Erratum: Investigating quantum transport with an initial value representation of the semiclassical propagator [Phys. Rev. E<b>80</b>, 031101 (2009)]

Goletz, Christoph-Marian; Großmann, Frank; Tomsovic, Steven

doi:10.1103/physreve.82.019902

Cited by 4 publications

(5 citation statements)

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“…For four phase space degrees of freedom typically 10 6 trajectories are needed for converged results. In cases of strongly chaotic dynamics (not considered here) and if long-time information is needed this number may, however, increase dramatically [31]. We note in passing that in contrast to the multi-trajectory Herman-Kluk method [32], the single trajectory Thawed Gaussian Wavepacket method [33] uses just a single trajectory to express the final wavefunction.…”

Section: A Semiclassical Initial Value Propagatormentioning

confidence: 99%

Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Großmann¹,

Kramer²

2011

J. Phys. A: Math. Theor.

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For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with Langer correction. The latter are restricted to integrable systems, however, whereas the timedependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential.

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Section: A Semiclassical Initial Value Propagatormentioning

confidence: 99%

Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Großmann¹,

Kramer²

2011

J. Phys. A: Math. Theor.

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“…For this reason, semiclassical approaches have great relevance in theoretical chemistry, especially in the study of atomic and molecular dynamics. [1][2][3][4][5][6][7][8][9] Second, the semiclassical formalism provides important tools for the deep understanding of the connections between classical and quantum theories. According to the correspondence principle, classical physics constitutes a limiting case of quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical Propagator in the Generalized Coherent-State Representation

Viscondi¹,

Grigolo²,

Aguiar³

2015

Preprint

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A detailed derivation of the semiclassical propagator in the generalized coherent-state representation is performed by applying the saddle-point method to a path integral over the classical phase space. With the purpose of providing greater accessibility and applicability to the developed formalism, a brief review of the generalized concept of coherent states is presented, in which three examples of coherent-state sets are examined, namely, the canonical, spin, and SU(n) bosonic coherent states.

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“…There are infinitely many partial barriers which are hierarchically organized with decreasing fluxes towards the regular regions [27][28][29][30][31]. The partial barriers strongly impact the system's classical [27][28][29][30][31][32][33] and quantum mechanical [34][35][36][37][38][39][40][41][42][43][44] properties, and lead to, e. g., the localization of eigenstates in phase space [34-36, 40, 44] and fractal conductance fluctuations [37,38,42].…”

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confidence: 99%

Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems

et al. 2013

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In open chaotic systems the number of long-lived resonance states obeys a fractal Weyl law, which depends on the fractal dimension of the chaotic saddle. We study the generic case of a mixed phase space with regular and chaotic dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of the chaotic phase-space component. This is based on our observation of hierarchical resonance states localizing on these regions. Numerically this is verified for the standard map and a hierarchical model system.

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Erratum: Investigating quantum transport with an initial value representation of the semiclassical propagator [Phys. Rev. E80, 031101 (2009)]

Cited by 4 publications

References 0 publications

Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Semiclassical Propagator in the Generalized Coherent-State Representation

Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems

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