Walter T. Strunz

Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion

Stochastic Schroedinger equations for quantum trajectories offer an alternative and sometimes superior approach to the study of open quantum system dynamics. Here we show that recently established convolutionless non-Markovian stochastic Schroedinger equations may serve as a powerful tool for the derivation of convolutionless master equations for non-Markovian open quantum systems. The most interesting example is quantum Brownian motion (QBM) of a harmonic oscillator coupled to a heat bath of oscillators, one of the most employed exactly soluble models of open system dynamics. We show explicitly how to establish the direct connection between the exact convolutionless master equation of QBM and the corresponding convolutionless exact stochastic Schroedinger equation.

Decoherence scenarios from microscopic to macroscopic superpositions

Environment induced decoherence entails the absence of quantum interference phenomena from the macroscopic world. The loss of coherence between superposed wave packets is a dynamical process the speed of which depends on the packet separation: The farther the packets are apart, the faster they decohere. The precise temporal course depends on the relative size of the time scales of decoherence and other processes taking place in the open system and its environment. We use the exactly solvable model of a harmonic oscillator coupled to a bath of harmonic oscillators to illustrate various decoherence scenarios: These range from exponential golden-rule decay for microscopic superpositions, system-specific decay for larger separations in a crossover regime, and finally the universal interaction-dominated decoherence for ever more macroscopic superpositions investigated in great generality in the accompanying Paper I [W. T. Strunz, F. Haake, and D. Braun, Phys. Rev. A

Volumes of conditioned bipartite state spaces

67,

Decoherence in Quantum Physics

022101

Finite Temperature Dynamics of the Total State in an Open System Model

(2003)].

Stochastic pure states for quantum Brownian motion

We analyze the metric properties of conditioned quantum state spaces These spaces are the convex sets of density matrices that, when partially traced over m degrees of freedom, respectively yield the given n × n density matrix η. For the case n = 2, the volume of equipped with the Hilbert–Schmidt measure can be conjectured to be a simple polynomial of the radius of η in the Bloch-ball. Remarkably, for we find numerically that the probability to find a separable state in is independent of η (except for η pure). For , the same holds for , the probability to find a state with a positive partial transpose in . These results are proven analytically for the case of the family of 4 × 4 X-states, and thoroughly numerically investigated for the general case. The important implications of these findings for the clarification of open problems in quantum theory are pointed out and discussed.

Electron spin tomography through counting statistics : A quantum trajectory approach

We study the Hilbert–Schmidt measure on the manifold of mixed Gaussian states in multi-mode continuous variable quantum systems. An analytical expression for the Hilbert–Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert–Schmidt measure.

Bose?Einstein condensate in a double-well potential: Feynman path integral variational approach

In quantum mechanics, two states |ψ 1〉 and |ψ 2〉 of a system may be superposed to give a new state |ψ〉 = (|ψ 1〉 + |ψ 2〉)/√2. Sometimes, due to environmental influences, such a superposition is not dynamically robust and decays into a mixture ρ = 1/2 (|ψ 1〉〈ψ 1|+|ψ 2〉〈ψ 2|). These lectures are concerned with the nature of robust states and the time scales involved during the transition from the coherent superposition to the mixture, i.e the time scale of decoherence.

Aspects of Open Quantum System Dynamics

We determine the dynamics of the total state of a system and environment for an open system model, at finite temperature. Based on a partial Husimi representation, our framework describes the full dynamics very efficiently through equations in the Hilbert space of the open system only. We briefly review the zero-temperature case and present the corresponding new finite temperature theory, within the usual Born-Markov approximation. As we will show, from a reduced point of view, our approach amounts to the derivation of a stochastic Schrödinger equation description of the dynamics. We show how the reduced density operator evolves according to the expected (finite temperature) master equation of Lindblad form.