We have investigated the time evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson’s boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann’s entropy and quantum purity. In addition, we have studied Wigner’s function. The timedependent behavior of the quantum entanglement between a free particle—in the lattice—and the phonon bath has been characterized analytically. This result strongly suggests the non-trivial time dependence of the off-diagonal elements of the reduced density matrix of the system. We have established a connection between the quantum decoherence and the dissipative parameter arising from interaction with the phonon bath. The time-dependent behavior of quantum correlations has also been pointed out, showing continuous transition from quantum random walk to classical random walk, when dissipation increases.We have investigated the time evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson’s boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann’s entropy and quantum purity. In addition, we have studied Wigner’s function. The timedependent behavior of the quantum entanglement between a free particle—in the lattice—and the phonon bath has been characterized analytically. This result strongly suggests the non-trivial time dependence of the off-diagonal elements of the reduced density matrix of the system. We have established a connection between the quantum decoherence and the dissipative parameter arising from interaction with the phonon bath. The time-dependent behavior of quantum correlations has also been pointed out, showing continuous transition from quantum random walk to classical random walk, when dissipation increases.

Jul 1, 20128 citations

Non-equilibrium transition from dissipative quantum walk to classical random walk

Marco Nizama, Manuel O Cáceres

We have investigated the time evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson's boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann's entropy and quantum purity. In addition, we have studied Wigner's function. The time-dependent behavior of the quantum entanglement between a free particle—in the lattice—and the phonon bath has been characterized analytically. This result strongly suggests the non-trivial time dependence of the off-diagonal elements of the reduced density matrix of the system. We have established a connection between the quantum decoherence and the dissipative parameter arising from interaction with the phonon bath. The time-dependent behavior of quantum correlations has also been pointed out, showing continuous transition from quantum random walk to classical random walk, when dissipation increases.We have investigated the time evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson's boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann's entropy and quantum purity. In addition, we have studied Wigner's function. The time-dependent behavior of the quantum entanglement between a free particle—in the lattice—and the phonon bath has been characterized analytically. This result strongly suggests the non-trivial time dependence of the off-diagonal elements of the reduced density matrix of the system. We have established a connection between the quantum decoherence and the dissipative parameter arising from interaction with the phonon bath. The time-dependent behavior of quantum correlations has also been pointed out, showing continuous transition from quantum random walk to classical random walk, when dissipation increases.

arXiv:1206.6061Journal of Physics A Mathematical and TheoreticalJul 30, 20129 citations

Quantum Random Walks

Swarnadeep Majumder, Austen Couvertier

Apr 27, 20181 citation

Phonon Random Walks: Using Classical Chains to Simulate Quantum Dynamics

Daxing Xiong, Eli Barkai

Inspired by quantum walks (QW), we propose the concept of classical phonon random walks (PRW). With this we show a correspondence between classical and quantum dynamics. To be specific, we explain how a classical chain of particles with linear interactions can be used to simulate a quantum like wave function $\psi_{m}(t)$ . In particular, the real (imaginary) part of $\psi_{m}(t)$ is the normalized classical momentum (a new $\pi/2$ shifted momentum) correlation function of the thermalized many-body system. Energy and heat densities are directly analogous to wave function's modulus squared $\left|\psi_{m}(t)\right|^{2}$ . We also propose a formula predicting the non-universal spreading of these energy packets in terms of the phonon dispersion of the system. Our equilibrium molecular dynamics simulations of several linear chains perfectly verify these relations. The extension of the concept to integrable Toda chain is also discussed.Inspired by quantum walks (QW), we propose the concept of classical phonon random walks (PRW). With this we show a correspondence between classical and quantum dynamics. To be specific, we explain how a classical chain of particles with linear interactions can be used to simulate a quantum like wave function $\psi_{m}(t)$. In particular, the real (imaginary) part of $\psi_{m}(t)$ is the normalized classical momentum (a new $\pi/2$ shifted momentum) correlation function of the thermalized many-body system. Energy and heat densities are directly analogous to wave function's modulus squared $\left|\psi_{m}(t)\right|^{2}$. We also propose a formula predicting the non-universal spreading of these energy packets in terms of the phonon dispersion of the system. Our equilibrium molecular dynamics simulations of several linear chains perfectly verify these relations. The extension of the concept to integrable Toda chain is also discussed.

Jun 15, 20160 citations

Quantum random walks

Luigi Accardi, G. S. Watson

Lecture notes in mathematicsJan 1, 198923 citations

\psi_{m}(t)

. In particular, the real (imaginary) part of

\psi_{m}(t)

is the normalized classical momentum (a new

\pi/2

shifted momentum) correlation function of the thermalized many-body system. Energy and heat densities are directly analogous to wave function's modulus squared

\left|\psi_{m}(t)\right|^{2}

. We also propose a formula predicting the non-universal spreading of these energy packets in terms of the phonon dispersion of the system. Our equilibrium molecular dynamics simulations of several linear chains perfectly verify these relations. The extension of the concept to integrable Toda chain is also discussed.