Tunneling-induced dephasing in InP quantum dots

We observed the tunneling process of photo-excited holes in neutral InP quantum dots and Pauli blocking of charged InP quantum dots. A highly sensitive heterodyne-detected photon echo method enabled us to observe the signal from one layer of self-assembled InP quantum dots under the electric field. The electric field could control the charging or neutralization of the InP quantum dots and hence the photon echo signal decreased considerably with the increase of electron doping. The photon echo of neutral InP quantum dots under the electric field showed tunneling-induced dephasing, which decays non-exponentially reflecting the non-Markovian nature of the tunneling process.     

Correlations between quantum and stochastic systems with a dephasing coupling

Correlations between single qubit and classical environment are studied by means of the stochastic Liouville equation, where a dephasing coupling between them is assumed. When the dephasing of the qubit is characterized by the two-state-jump Markov process, the properties of the total, classical and quantum correlations are examined.     

Acoustic phonon dephasing in shallow GaAs/Ga Al As single quantum wells

The intermediate dimensionality regime is studied on a set of shallow GaAs/Ga Al As single quantum wells. Such heterostructures exhibit 2D strong excitonic electroabsorption together with near 3D fast transport properties. We report dephasing time measurements of the heavy-hole exciton and we show that the acoustic phonon contribution decreases with to a value in good agreement with theoretical predictions for GaAs bulk.     

A singular perturbation approach to first passage times for Markov jump processes

We introduce singular perturbation methods for constructing asymptotic approximations to the mean first passage time for Markov jump processes. Our methods are applied directly to the integrai equation for the mean first passage time and do not involve the use of diffusion approximations. An absorbing interval condition is used to properly account for the possible jumps of the process over the boundary which leads to a Wiener-Hopf problem in the neighborhood of the boundary. A model of unimolecular dissociation is considered to illustrate our methods.     

Wave function multifractality and dephasing at metal–insulator and quantum Hall transitions

We analyze the critical behavior of the dephasing rate induced by short-range electron–electron interaction near an Anderson transition of metal–insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in 2 + ? dimensions) with numerical simulations on the Chalker–Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.     

A comment on the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T.D. Frank

The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and nonlinear Fokker-Planck equations, Physica A 331 (2004) 391]. Our comment centers on the claims of a “non-linear Markov process” and a “non-linear Fokker-Planck equation.” First, memory in transition densities is misidentified as a Markov process. Second, the paper assumes that one can derive a Fokker-Planck equation from a Chapman-Kolmogorov equation, but no proof was offered that a Chapman-Kolmogorov equation exists for the memory-dependent processes considered. A “non-linear Markov process” is claimed on the basis of a non-linear diffusion pde for a 1-point probability density. We show that, regardless of which initial value problem one may solve for the 1-point density, the resulting stochastic process, defined necessarily by the conditional probabilities (the transition probabilities), is either an ordinary linearly generated Markovian one, or else is a linearly generated non-Markovian process with memory. We provide explicit examples of diffusion coefficients that reflect both the Markovian and the memory-dependent cases. So there is neither a “non-linear Markov process”, nor a “non-linear Fokker-Planck equation” for a conditional probability density. The confusion rampant in the literature arises in part from labeling a non-linear diffusion equation for a 1-point probability density as “non-linear Fokker-Planck,” whereas neither a 1-point density nor an equation of motion for a 1-point density can define a stochastic process. In a closely related context, we point out that Borland misidentified a translation invariant 1-point probability density derived from a non-linear diffusion equation as a conditional probability density. Finally, in the Appendix A we present the theory of Fokker-Planck pdes and Chapman-Kolmogorov equations for stochastic processes with finite memory.     

Failure to direct detect magnetic field dephasing corresponding to ERP generation

Functional magnetic resonance imaging (fMRI) has become the method of choice for mapping brain activity in human subjects and detects changes in regional blood oxygenation and volume associated with local changes in neuronal activity. While imaging based on blood oxygenation level dependent (BOLD) contrast has good spatial resolution and sensitivity, the hemodynamic signal develops relatively slowly and is only indirectly related to neuronal activity. An alternative approach termed magnetic source magnetic resonance imaging (msMRI) is based on the premise that neural activity may be mapped by magnetic resonance imaging (MRI) with greater temporal resolution by detecting the local magnetic field perturbations associated with local neuronal electric currents. We used a hybrid ms/BOLD MRI method to investigate whether msMRI could detect signal changes that occur simultaneously at the time of the production of well-defined event-related potentials, the P300 and N170, in regions that previously have been identified as generators of these electrical signals. Robust BOLD activations occurred after some seconds, but we were unable to detect any significant changes in the T2*-weighted signal in these locations that correlated temporally with the timings of the evoked response potentials (ERPs).     

An invariance principle for reversible Markov processes. Applications to random motions in random environments

We present an invariance principle for antisymmetric functions of a reversible Markov process which immediately implies convergence to Brownian motion for a wide class of random motions in random environments. We apply it to establish convergence to Brownian motion (i) for a walker moving in the infinite cluster of the two-dimensional bond percolation model, (ii) for ad-dimensional walker moving in a symmetric random environment under very mild assumptions on the distribution of the environment, (iii) for a tagged particle in ad-dimensional symmetric lattice gas which allows interchanges, (iv) for a tagged particle in ad-dimensional system of interacting Brownian particles. Our formulation also leads naturally to bounds on the diffusion constant.     

A definition of metastability for Markov processes with detailed balance

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach [1]. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.     

Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.     

Dynamical Entropy of Generalized Quantum Markov Chains on Gauge-invariant C *-algebras

We prove that the mean entropy and the dynamical entropy are equal for generalized quantum Markov chains on gauge-invariant C ^*-algebras.     

Dynamical suppression of 1/f noise processes in qubit systems

We investigate the capability of dynamical decoupling techniques to reduce decoherence from a realistic environment generating 1/f noise. The predominance of low frequency modes in the noise profile allows for decoherence scenarios where relatively slow control rates suffice for a drastic improvement. However, the actual figure of merit is very sensitive to the details of the dynamics, with decoupling performance which may deteriorate for non-Gaussian noise and/or high frequency working points. Our results are promising for robust solid-state qubits and beyond.     

Universal Solutions of Quantum Dynamical Yang–Baxter Equations

We construct a universal trigonometric solution of the Gervais–Neveu–Felder equation in the case of finite-dimensional simple Lie algebras and finite-dimensional contragredient simple Lie superalgebras.     

A comparative study of two phenomenological models of dephasing in series and parallel resistors

We compare two recent phenomenological models of dephasing using a double barrier and a quantum ring geometry. While the stochastic absorption model generates controlled dephasing leading to Ohm's law for large dephasing strengths, a Gaussian random phase based statistical model shows many inconsistencies.     

Quantum theory of dissipative processes: The Markov approximation revisited

Adopting the standard mathematical framework for describing reduced dynamics, we derive two formal identities for the density operator of an open quantum system. Each of these is equivalent to the old Nakajima-Zwanzig equation. The first identity is local in time. It contains the inverse of the dynamical map which govern the evolution of the density operator. We indicate a time interval on which this inverse exists. The second identity constitutes a suitable starting point for going beyond the Markov approximation in a controlled way. On the basis of the Bloch equations we argue once more that in studying quantum dissipation one has to pay attention to the von Neumann conditions. In the Nakajima-Zwanzig equation we make the first Born approximation. The ensuing master equation possesses the correct weak-coupling limit. While proving this rather obvious but at the same time important statement, we elucidate the mathematical methods which underlie the weak-coupling limit. Moving to a two-dimensional Hilbert space, we find that both for short and for long times our approximate master equation respects the von Neumann conditions. Assuming exponential decay for correlation functions, we propose a physical limit in which the solutions for the density operator become Markovian in character. We confirm the well-known statement that, as seen from a macroscopic standpoint, the system starts from an effective initial condition. The approach to equilibrium is exponential. The accessory relaxation constants can differ from the usual Bloch parameters and by more than 50%.     

Active suppression of dephasing in Josephson-junction qubits

Simple majority code correcting k dephasing errors by encoding a qubit of information into 2k+1 physical qubits is studied quantitatively. We derive an equation for quasicontinuous evolution of the density matrix of encoded quantum information under the error correction procedure in the presence of correlated dephasing noise. A specific design of a Josephson-junction nanocircuit implementing this scheme is suggested.