Quantized Hamilton dynamics describes quantum discrete breathers in a simple way

Igumenshchev, Kirill; Prezhdo, Oleg V.

doi:10.1103/physreve.84.026616

Cited by 7 publications

(4 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Often, an opposite limit is consideredas follows from the representation of the delta functions by a limit of Gaussian distributions with infinitesimal width. In the limit of ℏ → 0, the Gaussian wavepacket becomes a delta function representing a classical particle. ,, Depending on the desired approximation for the adiabatic or non-adiabatic dynamics, one can choose the fully quantum description, utilizing the standard quantum-mechanical definition of the operators, the fully classical description, in which both operators are approximated using classical momentum: T nucl = ( P 2 /2 M ) and −ℏ 2 ( d⃗ ij (1) / M )∇⃗ = − i ℏ d⃗ ij (1) ( P⃗ / M ), or a semiclassical scheme, such as QHD, − in which the quantum nature of the operators is captured via higher order correlators of classical-like momentum and position variables. The fully classical limit straightforwardly follows from standard quantum-classical correspondence rules.…”

Section: Theory and Methodsmentioning

confidence: 99%

The PYXAID Program for Non-Adiabatic Molecular Dynamics in Condensed Matter Systems

Akimov

Prezhdo

2013

J. Chem. Theory Comput.

646

1,023

View full text Add to dashboard Cite

This work introduces the PYXAID program, developed for non-adiabatic molecular dynamics simulations in condensed matter systems. By applying the classical path approximation to the fewest switches surface hopping approach, we have developed an efficient computational tool that can be applied to study photoinduced dynamics at the ab initio level in systems composed of hundreds of atoms and involving thousands of electronic states. The technique is used to study in detail the ultrafast relaxation of hot electrons in crystalline pentacene. The simulated relaxation occurs on a 500 fs time scale, in excellent agreement with experiment, and is driven by molecular lattice vibrations in the 200-250 cm(-1) frequency range. The PYXAID program is organized as a Python extension module and can be easily combined with other Python-driven modules, enhancing user-friendliness and flexibility of the software. The source code and additional information are available on the Web at the address http://gdriv.es/pyxaid . The program is released under the GNU General Public License.

show abstract

Section: Theory and Methodsmentioning

confidence: 99%

The PYXAID Program for Non-Adiabatic Molecular Dynamics in Condensed Matter Systems

Akimov

Prezhdo

2013

J. Chem. Theory Comput.

646

1,023

View full text Add to dashboard Cite

show abstract

“…We have not, however, followed any of the elaborate approaches mentioned above. Nevertheless, we could show that the time-domain IVR semiclassical HK result with real width parameter γ does indeed give the decay and recurrence of the breather, in a similar way as the so-called quantized Hamiltonian dynamics does [42]. Furthermore, the LSC-IVR result (based on a similar set of trajectories as the HK result 4 ) for β = 0.4 unveils that classically, the system stays in its initial state to a large degree and the breather oscillation cannot be observed.…”

Section: 22mentioning

confidence: 70%

Interference nature of quantum breather oscillation

Zagoya

Schulman

Großmann

2014

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In a system of coupled nonlinear oscillators, the breather (or local mode) solution is studied fully quantum mechanically, as well as by a semiclassical initial value representation of the propagator and classical Wigner dynamics. We show that the initial breather state is a superposition of almost degenerate eigenstates. From this simple observation it follows that the breather must decay and revive (i.e., oscillate with energy localization for extended times). Numerical results are shown for a two degree of freedom system. The fact that the semiclassical real-time result reproduces the full quantum one to a large degree, whereas the classical Wigner dynamics based on a similar set of trajectories does not, indicates that the breather oscillation can be viewed as an interference phenomenon.

show abstract

“…Modeling highly non-linear phenomena such as DBs can be a challenge. With an exception of QHD [21], these methods have not been applied to QDBs. Studying the quantum dynamics of a coherent state will show the limitations of these techniques when applied to QDBs.…”

Section: Introductionmentioning

confidence: 99%

“…Since here we are interested in the dynamics of a coherent state rather than eigenstates, our approach involves simulating the dynamics of a superposition of eigenstates in a form of a coherent state. Motivation for this project came from our work on applying QHD [21] and HK [25] semi-classical methods to model QDBs; in these two works, the influence of tunneling modes (a quantum mechanical equivalent of DB modes) on the quantum dynamics of coherent state was unresolved.…”

Section: Introductionmentioning

confidence: 99%

Signatures of discrete breathers in coherent state quantum dynamics

Igumenshchev

Ovchinnikov

Maniadis

et al. 2013

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that involve a coherent state.

show abstract

Quantized Hamilton dynamics describes quantum discrete breathers in a simple way

Cited by 7 publications

References 49 publications

The PYXAID Program for Non-Adiabatic Molecular Dynamics in Condensed Matter Systems

The PYXAID Program for Non-Adiabatic Molecular Dynamics in Condensed Matter Systems

Interference nature of quantum breather oscillation

Signatures of discrete breathers in coherent state quantum dynamics

Contact Info

Product

Resources

About