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