Microscopic formula for transport coefficients of causal hydrodynamics

The Green-Kubo-Nakano formula should be modified in relativistic hydrodynamics because of the problem of acausality and the breaking of sum rules. In this work, we propose a formula to calculate the transport coefficients of causal hydrodynamics based on the projection operator method. As concrete examples, we derive the expressions for the diffusion coefficient, the shear viscosity coefficient, and corresponding relaxation times.Comment: 4 pages, title was modified, final version published in Phys. Rev.

Singlet-triplet decoherence due to nuclear spins in a double quantum dot

We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 1/2, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law ($\sim 1/t^{3/2}$) when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\pi/4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence, and find that there is an optimal operating point where orbital dephasing becomes negligible.Comment: 12 pages, 4 figure

Local forest structure variability increases resilience to wildfire in dry western U.S. coniferous forests.

A 'resilient' forest endures disturbance and is likely to persist. Resilience to wildfire may arise from feedback between fire behaviour and forest structure in dry forest systems. Frequent fire creates fine-scale variability in forest structure, which may then interrupt fuel continuity and prevent future fires from killing overstorey trees. Testing the generality and scale of this phenomenon is challenging for vast, long-lived forest ecosystems. We quantify forest structural variability and fire severity across >30 years and >1000 wildfires in California's Sierra Nevada. We find that greater variability in forest structure increases resilience by reducing rates of fire-induced tree mortality and that the scale of this effect is local, manifesting at the smallest spatial extent of forest structure tested (90 × 90 m). Resilience of these forests is likely compromised by structural homogenisation from a century of fire suppression, but could be restored with management that increases forest structural variability

Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method

We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation is consistent with causality and the sum rule associated with the number conservation in the low momentum limit, in contrast to usual acausal diffusion equations given by using the Fick's law. After employing the Markov approximation, we find that the equation has the similar form to the causal diffusion equation. Our result suggests that current-current correlations are not necessarily adequate as the definition of diffusion constants.Comment: 10 pages, 1 figure, Final version published in Phys. Rev.

Exponential decay in a spin bath

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.Comment: 4+ pages, 3 figures; v2: 9 pages, 3 figures (added four appendices with extensive technical details, version to appear in Phys. Rev. B

Free-induction decay and envelope modulations in a narrowed nuclear spin bath

We evaluate free-induction decay for the transverse components of a localized electron spin coupled to a bath of nuclear spins via the Fermi contact hyperfine interaction. Our perturbative treatment is valid for special (narrowed) bath initial conditions and when the Zeeman energy of the electron $b$ exceeds the total hyperfine coupling constant $A$: $b>A$. Using one unified and systematic method, we recover previous results reported at short and long times using different techniques. We find a new and unexpected modulation of the free-induction-decay envelope, which is present even for a purely isotropic hyperfine interaction without spin echoes and for a single nuclear species. We give sub-leading corrections to the decoherence rate, and show that, in general, the decoherence rate has a non-monotonic dependence on electron Zeeman splitting, leading to a pronounced maximum. These results illustrate the limitations of methods that make use of leading-order effective Hamiltonians and re-exponentiation of short-time expansions for a strongly-interacting system with non-Markovian (history-dependent) dynamics.Comment: 13 pages, 9 figure

Microscopic Theory for the Markovian Decay of Magnetization Fluctuations in Nanomagnets

We present a microscopic theory for the phonon-driven decay of the magnetization fluctuations in a wide class of nanomagnets where the dominant energy is set by isotropic exchange and/or uniaxial anisotropy. Based on the Zwanzig-Mori projection formalism, the theory reveals that the magnetization fluctuations are governed by a single decay rate $\omega_c$, which we further identify with the zero-frequency portion of the associated self-energy. This dynamical decoupling from the remaining slow degrees of freedom is attributed to a conservation law and the discreteness of the energy spectrum, and explains the omnipresent mono-exponential decay of the magnetization over several decades in time, as observed experimentally. A physically transparent analytical expression for $\omega_c$ is derived which highlights the three specific mechanisms of the slowing down effect which are known so far in nanomagnets.Comment: 7 page

Dynamical typicality of quantum expectation values

We show that the vast majority of all pure states featuring a common expectation value of some generic observable at a given time will yield very similar expectation values of the same observable at any later time. This is meant to apply to Schroedinger type dynamics in high dimensional Hilbert spaces. As a consequence individual dynamics of expectation values are then typically well described by the ensemble average. Our approach is based on the Hilbert space average method. We support the analytical investigations with numerics obtained by exact diagonalization of the full time-dependent Schroedinger equation for some pertinent, abstract Hamiltonian model. Furthermore, we discuss the implications on the applicability of projection operator methods with respect to initial states, as well as on irreversibility in general.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let

Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics

A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.Comment: 15 pages, no figure. Discussions are added in the concluding remarks. Accepted for publication in Phys. Rev.

Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics

We have performed a systematic calculation for the non-Markovian dynamics of a localized electron spin interacting with an environment of nuclear spins via the Fermi contact hyperfine interaction. This work applies to an electron in the s -type orbital ground state of a quantum dot or bound to a donor impurity, and is valid for arbitrary polarization p of the nuclear spin system, and arbitrary nuclear spin I in high magnetic fields. In the limit of p=1 and I=1/2, the Born approximation of our perturbative theory recovers the exact electron spin dynamics. We have found the form of the generalized master equation (GME) for the longitudinal and transverse components of the electron spin to all orders in the electron spin--nuclear spin flip-flop terms. Our perturbative expansion is regular, unlike standard time-dependent perturbation theory, and can be carried-out to higher orders. We show this explicitly with a fourth-order calculation of the longitudinal spin dynamics. In zero magnetic field, the fraction of the electron spin that decays is bounded by the smallness parameter \delta=1/p^{2}N, where N is the number of nuclear spins within the extent of the electron wave function. However, the form of the decay can only be determined in a high magnetic field, much larger than the maximum Overhauser field. In general the electron spin shows rich dynamics, described by a sum of contributions with non-exponential decay, exponential decay, and undamped oscillations. There is an abrupt crossover in the electron spin asymptotics at a critical dimensionality and shape of the electron envelope wave function. We propose a scheme that could be used to measure the non-Markovian dynamics using a standard spin-echo technique, even when the fraction that undergoes non-Markovian dynamics is small.Comment: 22 pages, 8 figure