Boltzmann-Gibbs infinite ergodic theory :

From Non-Normalizable Boltzmann-Gibbs Statistics to Infinite-Ergodic Theory
• E. Aghion, D. A. Kessler, and E. Barkai Phys. Rev. Lett. 122, 010601 (2019)
• Quantum Walks: the first detected passage time problem :

• Quantum Walks: The first detected passage time problem (Phys. Rev. selected publication)
• First Detected Arrival of a Qunatum Walker on an Infinite Line
• $1/f$ noise (one over f). :

• Fluctuations of 1/f noise and the low frequency cutoff paradox
• 1/f noise for intermittent quantum dots exhibits non-stationarity and critical exponents
• Aging Wiener-Khinchin Theorem
• Aging Wiener-Khinchin theorem and critical exponents of $1/f^\beta$ noise
• Conditional $1/f^\alpha$ noise: From single molecules to macroscopic measurement
• Renewal theory for a system with internal states
• Nonergodicity of a Time Series Obeying L\'evy Statistics
• Dynamics of cold atoms in optical lattices :

• Deviations from Boltzmann-Gibbs Statistics in Confined Optical Lettices
• Large Fluctuations for Spatial Diffusion of Cold Atoms
• Theory of Fractional L\'evy Kinetics for Cold Atoms Diffusing in Optical Lattices
• Infinite Covariant Density For Diffusion in Logarithmic Potentials and Optical Lattices
• From the area under tghe Bessel excursion to anomalous diffusion of cold atoms
• Transport and the first passage time problem with application to cold atoms in optical traps
• Theory of single molecule spectroscopy :

• Theory of Single Molecule Spectroscopy: Beyond the (Ensemble) Average (Review Article)
• Influence of Spectral Diffusion on Single-Molecule Photon-Statistics
• Super- and sub-Poissonian photon statistics for single molecule spectroscopy
• Time Dependent Fluctuations in Single Molecule Spectroscopy: a Generalized Wiener--Khintchine Approach
• Stochastic Theory of Single Molecule Spectroscopy
• L\'evy Distribution of Single Molecule Line Shape Cumulants in Glasses (theory)
• L\'evy Statistics for Random Single-Molecule Line Shapes in a Glass (experiment)
• Experimental Evidence for L\'evy Statistics in Single-Molecule Spectroscopy in a Low Temperature Glass- Manifestation of Long-Range Interactions.
• Transition From Simple to Complex Behavior of Single Molecule Line Shapes in Disordered Condensed Phase
• Phton Emission from a Driven Single Molecule Source: a Renormalization Group Approach
• Single Molecule Chemical Reactions: Reexamination of the Kramers approach
• Single Photon Spectroscopy and Nonlinear Single Molecule Spectroscopy :

• Photon Statistics for Single-Molecule Nonlinear Spectroscopy
• Probing Dynamics of Single Molecules: Nonlinear Spectroscopy Approach
• Theory of Single Photon Control from a Two Level System Source
• Theory of Single Photon On Demand from a Single Molecule Source
• Statistical Mechanics of Weak Ergodicity Breaking (Equilibrium) :

• Weakly Non-Ergodic Statistical Physics
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Weak Ergodicity Breaking in the Continuous Time Random Walk (short Letter)
• A Random Walk to a Non-Ergodic Equilibrium Concept (Longer Manuscript)
• Occupation Times and Weak Ergodicity Breaking in Biased Continuous Time Random Walks
• Weak Ergodicity Breaking with Deterministic Dynamics
• Residence Time Statistics for Normal and Fractional Diffusion in A Force Field
• Residence time statistics for N renewal processes
• Fractional Feynmam-Kac equation for weak ergodicity breaking,
• Nonergodicity of a Time Series Obeying L\'evy Statistics
• Fluctuations of time averages (ergodic systems) :

• Fluctuations of Time Averages for Langevin Dynamics
• Fluctuations around equilibrium laws in ergodic continuous-time random walks
• Non Self Averaging and its relation to Weak Ergodicity Breaking :

• Occupation Time Statistics in the Quenched Trap Model
• Random time averaged transport coefficients: Tracking single molecules in the cell environment :

• Anomalous diffusion models and their properties: non-stationarity, non-ergodicitym and ageing at the centenary of single particle tracking
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• In Vivo Anomalous Diffusion and Weak ergodicity Breaking of Lipid Granules
• Single Particle Tracking in Systems Showing Anomalous diffusion: the Role of Weak Ergodicity Breaking
• Random time averaged diffusivities for the L\'evy walk
• Noisy Continuous Time Random Walks
• Non-ergodicity, Aging, and L\'evy Statistics for Blinking Nano-Crystals :

• Beyond Quantum Jumps: Blinking Nanoscale Light Emitters (popular article)
• Residence time statistics for N renewal processes
• Nonergodicity of Blinking Nanocrystals and Other L\evy Walk Processes
• Aging Correlation Functions for Blinking Nano-Crystals, and Other On-Off Stochastic Processes
• Line shape Theory and Photon Counting Statistics for Blinking Quantum Dots: a Levy Walk Process
• Photon Counting Statistics For Blinking CdSe-ZnS Quantum Dots: A L\'evy Walk Process (Experiment)
• Infinite Invariant densities and their application :

• Non-Normalizable Densities in Strong Anomalous Diffusion: Beyond the Central Limit Theorem
• Large Fluctuations for Spatial Diffusion of Cold Atoms
• Infinite densities for L\'evy walks
• Infinite Covariant Density For Diffusion in Logarithmic Potentials and Optical Lattices
• Pesin-Type Identity for Intermittent Dynamics with a Zero Lyaponov Exponent
• Infinite invariant density determines statistics of time averages for weak chaos (short letter)
• Distribution of time averages for weakly chaotic systems: The role of infinite invariant density (longer manuscript)
• Numerical estimate of infinite invariant densities: application to Pesin-type identity
• Fractional Kinetic Equations: Foundations, Solutions, and Applications :

• Fractional Fokker--Planck Equation, Solution, and Application
• Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional Fokker--Planck Equation Approach
• Fractional Kramers Equation
• CTRW Pathways to the Fractional Diffusion Equation
• From Continuous Time Random Walks, to the Fractional Fokker--Planck Equation
• Fractional Dynamics Approach to Diffusion Assisted Reactions in Disordered Media
• Critical Exponent of the Fractional Langevin Equation
• Ergodic Properties of Fractional Brownian-Langevin Motion
• Fractional Feynman-Kac Equation for Non-Brownian Functionals
• On Distributions of Functionals of Anomalous Diffusion Paths
• Foundation of fractional Langevin equation: Harmonization of a many-body problem
• Statistical Aging :

• Aging Wiener-Khinchin Theorem
• Aging renewal theory and application to random walks
• Scaling Green-Kubo relation and application to three aging systems
• Aging and nonergodicity beyond the Khinchin theorem
• Aging Continuous Time Random Walk
• Strong correlations between fluctuations and response in aging transport
• Multi-point distribution function for the continuous time random walk
• Weak Chaos: generalized Pesin identity, Anomalous Diffusion, Aging and Ergodicity Breaking, infinite invariant measure :

• Pesin-Type Identity for Intermittent Dynamics with a Zero Lyaponov Exponent
• Separation of trajectories and its relation to entropy for systems with a zero Lyapunov exponent
• Aging in A Chaotic System
• Transition from Dispersive to Regular Transport in Biased Maps
• Weak Ergodicity Breaking with Deterministic Dynamics
• Dynamics of interacting particles in 1d :

• Theory of Single File Diffusion in a Force Field
• Diffusion of a Tagged Particle in an Exclusion Process
• Foundation of fractional Langevin equation: Harmonization of a many-body problem
• Everlasting effect of initial conditions on single-file diffusion
• Diffusion in the quenched trap model: weak subordination breaking :

• Time transformation for random walks in the quenched trap model
• Weak subordination breaking for the quenched trap model
• Universal fluctuations of single-particle diffsivity in a quenched environment
• Transport in Disordered Systems :

• Scaling Green-Kubo relation and application to three aging systems
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Paradoxes of sub-diffusive infiltration in disordered systems
• Generalized Einstein Relation: A Stochastic Approach
• Time averaged Einstein relation and diffusivities for the L\'evy walk
• No-go theorem for ergodicity and an Einstein relation
• Time transformation for random walks in the quenched trap model
• The L\'evy Lorentz Gas
• One Dimensional Stochastic Lorentz Gas
• Universal fluctuations of single-particle diffsivity in a quenched environment
• Stable Equilibrium Based on L\'evy Statistics :

• Stable Equilibrium Based on L\'evy Statistics: Stochastic Collision Models Approach
• Stable Equilibrium Based on L\'evy Statistics: A Linear Boltzmann Equation Approach
• Excursion and Meanders :

• Distribution of the area under a Bessel excursion and its moments
• Random Walks :

• Anomalous Diffusion in the Strong Scattering Limit a L\'evy Walk Approach
• Aging Continuous Time Random Walk
• Noisy Continuous Time Random Walks
• Superdiffusive dispersals impart the geometry of underlying random walks
• Aging renewal theory and application to random walks
• Infinite densities for L\'evy walks
• Renewal Theoory :

• Renewal theory for a system with internal states
• Dissipation and fluctuation for a randomly kicked particle: Normal and anomalous diffusion