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

arXiv:1801.02429 · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Statistical correlations in the oscillator model of quantum dissipative systems

Marco Patriarca

Published Jan 1, 1996• 15 citations
arXivHTMLPDF
DOI
10.1007/bf02726201

Related papers

Control of decoherence and correlation in single quantum dissipative oscillator systems

R. W. Rendell, A. K. Rajagopal

arXiv:quant-ph/0008099•Physics Letters A•Jan 1, 2001•5 citations

Quantum Statistics of Dissipative Nonlinear Oscillators

Vlasta Peřinová, A. Lukš

Progress in optics•Jan 1, 1994•8 citations

Statistical control of relaxation and synchronization in open anyonic systems

Eric R. Bittner, Bhavay Tyagi

Quantum statistics dictate how particles exchange and correlate-but in two-dimensional systems, these rules extend beyond bosons and fermions to anyons, quasiparticles with continuously tunable exchange phases. Here, we develop a Lindblad framework for anyonic oscillators and show that fractional statistics enable statistical control of decoherence in open quantum systems. By varying the anyonic phase and environmental correlations, we demonstrate tunable mode protection, identify exceptional points in the dissipative spectrum, and reveal temperature-dependent coherence bifurcations. We also demonstrate that signatures of the statistical phase should also be manifest in 2D coherent spectroscopic probes of these systems. These results establish the exchange phase as a functional control parameter for engineering dissipation-resilient quantum states.

arXiv:2504.02173•Scientific Reports•Dec 2, 2025•2 citations

Pairwise and higher-order statistical correlations in excited states of quantum oscillator systems

Saúl J. C. Salazar, Humberto G. Laguna, Robin P. Sagar

The European Physical Journal Plus•Dec 14, 2021•10 citations

Quantum Dissipative Systems

Fundamentals Survey of the Various Approaches Path Integral Description of Open Quantum Systems Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic System-Plus-Reservoir Models Linear and Nonlinear Quantum Environments Ohmic, Super-Ohmic, and Sub-Ohmic Dissipation Quantum Decoherence and Relaxation Correlation Functions, Response Functions, and Fluctuation-Dissipation Theorem Damped Quantum Mechanical Harmonic Oscillator Quantum Brownian Motion Thermodynamic Variational Approach and Effective Potential Method Unified Approach to Quantum-Statistical Metastability: From Thermal Activation to Quantum Tunneling Electron Transfer and Incoherent Tunneling Macroscopic Quantum Effects in Josephson Systems Spin-Boson Model and Qubit Dissipative Two-State System: Thermodynamics and Dynamics Single-Charge and Cooper-Pair Tunneling Magnetic and Spin Tunneling Driven Quantum Tunneling Nonequilibrium Quantum Transport Full Counting Statistics Charge Transport in Quantum Impurity Systems Duality and Self-Duality.

WORLD SCIENTIFIC eBooks•Jan 1, 2012•2,331 citations

Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator

Haifeng Li, Jiushu Shao, Shikuan Wang

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

arXiv:1110.4947•Physical Review E•Nov 14, 2011•17 citations
Quantum statistics dictate how particles exchange and correlate-but in two-dimensional systems, these rules extend beyond bosons and fermions to anyons, quasiparticles with continuously tunable exchange phases. Here, we develop a Lindblad framework for anyonic oscillators and show that fractional statistics enable statistical control of decoherence in open quantum systems. By varying the anyonic phase and environmental correlations, we demonstrate tunable mode protection, identify exceptional points in the dissipative spectrum, and reveal temperature-dependent coherence bifurcations. We also demonstrate that signatures of the statistical phase should also be manifest in 2D coherent spectroscopic probes of these systems. These results establish the exchange phase as a functional control parameter for engineering dissipation-resilient quantum states.
Fundamentals Survey of the Various Approaches Path Integral Description of Open Quantum Systems Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic System-Plus-Reservoir Models Linear and Nonlinear Quantum Environments Ohmic, Super-Ohmic, and Sub-Ohmic Dissipation Quantum Decoherence and Relaxation Correlation Functions, Response Functions, and Fluctuation-Dissipation Theorem Damped Quantum Mechanical Harmonic Oscillator Quantum Brownian Motion Thermodynamic Variational Approach and Effective Potential Method Unified Approach to Quantum-Statistical Metastability: From Thermal Activation to Quantum Tunneling Electron Transfer and Incoherent Tunneling Macroscopic Quantum Effects in Josephson Systems Spin-Boson Model and Qubit Dissipative Two-State System: Thermodynamics and Dynamics Single-Charge and Cooper-Pair Tunneling Magnetic and Spin Tunneling Driven Quantum Tunneling Nonequilibrium Quantum Transport Full Counting Statistics Charge Transport in Quantum Impurity Systems Duality and Self-Duality.
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.