Time-domain scars: resolving the spectral form factor in phase space

We study the relationship of the spectral form factor with quantum as well as classical probabilities to return. Defining a quantum return probability in phase space as a trace over the propagator of the Wigner function allows us to identify and resolve manifolds in phase space that contribute to the form factor. They can be associated to classical invariant manifolds such as periodic orbits, but also to non-classical structures like sets of midpoints between periodic points. By contrast to scars in wavefunctions, these features are not subject to the uncertainty relation and therefore need not show any smearing. They constitute important exceptions from a continuous convergence in the classical limit of the Wigner towards the Liouville propagator. We support our theory with numerical results for the quantum cat map and the harmonically driven quartic oscillator.Comment: 10 pages, 4 figure

Driven Tunneling: Chaos and Decoherence

Chaotic tunneling in a driven double-well system is investigated in absence as well as in the presence of dissipation. As the constitutive mechanism of chaos-assisted tunneling, we focus on the dynamics in the vicinity of three-level crossings in the quasienergy spectrum. The coherent quantum dynamics near the crossing is described satisfactorily by a three-state model. It fails, however, for the corresponding dissipative dynamics, because incoherent transitions due to the interaction with the environment indirectly couple the three states in the crossing to the remaining quasienergy states. The asymptotic state of the driven dissipative quantum dynamics partially resembles the, possibly strange, attractor of the corresponding damped driven classical dynamics, but also exhibits characteristic quantum effects.Comment: 32 pages, 35 figures, lamuphys.st

Non-adiabatic pumping in an oscillating-piston model

We consider the prototypical "piston pump" operating on a ring, where a circulating current is induced by means of an AC driving. This can be regarded as a generalized Fermi-Ulam model, incorporating a finite-height moving wall (piston) and non trivial topology (ring). The amount of particles transported per cycle is determined by a layered structure of phase-space. Each layer is characterized by a different drift velocity. We discuss the differences compared with the adiabatic and Boltzmann pictures, and highlight the significance of the "diabatic" contribution that might lead to a counter-stirring effect.Comment: 6 pages, 4 figures, improved versio

Semiclassical propagator of the Wigner function

Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a \emph{pair} of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.Comment: 4 pages, 3 figure

Toppling pencils -- Macroscopic Randomness from Microscopic Fluctuations

We construct a microscopic model to study discrete randomness in bistable systems coupled to an environment comprising many degrees of freedom. A quartic double well is bilinearly coupled to a finite number $N$ of harmonic oscillators. Solving the time-reversal invariant Hamiltonian equations of motion numerically, we show that for $N = 1$, the system exhibits a transition with increasing coupling strength from integrable to chaotic motion, following the KAM scenario. Raising $N$ to values of the order of 10 and higher, the dynamics crosses over to a quasi-relaxation, approaching either one of the stable equilibria at the two minima of the potential. We corroborate the irreversibility of this relaxation on other characteristic timescales of the system by recording the time dependences of autocorrelation, partial entropy, and the frequency of jumps between the wells as functions of $N$ and other parameters. Preparing the central system in the unstable equilibrium at the top of the barrier and the bath in a random initial state drawn from a Gaussian distribution, symmetric under spatial reflection, we demonstrate that the decision whether to relax into the left or the right well is determined reproducibly by residual asymmetries in the initial positions and momenta of the bath oscillators. This result reconciles the randomness and spontaneous symmetry breaking of the asymptotic state with the conservation of entropy under canonical transformations and the manifest symmetry of potential and initial condition of the bistable system.Comment: 22 pages, 10 figure

A multidisciplinary survey of modeling techniques for biochemical networks

All processes of life are dominated by networks of interacting biochemical components. The purpose of modeling these networks is manifold. From a theoretical point of view it allows the exploration of network structures and dynamics, to find emergent properties or to explain the organization and evolution of networks. From a practical point of view, in silico experiments can be performed that would be very expensive or impossible to achieve in the laboratory, such as hypothesis-testing with regard to knockout experiments or overexpression, or checking the validity of a proposed molecular mechanism. The literature on modeling biochemical networks is growing rapidly and the motivations behind different modeling techniques are sometimes quite distant from each other. To clarify the current context, we present a systematic overview of the different philosophies to model biochemical networks. We put particular emphasis on three main domains which have been playing a major role in the past, namely: mathematics with ordinary and partial differential equations, statistics with stochastic simulation algorithms, Bayesian networks and Markov chains, and the field of computer science with process calculi, term rewriting systems and state based systems. For each school, we evaluate advantages and disadvantages such as the granularity of representation, scalability, accessibility or availability of analysis tools. Following this, we describe how one can combine some of those techniques and thus take advantages of several techniques through the use of bridging tools. Finally, we propose a next step for modeling biochemical networks by using artificial chemistries and evolutionary computation. This work was funded by ESIGNET (Evolving Cell Signaling Networks in Silico), an European Integrated Project in the EU FP6 NEST Initiative (contract no. 12789)