control parameter, so that it responds to the system's evolution, can significantly increase the fraction of trajectories that cross a separatrix. We then explain how a post-adiabatic theorem due to Neishtadt can quantitatively describe this kind of enhancement without having to solve the equations of motion, allowing systematic understanding and design of a class of self-controlling dynamical systems.

Hamiltonian active particles in an environment.

We examine a Hamiltonian system which represents an active particle that can move against an opposing external force by drawing energy from an internal depot while immersed in a noisy and dissipative environment. The Hamiltonian consists of two subsystems, one representing the active particle's motion and the other its depot of "fuel." We show that although the active particle loses some of its energy to dissipation from the environment, dissipation can also help to stabilize the dynamical process that makes the particle active.

Prethermalization with negative specific heat.

We study noncanonical relaxation in an aggregate of subsystems with negative specific heat. The Thirring instability drives the constituent subsystems towards the edges of their energy spectrum, so that the existence of a single adiabatic invariant results in structured noncanonical steady states that are spectacularly different from the grand-canonical prediction. For parameter regimes where this adiabatic invariance breaks down, the system exhibits prethermalization far away from integrability, with an unprecedented contrast between the prethermal- and thermal states.

Probabilistic Hysteresis in Integrable and Chaotic Isolated Hamiltonian Systems.

We propose currently feasible experiments using small, isolated systems of ultracold atoms to investigate the effects of dynamical chaos in the microscopic onset of irreversibility. A control parameter is tuned past a critical value, then back to its initial value; hysteresis appears as a finite probability that the atoms fail to return to their initial state even when the parameter sweep is arbitrarily slow. We show that an episode of chaotic dynamics during part of the sweep time produces distinctive features in the distribution of final states that will be clearly observable in experiments.

Quantum Hamiltonian daemons: Unitary analogs of combustion engines.

Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom (steady downconversion), analogous to the steady transfer of energy in a combustion engine from the high terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [L. Gilz, E. P.

Hamiltonian analogs of combustion engines: A systematic exception to adiabatic decoupling.

Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of adiabatic decoupling: the high-frequency modes "dress" the low-frequency modes, and renormalize their Hamiltonian, but they do not steadily inject energy into the low-frequency sector. Here, however, we identify a broad class of dynamical systems in which adiabatic decoupling fails to hold, and steady energy transfer across a large gap in natural frequency ("steady downconversion") instead becomes possible, through nonlinear resonances of a certain form.

Minimal Fokker-Planck theory for the thermalization of mesoscopic subsystems.

We explore a minimal paradigm for thermalization, consisting of two weakly coupled, low dimensional, nonintegrable subsystems. As demonstrated for Bose-Hubbard trimers, chaotic ergodicity results in a diffusive response of each subsystem, insensitive to the details of the drive exerted on it by the other. This supports the hypothesis that thermalization can be described by a Fokker-Planck equation.

Quantum kinetic theory of collisionless superfluid internal convection.

Superfluids can transport heat via simultaneous opposite flows of their spatially interpenetrating condensate and noncondensate components. While this internal convection is usually described within Landau's phenomenological two-fluid hydrodynamics, we apply quantum kinetic theory to a dilute Bose gas held between thermal reservoirs at different temperatures and show that the phenomenon also appears in collisionless kinetic regimes and should be directly observable in currently feasible experiments on trapped ultracold vapors.

Collisions in zero temperature Fermi gases.

We examine the collisional behavior of two-component Fermi gases released at zero temperature from a harmonic trap. Using a phase-space formalism to calculate the collision rate during expansion, we find that Pauli blocking plays only a minor role for momentum changing collisions. As a result, for a large scattering cross section, Pauli blocking will not prevent the gas from entering the collisionally hydrodynamic regime.

Bose-Einstein condensation of atomic gases.

The early experiments on Bose-Einstein condensation in dilute atomic gases accomplished three long-standing goals. First, cooling of neutral atoms into their motional ground state, thus subjecting them to ultimate control, limited only by Heisenberg's uncertainty relation. Second, creation of a coherent sample of atoms, in which all occupy the same quantum state, and the realization of atom lasers - devices that output coherent matter waves.