Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Dynamics of indistinguishable free particles driven by a quantum bath

Marco Nizama, Manuel O. Cáceres

Published Apr 8, 2019• 2 citations
Publisher

Abstract

The time evolution of correlations for two indistinguishable free particles, in a one-dimensional lattice interacting with a quantum bath, is studied in the Born-Markov approximation. The analytical solution for the density matrix is obtained, for bosons and fermions, in the second quantization formalism. The time evolution of the negativity of indistinguishable particles is analyzed for quantum mixed states. Quantum correlations heavily depend on the selected bipartition; in return, a small difference between the statistics of the particles is noted, due to the Pauli exclusion principle. In the presence of dissipation, the negativity (a nonclassical correlation) shows a time-oscillatory behavior for a particular geometrical bipartition. The total probability of finding one particle in each subsystem is also calculated and shows consistent behavior.

DOI
10.1103/physreva.99.042107

Related papers

Quantum correlations and coherence between two particles interacting with a thermal bath

Marco Nizama, Manuel O. Cáceres

Quantum correlations and coherence generated between two free spinless particles in the lattice, interacting with a common quantum phonon bath, are studied. The reduced density matrix is solved using the Markov approach. We show that the bath induces correlations between the particles. The coherence induced by the bath is studied, calculating off-diagonal elements of the density matrix, spatiotemporal dispersion, purity and quantum mutual information. We find a characteristic time-scale pointing out when this coherence is maximum. In addition, a Wigner-like distribution in the phase-space (lattice) is introduced as an indirect indicator of the quantumness of total correlations and coherence induced by the thermal bath. The negative volume of the Wigner function also shows a behavior which is in agreement with the time-scale that we have found. A Gaussian distribution for the profile of particles is not obtained, and interference patterns are observed as the result of bath-induced coherence. As the temperature of the bath vanishes, the ballistic behavior of the tight-binding model is recovered. The geometric quantum discord is calculated, to characterize the nature of the correlations.

•May 1, 2017•2 citations

Quantum correlations and coherence between two particles interacting with a thermal bath

Marco Nizama, Manuel O Cáceres

Abstract Quantum correlations and coherence generated between two free spinless particles in the lattice, interacting with a common quantum phonon bath, are studied. The reduced density matrix is solved using the Markov approach. We show that the bath induces correlations between the particles. The coherence induced by the bath is studied, calculating off-diagonal elements of the density matrix, spatiotemporal dispersion, purity and quantum mutual information. We find a characteristic time-scale pointing out when this coherence is maximum. In addition, a Wigner-like distribution in the phase-space (lattice) is introduced as an indirect indicator of the quantumness of total correlations and coherence induced by the thermal bath. The negative volume of the Wigner function also shows a behavior which is in agreement with the time-scale that we have found. A Gaussian distribution for the profile of particles is not obtained, and interference patterns are observed as the result of bath-induced coherence. As the temperature of the bath vanishes, the ballistic behavior of the tight-binding model is recovered. The geometric quantum discord is calculated, to characterize the nature of the correlations.

arXiv:1512.08700•Journal of Physics A Mathematical and Theoretical•May 5, 2017•3 citations

Numerical and analytical approach to the quantum dynamics of two coupled spins in bosonic baths

Alessandro Sergi, Ilya Sinayskiy, Francesco Petruccione

The quantum dynamics of a spin chain interacting with multiple bosonic baths is described in a mixed Wigner-Heisenberg representation. The formalism is illustrated by simulating the time evolution of the reduced density matrix of two coupled spins, where each spin is also coupled to its own bath of harmonic oscillators. In order to prove the validity of the approach, an analytical solution in the Born-Markov approximation is found. The agreement between the two methods is shown.

arXiv:0903.5181•Physical Review A•Jul 15, 2009•27 citations

Interacting with a quantum bath is not only decoherence producing: distinguishable particles

Marco Nizama, Manuel O. Cáceres

Bath-induced correlations in an infinite dimension Hilbert space has been shown. Quantum correlations between two free spinless dissipative distinguishable particles (initially uncorrelated) are studied analytically using the quantum master equation. We show that for temperature $T>0$ the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We found a time-scale that characterizes the time when the bath-induced correlation is maximum before being wipe out by dissipation (purity, spatial, and mirror correlations are studied). We introduce a Wigner function associated to the Wannier lattice where the dissipative quantum walks move. Thus we discuss the peculiarities of the scenario of enlarging the lattice to the semi-integers in order to fulfilll all the fundamental properties of the Wigner function. We have supported the quantum character of the correlations by analyzing the negativity of the Wigner function.

•Dec 29, 2015•0 citations

Quantum correlations in continuous-time quantum walks of two indistinguishable particles

Claudia Benedetti, Fabrizio Buscemi, Paolo Bordone

We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous-time quantum walks in a one-dimensional (1D) ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is considered. We show that the interference effects due to exchange symmetry can result into the appearance of nonclassical correlations. The role played onto the appearance of quantum correlations by the quantum statistics of the particles, the boundary conditions, and the partition of the system is widely investigated. Quantum correlations have also been investigated in a model mimicking the ballistic evolution of two indistinguishable particles in a 1D continuous-space structure. Our results are consistent with recent quantum optics and electron quantum optics experiments where the showing up of two-particle nonclassical correlations has been observed even in the absence of mutual interaction between the particles.

arXiv:1202.6145•Physical Review A•Apr 13, 2012•29 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.

arXiv:1206.6061•Journal of Physics A Mathematical and Theoretical•Jul 30, 2012•9 citations
The time evolution of correlations for two indistinguishable free particles, in a one-dimensional lattice interacting with a quantum bath, is studied in the Born-Markov approximation. The analytical solution for the density matrix is obtained, for bosons and fermions, in the second quantization formalism. The time evolution of the negativity of indistinguishable particles is analyzed for quantum mixed states. Quantum correlations heavily depend on the selected bipartition; in return, a small difference between the statistics of the particles is noted, due to the Pauli exclusion principle. In the presence of dissipation, the negativity (a nonclassical correlation) shows a time-oscillatory behavior for a particular geometrical bipartition. The total probability of finding one particle in each subsystem is also calculated and shows consistent behavior.
Quantum correlations and coherence generated between two free spinless particles in the lattice, interacting with a common quantum phonon bath, are studied. The reduced density matrix is solved using the Markov approach. We show that the bath induces correlations between the particles. The coherence induced by the bath is studied, calculating off-diagonal elements of the density matrix, spatiotemporal dispersion, purity and quantum mutual information. We find a characteristic time-scale pointing out when this coherence is maximum. In addition, a Wigner-like distribution in the phase-space (lattice) is introduced as an indirect indicator of the quantumness of total correlations and coherence induced by the thermal bath. The negative volume of the Wigner function also shows a behavior which is in agreement with the time-scale that we have found. A Gaussian distribution for the profile of particles is not obtained, and interference patterns are observed as the result of bath-induced coherence. As the temperature of the bath vanishes, the ballistic behavior of the tight-binding model is recovered. The geometric quantum discord is calculated, to characterize the nature of the correlations.
Abstract Quantum correlations and coherence generated between two free spinless particles in the lattice, interacting with a common quantum phonon bath, are studied. The reduced density matrix is solved using the Markov approach. We show that the bath induces correlations between the particles. The coherence induced by the bath is studied, calculating off-diagonal elements of the density matrix, spatiotemporal dispersion, purity and quantum mutual information. We find a characteristic time-scale pointing out when this coherence is maximum. In addition, a Wigner-like distribution in the phase-space (lattice) is introduced as an indirect indicator of the quantumness of total correlations and coherence induced by the thermal bath. The negative volume of the Wigner function also shows a behavior which is in agreement with the time-scale that we have found. A Gaussian distribution for the profile of particles is not obtained, and interference patterns are observed as the result of bath-induced coherence. As the temperature of the bath vanishes, the ballistic behavior of the tight-binding model is recovered. The geometric quantum discord is calculated, to characterize the nature of the correlations.
Bath-induced correlations in an infinite dimension Hilbert space has been shown. Quantum correlations between two free spinless dissipative distinguishable particles (initially uncorrelated) are studied analytically using the quantum master equation. We show that for temperature T>0T>0T>0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We found a time-scale that characterizes the time when the bath-induced correlation is maximum before being wipe out by dissipation (purity, spatial, and mirror correlations are studied). We introduce a Wigner function associated to the Wannier lattice where the dissipative quantum walks move. Thus we discuss the peculiarities of the scenario of enlarging the lattice to the semi-integers in order to fulfilll all the fundamental properties of the Wigner function. We have supported the quantum character of the correlations by analyzing the negativity of the Wigner function.
We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous-time quantum walks in a one-dimensional (1D) ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is considered. We show that the interference effects due to exchange symmetry can result into the appearance of nonclassical correlations. The role played onto the appearance of quantum correlations by the quantum statistics of the particles, the boundary conditions, and the partition of the system is widely investigated. Quantum correlations have also been investigated in a model mimicking the ballistic evolution of two indistinguishable particles in a 1D continuous-space structure. Our results are consistent with recent quantum optics and electron quantum optics experiments where the showing up of two-particle nonclassical correlations has been observed even in the absence of mutual interaction between the particles.
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.