The persistence of bipartite ecological communities with Lotka-Volterra dynamics.

The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific interactions are organised according to a bipartite network. Considering the dynamics of species abundances to be governed by generalised Lotka-Volterra equations, we extend work on unipartite networks to we derive exact results for the phase diagram of this model.

Ternary network models for disturbed ecosystems.

The complex network of interactions between species makes understanding the response of ecosystems to disturbances an enduring challenge. One commonplace way to deal with this complexity is to reduce the description of a species to a binary presence-absence variable. Though convenient, this limits the patterns of behaviours representable within such models.

Stability-instability transition in tripartite merged ecological networks.

Although ecological networks are typically constructed based on a single type of interaction, e.g. trophic interactions in a food web, a more complete picture of ecosystem composition and functioning arises from merging networks of multiple interaction types.

Enhanced violations of Leggett-Garg inequalities in an experimental three-level system.

Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests.

Atomic "bomb testing": the Elitzur-Vaidman experiment violates the Leggett-Garg inequality.

Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object-in a dramatic scenario, a bomb-without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the "bomb test" with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett-Garg inequality-a quantitative criterion fulfilled by macro-realistic physical theories.

Feedback control of waiting times.

Feedback loops are known as a versatile tool for controlling transport in small systems, which usually have large intrinsic fluctuations. Here we investigate the control of a temporal correlation function, the waiting-time distribution, under active and passive feedback conditions. We develop a general formalism and then specify to the simple unidirectional transport model, where we compare costs of open-loop and feedback control and use methods from optimal control theory to optimize waiting-time distributions.

Waiting time distribution for continuous stochastic systems.

The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers.

Temporal quantum correlations and Leggett-Garg inequalities in multilevel systems.

We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels N that can be accessed by the measurement apparatus via projective measurements. We provide exact bounds for small N that exceed the known bound for the Leggett-Garg inequality, and we show that in the limit N→∞ the Leggett-Garg inequality can be violated up to its algebraic maximum.

Full-counting statistics of random transition-rate matrices.

We study the full-counting statistics of current of large open systems through the application of random-matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating functions based on an expansion in terms of the inverse system size. We investigate how different symmetry properties and different counting schemes affect the results.

Delayed feedback control in quantum transport.

Feedback control in quantum transport has been predicted to give rise to several interesting effects, among them quantum state stabilization and the realization of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system are affected instantaneously after the measurement of electronic jumps through it. In this contribution, I describe how to include a delay between detection and control operation in the master equation theory of feedback-controlled quantum transport.

Minimal model for short-time diffusion in periodic potentials.

We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the density field, that is, average position and the mean-squared displacement, show nontrivial (nondiffusive) short-time behavior characterized by the appearance of plateaus. We demonstrate that this "cage-like" dynamics can be well described by a discretized master equation model involving two states (related to two positions) within each potential valley.

Charge qubit purification by an electronic feedback loop.

We propose the manipulation of an isolated qubit by a simple instantaneous closed-loop feedback scheme in which a time-dependent electronic detector current is directly back-coupled into qubit parameters. As a specific detector model, we employ a capacitively coupled single-electron transistor. We demonstrate the stabilization of pure delocalized qubit states above a critical detector-qubit coupling.

Self-consistent electron counting statistics.

We develop a self-consistent version of perturbation theory in Liouville space which seeks to combine the advantages of master equation approaches in quantum transport with the nonperturbative features that a self-consistent treatment brings. We describe how counting fields may be included in a self-consistent manner in this formalism such that the full counting statistics can be calculated. Non-Markovian effects are also incorporated.

Distinguishing quantum and classical transport through nanostructures.

We consider the question of how to distinguish quantum from classical transport through nanostructures. To address this issue we have derived two inequalities for temporal correlations in nonequilibrium transport in nanostructures weakly coupled to leads. The first inequality concerns local charge measurements and is of general validity; the second concerns the current flow through the device and is relevant for double quantum dots.

Chaos and the quantum phase transition in the Dicke model.

We investigate the quantum-chaotic properties of the Dicke Hamiltonian; a quantum-optical model that describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N --> infinity limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N, and by analyzing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase transition.

Spin-orbit-driven coherent oscillations in a few-electron quantum dot.

We propose an experiment to observe coherent oscillations in a single quantum dot with the oscillations driven by spin-orbit interaction. This is achieved without spin-polarized leads, and relies on changing the strength of the spin-orbit coupling via an applied gate pulse. We derive an effective model of this system which is formally equivalent to the Jaynes-Cummings model of quantum optics.

Entanglement and the phase transition in single-mode superradiance.

We consider the entanglement properties of the quantum phase transition in the single-mode superradiance model, involving the interaction of a boson mode and an ensemble of atoms. For an infinite size system, the atom-field entanglement diverges logarithmically with the correlation length exponent. Using a continuous variable representation, we compare this to the divergence of the entropy in conformal field theories and derive an exact expression for the scaled concurrence and the cusplike nonanalyticity of the momentum squeezing.

Quantum chaos triggered by precursors of a quantum phase transition: the dicke model.

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localization-delocalization transition in which a macroscopic superposition is generated.