8,121 research outputs found
Collapse and revival oscillations as a probe for the tunneling amplitude in an ultra-cold Bose gas
We present a theoretical study of the quantum corrections to the revival time
due to finite tunneling in the collapse and revival of matter wave interference
after a quantum quench. We study hard-core bosons in a superlattice potential
and the Bose-Hubbard model by means of exact numerical approaches and
mean-field theory. We consider systems without and with a trapping potential
present. We show that the quantum corrections to the revival time can be used
to accurately determine the value of the hopping parameter in experiments with
ultracold bosons in optical lattices.Comment: 10 pages, 12 figures, typos in section 3A correcte
A Strictly Single-Site DMRG Algorithm with Subspace Expansion
We introduce a strictly single-site DMRG algorithm based on the subspace
expansion of the Alternating Minimal Energy (AMEn) method. The proposed new MPS
basis enrichment method is sufficient to avoid local minima during the
optimisation, similarly to the density matrix perturbation method, but
computationally cheaper. Each application of to in the
central eigensolver is reduced in cost for a speed-up of ,
with the physical site dimension. Further speed-ups result from cheaper
auxiliary calculations and an often greatly improved convergence behaviour.
Runtime to convergence improves by up to a factor of 2.5 on the Fermi-Hubbard
model compared to the previous single-site method and by up to a factor of 3.9
compared to two-site DMRG. The method is compatible with real-space
parallelisation and non-abelian symmetries.Comment: 9 pages, 6 figures; added comparison with two-site DMR
Spectral functions and time evolution from the Chebyshev recursion
We link linear prediction of Chebyshev and Fourier expansions to analytic
continuation. We push the resolution in the Chebyshev-based computation of
many-body spectral functions to a much higher precision by deriving a
modified Chebyshev series expansion that allows to reduce the expansion order
by a factor . We show that in a certain limit the Chebyshev
technique becomes equivalent to computing spectral functions via time evolution
and subsequent Fourier transform. This introduces a novel recursive time
evolution algorithm that instead of the group operator only involves
the action of the generator . For quantum impurity problems, we introduce an
adapted discretization scheme for the bath spectral function. We discuss the
relevance of these results for matrix product state (MPS) based DMRG-type
algorithms, and their use within dynamical mean-field theory (DMFT). We present
strong evidence that the Chebyshev recursion extracts less spectral information
from than time evolution algorithms when fixing a given amount of created
entanglement.Comment: 12 pages + 6 pages appendix, 11 figure
Exact real-time dynamics of the quantum Rabi model
We use the analytical solution of the quantum Rabi model to obtain absolutely
convergent series expressions of the exact eigenstates and their scalar
products with Fock states. This enables us to calculate the numerically exact
time evolution of and for all regimes of the
coupling strength, without truncation of the Hilbert space. We find a
qualitatively different behavior of both observables which can be related to
their representations in the invariant parity subspaces.Comment: 8 pages, 7 figures, published versio
Imaginary-time matrix product state impurity solver for dynamical mean-field theory
We present a new impurity solver for dynamical mean-field theory based on
imaginary-time evolution of matrix product states. This converges the
self-consistency loop on the imaginary-frequency axis and obtains
real-frequency information in a final real-time evolution. Relative to
computations on the real-frequency axis, required bath sizes are much smaller
and less entanglement is generated, so much larger systems can be studied. The
power of the method is demonstrated by solutions of a three band model in the
single and two-site dynamical mean-field approximation. Technical issues are
discussed, including details of the method, efficiency as compared to other
matrix product state based impurity solvers, bath construction and its relation
to real-frequency computations and the analytic continuation problem of quantum
Monte Carlo, the choice of basis in dynamical cluster approximation, and
perspectives for off-diagonal hybridization functions.Comment: 8 pages + 4 pages appendix, 9 figure
Dynamical correlation functions and the quantum Rabi model
We study the quantum Rabi model within the framework of the analytical
solution developed in Phys. Rev. Lett. 107,100401 (2011). In particular,
through time-dependent correlation functions, we give a quantitative criterion
for classifying two regions of the quantum Rabi model, involving the
Jaynes-Cummings, the ultrastrong, and deep strong coupling regimes. In
addition, we find a stationary qubit-field entangled basis that governs the
whole dynamics as the coupling strength overcomes the mode frequency.Comment: 8 pages, 8 figures. Revised version, accepted for publication in
Physical Review
Empirical-deterministic prediction of disease and losses caused by Cercospora leaf spots in sugar beets
Neben einer Negativ-Prognose des Epidemiebeginns, epidemieorientierten Bekämpfungsschwellen (BK) und einer wirtschaftlichen Schadensschwelle (WS) beinhaltet das Quaternäre IPS (Integriertes Pflanzenschutz)-Konzept zur Kontrolle des Cercospora-Befalls eine Verlustprognose. Die Verlustprognose erhält ihren praktischen Sinn dadurch, dass die epidemischen Stadien von BK und WS ein Intervall von 5–10 Wochen beinhalten. Die Befallsstärke (BS) zum Zeitpunkt von BK beträgt 0,01%, hingegen toleriert die Zuckerrübe 5% BS ohne wirtschaftlichen Schaden. Die Verlustprognose trifft daher Vorhersagen, ob der künftige Befallsverlauf die WS zum Erntezeitpunkt überschreiten wird und insofern, ob Bekämpfungsmaßnahmen benötigt werden. Das Modell ist als empirisch zu charakterisieren, nachdem die Herleitung der Verlustprognose auf 105 Feldstudien (Deutschland und Österreich) einer Epidemie von Cercospora beticola und ihren ertraglichen Konsequenzen beruht. Des Weiteren ist das Modell deterministisch, weil die Krankheitssituation zum gegenwärtigen Zeitpunkt die Prognose der zukünftigen Befallsentwicklung determiniert. In jeglicher Feldstudie implizierte der Epidemieverlauf eine Phase geringer Progression der BS, gefolgt von einem steilen Anstieg mit Tendenz zu einem Maximum des Befalls. Die Prognose des Befallsverlaufes in Submodul (i) basiert daher auf der sigmoiden Funktion „BS = BSmax/(1+exp(-(CW-a)/b))“. Demnach hängt die Kalkulation von BS von der Kalenderwoche (CW) und den Variablen BSmax, a und b ab. Letztere werden geschätzt mittels mathematischer Funktionen in Abhängigkeit vom Epidemiebeginn (CWBH5%), definiert als jene Kalenderwoche, zu der eine Befallshäufigkeit (BH) der Blätter von ≥5% eintritt. Die Verluste sind hierbei abhängig von der Fläche unter der Befallskurve (AUDPC). Für die Kalkulation der AUDPC-Werte finden die BS-Werte Verwendung, wie mit Submodul (i) geschätzt. Die Prognose von Verlusten an Rüben- und Bereinigtem Zuckerertrag geschieht auf Basis von Befalls-Verlust-Relationen (Submodul ii, iii). Die wirtschaftliche Schadensschwelle ist definiert als AUDPC=1, entsprechend einem Verlust an Bereinigtem Zuckerertrag von ≉1,5%. Folglich sind Fungizidapplikationen entbehrlich, sofern der Befall bis zur Ernte <AUDPC=1 verbleibt. Alle Berechnungen zur Modellentwicklung haben die Sorten-Anfälligkeiten „hoch“ und „gering“ berücksichtigt. Darüber hinaus benötigt die Verlustprognose Angaben über den zu erwartenden Ertrag und den voraussichtlichen Erntetermin. Diagnose und Erhebung des Befalls sind Voraussetzungen für die Anwendung des Modells, da die Einschätzung der zukünftigen Entwicklung auf einer Konkretisierung der gegenwärtigen Krankheitssituation gründet.Besides negative-prognosis of epidemic onset, epidemic spraying thresholds (ET) and economic damage threshold (DT), loss prediction is a part of the Quaternary IPM (Integrated Pest Management)-concept to control Cercospora leaf spots (CLS). The practical need of loss prediction originates from the fact, that disease levels of ET and DT implicate an interval of 5–10 weeks. Disease severity (DS) of ET for an initial treatment is 0.01, whereas the beet plant may tolerate 5% DS without economic losses. Therefore, in order to assess the necessity of control measures, the model is focused on to predict whether DS will exceed DT at harvest time. The model is empiric, because loss prediction was derived from epidemic and yield data of 105 field trials conducted in Germany and Austria (1993-2000). The model is also deterministic, because the disease incidence at present date and cultivar susceptibility determine the prediction of future disease progress. In every field study, course of DS involved a period of slight followed by a more or less steep increase tending to a maximum of DS. The incidence prediction in submodel (i), therefore, was based on the sigmoidal function “DS = DSmax/(1+exp(-(CW-a)/b))”, where the calculation of DS is depending on the actual calendar week (CW) and the variables DSmax, a and b. These variables are estimated through curve fittings depending on the epidemic onset (CWDIL5%), respectively the calendar week when disease incidence per leaf (DIL) increases to ≥5%. Losses are dependent on the area under disease progress curve (AUDPC). Creation of AUDPC-values is based on the DS-values as calculated by submodel (i). The prediction of losses is performed through disease-loss-relationships (submodel ii, iii). The economic damage threshold is defined as AUDPC=1, equal to a loss of ≉1.5% sugar. Therefore fungicide sprays may be avoided, if the AUDPC remains beneath 1 till scheduled harvest time. All calculations for model development involved two grades of cultivar susceptibility, either highly or low susceptible. Moreover, prediction of yield loss needs indications of expected yield and scheduled harvest time. Proper diagnosis and disease scoring is a precondition for error free functioning of the model, since future progress is estimated by an assessment of the actual incidence situation
Solving nonequilibrium dynamical mean-field theory using matrix product states
We solve the nonequilibrium dynamical mean-field theory (DMFT) using matrix
product states (MPS). This allows us to treat much larger bath sizes and by
that reach substantially longer times (factor 2 -- 3) than with exact
diagonalization. We show that the star geometry of the underlying impurity
problem can have substantially better entanglement properties than the
previously favoured chain geometry. This has immense consequences for the
efficiency of an MPS-based description of general impurity problems: in the
case of equilibrium DMFT, it leads to an orders-of-magnitude speedup. We
introduce an approximation for the two-time hybridization function that uses
time-translational invariance, which can be observed after a certain relaxation
time after a quench to a time-independent Hamiltonian.Comment: 11 pages + 3 pages appendix, 14 figure
Second Harmonic Generation from Phononic Epsilon-Near-Zero Berreman Modes in Ultrathin Polar Crystal Films
Immense optical field enhancement was predicted to occur for the Berreman
mode in ultrathin films at frequencies in the vicinity of epsilon near zero
(ENZ). Here, we report the first experimental proof of this prediction in the
mid-infrared by probing the resonantly enhanced second harmonic generation
(SHG) at the longitudinal optic phonon frequency from a deeply
subwavelength-thin aluminum nitride (AlN) film. Employing a transfer matrix
formalism, we show that the field enhancement is completely localized inside
the AlN layer, revealing that the observed SHG signal of the Berreman mode is
solely generated in the AlN film. Our results demonstrate that ENZ Berreman
modes in intrinsically low-loss polar dielectric crystals constitute a
promising platform for nonlinear nanophotonic applications
- …