A short note on spin pumping theory with Landau-Lifshitz-Gilbert equation under quantum fluctuation; necessity for quantization of localized spin

We would like to point out the blind spots of the approach combining the spin pumping theory proposed by Tserkovnyak et al. with the Landau-Lifshitz-Gilbert equation; this method has been widely used for interpreting vast experimental results. The essence of the spin pumping effect is the quantum fluctuation. Thus, localized spin degrees of freedom should be quantized, i.e. be treated as magnons not as classical variables. Consequently, the precessing ferromagnet can be regarded as a magnon battery. This point of view will be useful for further progress of spintronics.Comment: 10pages, 1 figure. This article is closely related to the work by K. N.; arXiv:1201.194

Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The method we employ in the proof can be considered as fundamental to the integrability of ultradiscrete soliton equations.Comment: 14 pages, 10 figures Added citations in v

Syn-eruptive degassing of a single submarine lava flow : constraints on MORB CO2 variability, vesiculation, and eruption dynamics

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2010Mid-ocean ridge basalts (MORBs) exhibit a wide range of CO2 concentrations, reflecting saturation to supersaturation (and rarely undersaturation) relative to their emplacement depths. In this study, we explore the mechanisms of CO2 degassing and the implications this has for estimating the advance rates and durations of seafloor eruptions. We present dissolved volatile concentrations (mainly of CO2 and H2O) and vesicle size distributions (VSDs) for a unique suite of MORB glasses collected at the East Pacific Rise, ~9° 50′ N. These MORB glasses were collected at ~200 m intervals along an across-axis track over a single flow pathway within the recently emplaced 2005-06 eruption boundaries; systematic sample collection provides one of the first opportunities to characterize intra-flow geochemical and physical evolution during a single eruption at a fast-spreading ridge. Compared to measurements of MORB volatiles globally, dissolved H2O concentrations are relatively uniform (0.10 - 0.16 weight percent), whereas dissolved CO2 contents exhibit a range of concentrations (154 - 278 ppm) and decrease with distance from the EPR axis (i.e., eruptive vent). Ion microprobe analyses of dissolved volatiles within the MORB glasses suggest that the magma erupted supersaturated (pressure equilibrium with 920 - 1224 mbsf) and in near-equilibrium with the melt lens of the axial magma chamber (~1250 - 1500 mbsf), and degassed to near equilibrium (299 - 447 mbsf) with seafloor depths over the length of the flow. The decrease in CO2 concentrations spans nearly the full range of dissolved CO2 contents observed at the EPR and shows that the varying degrees of volatile saturation that have been observed in other MORB sample suites may be explained by degassing during emplacement. Vesicularity (0.1 - 1.2%) increases with decreasing dissolved CO2 concentrations. We use vesicle size distributions (VSDs)—vesicle sizes and number densities—to quantify the physical evolution of the CO2 degassing process. VSDs suggest that diffusion of CO2 into preexisting vesicles, and not nucleation of new vesicles, is the dominant mechanism of increasing CO2 in the vapor phase. We also use VSDs, along with estimates of vesicle growth rates, to constrain emplacement time of the 2005-06 eruption to <~24 hours and to resolve variations in advance rate with downflow distance

Laser control of magnonic topological phases in antiferromagnets

We study the laser control of magnon topological phases induced by the Aharonov-Casher effect in insulating antiferromagnets (AFs). Since the laser electric field can be considered as a time-periodic perturbation, we apply the Floquet theory and perform the inverse frequency expansion by focusing on the high frequency region. Using the obtained effective Floquet Hamiltonian, we study nonequilibrium magnon dynamics away from the adiabatic limit and its effect on topological phenomena. We show that a linearly polarized laser can generate helical edge magnon states and induce the magnonic spin Nernst effect, whereas a circularly polarized laser can generate chiral edge magnon states and induce the magnonic thermal Hall effect. In particular, in the latter, we find that the direction of the magnon chiral edge modes and the resulting thermal Hall effect can be controlled by the chirality of the circularly polarized laser through the change from the left-circular to the right-circular polarization. Our results thus provide a handle to control and design magnon topological properties in the insulating AF

(Pseudo) Random Quantum States with Binary Phase

We prove a quantum information-theoretic conjecture due to Ji, Liu and Song (CRYPTO 2018) which suggested that a uniform superposition with random \emph{binary} phase is statistically indistinguishable from a Haar random state. That is, any polynomial number of copies of the aforementioned state is within exponentially small trace distance from the same number of copies of a Haar random state. As a consequence, we get a provable elementary construction of \emph{pseudorandom} quantum states from post-quantum pseudorandom functions. Generating pseduorandom quantum states is desirable for physical applications as well as for computational tasks such as quantum money. We observe that replacing the pseudorandom function with a $(2t)$-wise independent function (either in our construction or in previous work), results in an explicit construction for \emph{quantum state $t$-designs} for all $t$. In fact, we show that the circuit complexity (in terms of both circuit size and depth) of constructing $t$-designs is bounded by that of $(2t)$-wise independent functions. Explicitly, while in prior literature $t$-designs required linear depth (for $t > 2$), this observation shows that polylogarithmic depth suffices for all $t$. We note that our constructions yield pseudorandom states and state designs with only real-valued amplitudes, which was not previously known. Furthermore, generating these states require quantum circuit of restricted form: applying one layer of Hadamard gates, followed by a sequence of Toffoli gates. This structure may be useful for efficiency and simplicity of implementation

Phase-random states: ensembles of states with fixed amplitudes and uniformly distributed phases in a fixed basis

Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that canonical states typically appear in subsystems of phase-random states. We then investigate the simulatability of phase-random states, which is directly related to that of time evolution in closed systems, by studying their entanglement properties. We find that starting from a separable state, time evolutions under Hamiltonians composed of only separable eigenstates generate extremely high entanglement and are difficult to simulate with matrix product states. We also show that random quantum circuits consisting of only two-qubit diagonal unitaries can generate an ensemble with the same average entanglement as phase-random states.Comment: Revised, 12 pages, 4 figur