Computer Simulation of Quantum Phenomena in Nanoscale Devices

Raedt, Hans De

doi:10.1142/9789812830050_0004

Cited by 24 publications

(26 citation statements)

References 30 publications

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“…(7), we can complete our previous analysis obtaining the time evolution of surface displacement by performing a numerical Fourier transform of the analytical expression for D 00 (ω). These results coincide with the numerical integration of the equation of motion in the HamiltonJacobi representation which is performed with an ad hoc version of the Trotter-Suzuki method [12]. Setting the ratio α between masses and Fourier transforming for several ω 0 values in the previously mentioned regimes, we obtain the displacement pattern shown in Fig.3.…”

Section: Dynamical Phasessupporting

confidence: 78%

Dynamical phase transition in vibrational surface modes

Calvo¹,

Pastawski²

2006

Braz. J. Phys.

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We consider the dynamical properties of a simple model of vibrational surface modes. We obtain the exact spectrum of surface excitations and discuss their dynamical features. In addition to the usually discussed localized and oscillatory regimes we also find a second phase transition where the surface mode frequency becomes purely imaginary and describes an overdamped regime. Noticeably, this transition has an exact correspondence to the oscillatory -overdamped transition of the standard oscillator with a frictional force proportional to velocity.

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Section: Dynamical Phasessupporting

confidence: 78%

Dynamical phase transition in vibrational surface modes

Calvo¹,

Pastawski²

2006

Braz. J. Phys.

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“…This condition, already presented in Eq. (35), can be translated into the inequality λ ≪ v/ℓ. Indeed, the results of the simulations, as presented in Fig.…”

Section: Numerical Resultsmentioning

confidence: 91%

Measuring the Lyapunov exponent using quantum mechanics

et al. 2002

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We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the wave packet overlap function. We show that for sufficiently weak perturbations, the exponential decay follows a Fermi golden rule, while by making the difference between the two Hamiltonians larger, the characteristic exponential decay time becomes the Lyapunov exponent of the classical system. We illustrate our theoretical findings by investigating numerically the overlap decay function of a two-dimensional dynamical system.

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“…Some early results show that eigendecomposition does not scale linearly beyond a small number of nodes. An alternative method, the so-called Trotter-Suzuki algorithm [14], avoids the decomposition in calculating the evolution of a quantum system. Highly optimized CPU and GPU kernels for a single node have already been developed [6].…”

Section: Discussionmentioning

confidence: 99%

High-performance dynamic quantum clustering on graphics processors

Wittek

2013

Journal of Computational Physics

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Clustering methods in machine learning may benefit from borrowing metaphors from physics. Dynamic quantum clustering associates a Gaussian wave packet with the multidimensional data points and regards them as eigenfunctions of the Schrödinger equation. The clustering structure emerges by letting the system evolve and the visual nature of the algorithm has been shown to be useful in a range of applications. Furthermore, the method only uses matrix operations, which readily lend themselves to parallelization. In this paper, we develop an implementation on graphics hardware and investigate how this approach can accelerate the computations. We achieve a speedup of up to two magnitudes over a multicore CPU implementation, which proves that quantum-like methods and acceleration by graphics processing units have a great relevance to machine learning.

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Computer Simulation of Quantum Phenomena in Nanoscale Devices

Cited by 24 publications

References 30 publications

Dynamical phase transition in vibrational surface modes

Dynamical phase transition in vibrational surface modes

Measuring the Lyapunov exponent using quantum mechanics

High-performance dynamic quantum clustering on graphics processors

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