A quantum jump description for the non-Markovian dynamics of the spin-boson model

We derive a time-convolutionless master equation for the spin-boson model in the weak coupling limit. The temporarily negative decay rates in the master equation indicate short time memory effects in the dynamics which is explicitly revealed when the dynamics is studied using the non-Markovian jump description. The approach gives new insight into the memory effects influencing the spin dynamics and demonstrates, how for the spin-boson model the the co-operative action of different channels complicates the detection of memory effects in the dynamics.Comment: 9 pages, 6 figures, submitted to Proceedings of CEWQO200

Test aspects of the JPL Viterbi decoder

The generation of test vectors and design-for-test aspects of the Jet Propulsion Laboratory (JPL) Very Large Scale Integration (VLSI) Viterbi decoder chip is discussed. Each processor integrated circuit (IC) contains over 20,000 gates. To achieve a high degree of testability, a scan architecture is employed. The logic has been partitioned so that very few test vectors are required to test the entire chip. In addition, since several blocks of logic are replicated numerous times on this chip, test vectors need only be generated for each block, rather than for the entire circuit. These unique blocks of logic have been identified and test sets generated for them. The approach employed for testing was to use pseudo-exhaustive test vectors whenever feasible. That is, each cone of logid is tested exhaustively. Using this approach, no detailed logic design or fault model is required. All faults which modify the function of a block of combinational logic are detected, such as all irredundant single and multiple stuck-at faults

Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems

We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.Comment: 4 pages, 2 figures, published versio

Witness for initial system-environment correlations in open system dynamics

We study the evolution of a general open quantum system when the system and its environment are initially correlated. We show that the trace distance between two states of the open system can increase above its initial value, and derive tight upper bounds for the growth of the distinguishability of open system states. This represents a generalization of the contraction property of quantum dynamical maps. The obtained inequalities can be interpreted in terms of the exchange of information between the system and the environment, and lead to a witness for system-environment correlations which can be determined through measurements on the open system alone.Comment: 4 pages, 1 figur

Hierarchical social modularity in gorillas

Modern human societies show hierarchical social modularity (HSM) in which lower-order social units like nuclear families are nested inside increasingly larger units. It has been argued that this HSM evolved independently and after the chimpanzee–human split due to greater recognition of, and bonding between, dispersed kin. We used network modularity analysis and hierarchical clustering to quantify community structure within two western lowland gorilla populations. In both communities, we detected two hierarchically nested tiers of social structure which have not been previously quantified. Both tiers map closely to human social tiers. Genetic data from one population suggested that, as in humans, social unit membership was kin structured. The sizes of gorilla social units also showed the kind of consistent scaling ratio between social tiers observed in humans, baboons, toothed whales, and elephants. These results indicate that the hierarchical social organization observed in humans may have evolved far earlier than previously asserted and may not be a product of the social brain evolution unique to the hominin lineage

Phenomenological memory-kernel master equations and time-dependent Markovian processes

Do phenomenological master equations with memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity? We show by a counterexample that this is not always the case. We consider two commonly used phenomenological integro-differential master equations describing the dynamics of a spin 1/2 in a thermal bath. By using a recently introduced measure to quantify non-Markovianity [H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)] we demonstrate that as far as the equations retain their physical sense, the key feature of non-Markovian behavior does not appear in the considered memory kernel master equations. Namely, there is no reverse flow of information from the environment to the open system. Therefore, the assumption that the integration over a memory kernel always leads to a non-Markovian dynamics turns out to be vulnerable to phenomenological approximations. Instead, the considered phenomenological equations are able to describe time-dependent and uni-directional information flow from the system to the reservoir associated to time-dependent Markovian processes.Comment: 5 pages, no figure

Decoherence and Quantum-Classical Master Equation Dynamics

The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still non-Markovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of non-equilibrium average values or correlation functions is considered, the non-Markovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a model nonadiabatic chemical reaction.Comment: 13 pages, 6 figures, revision includes: Added references on mixed quantum-classical Liouville theory, and some minor details that address the comments of the reviewe

New method to simulate quantum interference using deterministic processes and application to event-based simulation of quantum computation

We demonstrate that networks of locally connected processing units with a primitive learning capability exhibit behavior that is usually only attributed to quantum systems. We describe networks that simulate single-photon beam-splitter and Mach-Zehnder interferometer experiments on a causal, event-by-event basis and demonstrate that the simulation results are in excellent agreement with quantum theory. We also show that this approach can be generalized to simulate universal quantum computers.Comment: J. Phys. Soc. Jpn. (in press) http://www.compphys.net/dl