403 research outputs found
Exploring the Past, Present, and Future of Romanticism: Analyses with Brief Biographies of Works Performed in a Senior Recital
A melodic and harmonic analysis of four instrumental works performed in a senior recital is presented in this thesis with brief biographical outlines of each composer. Three of the works, Johann Wenzel Kalliwoda\u27s Morceau de Salon, Edmund Rubbra\u27s Sonata in C, and Robert Schumann\u27s Three Romances are written for oboe and piano. The remaining piece, Paul Hindemith\u27s English Horn Sonata, is written for English horn and piano. The author provides a detailed and methodical approach for understanding the functionality of each piece
Making Almost Commuting Matrices Commute
Suppose two Hermitian matrices almost commute (). Are they close to a commuting pair of Hermitian matrices, ,
with ? A theorem of H. Lin
shows that this is uniformly true, in that for every there exists
a , independent of the size of the matrices, for which almost
commuting implies being close to a commuting pair. However, this theorem does
not specify how depends on . We give uniform bounds relating
and . We provide tighter bounds in the case of block
tridiagonal and tridiagonal matrices and a fully constructive method in that
case. Within the context of quantum measurement, this implies an algorithm to
construct a basis in which we can make a {\it projective} measurement that
approximately measures two approximately commuting operators simultaneously.
Finally, we comment briefly on the case of approximately measuring three or
more approximately commuting operators using POVMs (positive operator-valued
measures) instead of projective measurements.Comment: 22 pages; tighter bounds; Note: fixed mistake in proof pointed out by
Filonov and Kachkovski
Schrieffer-Wolff transformation for quantum many-body systems
The Schrieffer-Wolff (SW) method is a version of degenerate perturbation
theory in which the low-energy effective Hamiltonian H_{eff} is obtained from
the exact Hamiltonian by a unitary transformation decoupling the low-energy and
high-energy subspaces. We give a self-contained summary of the SW method with a
focus on rigorous results. We begin with an exact definition of the SW
transformation in terms of the so-called direct rotation between linear
subspaces. From this we obtain elementary proofs of several important
properties of H_{eff} such as the linked cluster theorem. We then study the
perturbative version of the SW transformation obtained from a Taylor series
representation of the direct rotation. Our perturbative approach provides a
systematic diagram technique for computing high-order corrections to H_{eff}.
We then specialize the SW method to quantum spin lattices with short-range
interactions. We establish unitary equivalence between effective low-energy
Hamiltonians obtained using two different versions of the SW method studied in
the literature. Finally, we derive an upper bound on the precision up to which
the ground state energy of the n-th order effective Hamiltonian approximates
the exact ground state energy.Comment: 47 pages, 3 figure
Isotopic evidence for dominant secondary production of HONO in near-ground wildfire plumes
Nitrous acid (HONO) is an important precursor to hydroxyl radical (OH) that determines atmospheric oxidative capacity and thus impacts climate and air quality. Wildfire is not only a major direct source of HONO, it also results in highly polluted conditions that favor the heterogeneous formation of HONO from nitrogen oxides (NOx= NO + NO2) and nitrate on both ground and particle surfaces. However, these processes remain poorly constrained. To quantitatively constrain the HONO budget under various fire and/or smoke conditions, we combine a unique dataset of field concentrations and isotopic ratios (15N / 14N and 18O / 16O) of NOx and HONO with an isotopic box model. Here we report the first isotopic evidence of secondary HONO production in near-ground wildfire plumes (over a sample integration time of hours) and the subsequent quantification of the relative importance of each pathway to total HONO production. Most importantly, our results reveal that nitrate photolysis plays a minor role (\u3c5 %) in HONO formation in daytime aged smoke, while NO2-to-HONO heterogeneous conversion contributes 85 %–95 % to total HONO production, followed by OH + NO (5 %–15 %). At nighttime, heterogeneous reduction of NO2 catalyzed by redox active species (e.g., iron oxide and/or quinone) is essential (≥ 75 %) for HONO production in addition to surface NO2 hydrolysis. Additionally, the 18O / 16O of HONO is used for the first time to constrain the NO-to-NO2 oxidation branching ratio between ozone and peroxy radicals. Our approach provides a new and critical way to mechanistically constrain atmospheric chemistry and/or air quality models on a diurnal timescale
Tensor network states and geometry
Tensor network states are used to approximate ground states of local
Hamiltonians on a lattice in D spatial dimensions. Different types of tensor
network states can be seen to generate different geometries. Matrix product
states (MPS) in D=1 dimensions, as well as projected entangled pair states
(PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the
lattice model; in contrast, the multi-scale entanglement renormalization ansatz
(MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on
homogeneous tensor networks, where all the tensors in the network are copies of
the same tensor, and argue that certain structural properties of the resulting
many-body states are preconditioned by the geometry of the tensor network and
are therefore largely independent of the choice of variational parameters.
Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for
D=1 systems is seen to be determined by the structure of geodesics in the
physical and holographic geometries, respectively; whereas the asymptotic
scaling of entanglement entropy is seen to always obey a simple boundary law --
that is, again in the relevant geometry. This geometrical interpretation offers
a simple and unifying framework to understand the structural properties of, and
helps clarify the relation between, different tensor network states. In
addition, it has recently motivated the branching MERA, a generalization of the
MERA capable of reproducing violations of the entropic boundary law in D>1
dimensions.Comment: 18 pages, 18 figure
Many body physics from a quantum information perspective
The quantum information approach to many body physics has been very
successful in giving new insight and novel numerical methods. In these lecture
notes we take a vertical view of the subject, starting from general concepts
and at each step delving into applications or consequences of a particular
topic. We first review some general quantum information concepts like
entanglement and entanglement measures, which leads us to entanglement area
laws. We then continue with one of the most famous examples of area-law abiding
states: matrix product states, and tensor product states in general. Of these,
we choose one example (classical superposition states) to introduce recent
developments on a novel quantum many body approach: quantum kinetic Ising
models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of
correlated electron systems". Improved version new references adde
Uncovering the Dynamics of Cardiac Systems Using Stochastic Pacing and Frequency Domain Analyses
Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca2+ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λalt) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λalt≤−1. For different BCLs, control values of λalt were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λalt. Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λalt. In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell
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