Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains

Abstract

The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schrödinger equation in which the wave function is the probability distribution and the Hamiltonian is that of a quantum chain with nearest neighbor interactions. Since many one-dimensional quantum chains are integrable, this opens a new field of applications. At the same time physical intuition and probabilistic methods bring new insight into the understanding of the properties of quantum chains. A simple example is the asymmetric diffusion of several species of particles which leads naturally to Hecke algebras and $q$-deformed quantum groups. Many other examples are given. Several relevant technical aspects like critical exponents, correlation functions and finite-size scaling are also discussed in detail.

Latex 52 pages (2 figures appended at the end), UGVA-DPT 1992/12-799

Cited by in corpus (214)

• The density-matrix renormalization group
• Traffic and Related Self-Driven Many-Particle Systems
• Making Sense of Non-Hermitian Hamiltonians
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Glassy dynamics of kinetically constrained models
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Partially Asymmetric Exclusion Process with Open Boundaries
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Strong disorder fixed point in absorbing state phase transitions
• Integral Formulas for the Asymmetric Simple Exclusion Process
• Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka-Volterra Models
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• Infinite-randomness critical point in the two-dimensional disordered contact process
• Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition
• Absorbing state phase transitions with quenched disorder
• Master equations and the theory of stochastic path integrals
• Critical behavior and Griffiths effects in the disordered contact process
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains
• Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case
• Critical properties of the reaction - diffusion model 2A -> 3A, 2A ->0
• Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model
• Reaction-Diffusion Processes of Hard-Core Particles
• Master equation approach to protein folding and kinetic traps
• Kinetic model for q-deformed bosons and fermions
• On U_q(SU(2))-symmetric Driven Diffusion
• On Matrix Product Ground States for Reaction-Diffusion Models
• Criticality and quenched disorder: rare regions vs. Harris criterion
• EQUIVALENCES BETWEEN STOCHASTIC SYSTEMS
• Generalized Kinetic Equations for a System of Interacting Atoms and Photons: Theory and Simulations
• Concentration for One and Two Species One-Dimensional Reaction-Diffusion Systems
• Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process
• Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics
• Field Theory Approaches to Nonequilibrium Dynamics
• Some Exact Results for the Exclusion Process
• On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model
• Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• Exact solutions of exactly integrable quantum chains by a matrix product ansatz
• Nonequilibrium Dynamics in Low Dimensional Systems
• Conservation Laws and Integrability of a One-dimensional Model of Diffusing Dimers
• Diffusion-Annihilation in the Presence of a Driving Field
• Spectra of Quantum Chains without the Yang-Baxter Equation
• The Bethe ansatz as a matrix product ansatz
• Coupled Kardar-Parisi-Zhang Equations in One Dimension
• Deformed Yangians and Integrable Models
• Dynamical simulations of classical stochastic systems using matrix product states
• Phase Transitions and Scaling in Systems Far From Equilibrium
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
• Field theoretic approach to metastability in the contact process
• Order and symmetry-breaking in the fluctuations of driven systems
• On the ubiquity of matrix-product states in one-dimensional stochastic processes with boundary interactions
• An Introduction To Monte Carlo Simulations Of Surface Reactions
• Measurement of a reaction-diffusion crossover in exciton-exciton recombination inside carbon nanotubes using femtosecond optical absorption
• Weakly disordered absorbing-state phase transitions
• Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
• Universal finite-size scaling amplitudes in anisotropic scaling
• Reaction Diffusion Models in One Dimension with Disorder
• Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
• The duality relation between Glauber dynamics and the diffusion-annihilation model as a similarity transformation
• Fluctuations and correlations in chemical reaction kinetics and population dynamics
• Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
• Imperfect Diffusion-Controlled Reactions
• Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz
• Broadening of a nonequilibrium phase transition by extended structural defects
• Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton
• Multispecies reaction-diffusion systems
• Asymmetric stochastic transport models with ${\mathcal{U}}_q(\mathfrak{su}(1,1))$ symmetry
• Exactly Solvable Quasi-hermitian Transverse Ising Model
• Open two-species exclusion processes with integrable boundaries
• Phase diagram of the non-hermitean asymmetric XXZ spin chain
• A renormalization group study of a class of reaction-diffusion model, with particles input
• On the asymmetric simple exclusion process with multiple species
• Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input
• Phase transition in an asymmetric generalization of the zero-temperature Glauber model
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0
• Similarity transformation in one-dimensional reaction-diffusion systems; voting model as an example
• Duality and hidden equilibrium in transport models
• Non-unitarity in quantum affine Toda theory and perturbed conformal field theory
• On the universality of a class of annihilation-coagulation models
• Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models
• Quantum Crystals and Spin Chains
• Dynamical phase transition of a one-dimensional kinetic Ising model with boundaries
• Matrix product approach for the asymmetric random average process
• Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance
• Integrable dissipative exclusion process: Correlation functions and physical properties
• Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions
• Diffusion-limited Reactions of hard-core Particles in one-dimension
• Exact solution of a class of one-dimensional nonequilibrium stochastic models
• A reverse duality for the ASEP with open boundaries
• Exactly solvable models through the empty interval method
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Models solvable through the empty-interval method
• Monte-Carlo simulations of the smeared phase transition in a contact process with extended defects
• Symmetry and species segregation in diffusion-limited pair annihilation
• Precise Critical Exponents for the Basic Contact Process
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Exact results for an asymmetric annihilation process with open boundaries
• Phase transitions in systems possessing Shock solutions
• A new class of integrable diffusion-reaction processes
• Exact solution of an integrable non-equilibrium particle system
• The generalized contact process with n absorbing states
• Exactly solvable models through the empty interval method, for more-than-two-site interactions
• Fermionic field theory for directed percolation in (1+1) dimensions
• Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods
• Solution of classical stochastic one dimensional many-body systems
• Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
• Reaction-Diffusion Processes Described by Three-State Quantum Chains and Integrability
• Nonlinear reactive systems viewed as Boolean dynamical systems
• Phase transitions in autonomous reaction-diffusion systems on a one-dimensional lattice with boundaries
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Branching-annihilating random walks in one dimension: Some exact results
• Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method
• Path integral formulation and Feynman rules for phylogenetic branching models
• Fluctuation Effects in Steric Reaction-Diffusion Systems
• Annihilating random walks in one-dimensional disordered media
• On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• Quantum kinetic Ising models
• Segregation in diffusion-limited multispecies pair annihilation
• Anomalous bulk behaviour in the free parafermion $Z(N)$ spin chain
• Hidden symmetries in the asymmetric exclusion process
• Exactly solvable models through the generalized empty interval method: multi-species and more-than-two-site interactions
• Corrections to the Law of Mass Action and Properties of the Asymptotic $t=\infty$ State for Reversible Diffusion-Limited Reactions
• Selection rules for Single-Chain-Magnet behavior in non-collinear Ising systems
• Spectral flow of non-hermitian Heisenberg spin chain with complex twist
• Non-universal dynamics of staggered non-equilibrium particle systems and Ising chains
• Solution of a class of one-dimensional reaction-diffusion models in disordered media
• Application of the Bogolyubov's theory of weakly non-ideal Bose gas on the A+A, A+B, B+B reaction-diffusion system
• Exactly solvable statistical model for two-way traffic
• Multi shocks in Reaction-diffusion models
• Infinitely-fast diffusion in Single-File Systems
• Partially Asymmetric Simple Exclusion Model in the Presence of an Impurity on a Ring
• Directed abelian algebras and their applications to stochastic models
• Critical Properties of the One-Dimensional Forest-Fire Model
• Phase transition in an asymmetric generalization of the zero-temperature q-state Potts model
• $A+A\to \varnothing$ model with a bias towards nearest neighbor
• Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation
• Multi-Species Asymmetric Exclusion Process in Ordered Sequential Update
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model
• Transient behavior in Single-File Systems
• Exactly solvable reaction diffusion models on a Cayley tree
• Diffusion in disordered lattices and related Heisenberg ferromagnets
• Quantum Scaling Approach to Nonequilibrium Models
• Quantum Field Theory and Phylogenetic Branching
• Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs
• Quantum Chains with U_q(SL(2)) Symmetry and Unrestricted Representations
• Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring
• General Reaction-Diffusion Processes With Separable Equations for Correlation Functions
• Examples of interacting particle systems on $\mathbb{Z}$ as Pfaffian point processes: coalescing branching random walks and annihilating random walks with immigration
• Non-equilibrium relaxations: ageing and finite-size effects
• Non-Bloch dynamics and topology in a classical non-equilibrium process
• Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains
• KPZ fluctuations in finite volume
• Four State Models and Clifford Algebras
• Asymmetric exclusion model with impurities
• Fragmentation of a sheet by propagating, branching and merging cracks
• Two Magnetic Impurities with Arbitrary Spins in Open Boundary t-J Model
• Crossover properties of a one-dimensional reaction-diffusion process with a transport current
• Remarks on the multi-species exclusion process with reflective boundaries
• Roughening Transition of a Restricted Solid-on-Solid Model in the Directed Percolation Universality Class
• Reaction-controlled diffusion
• A coupled two-species model for the pair contact process with diffusion
• Ferromagnetic Ordering of Energy Levels for $U_q({\mathfrak{sl}}_2)$ Symmetric Spin Chains
• Effect of bias in a reaction diffusion system in two dimensions
• Static- and dynamical-phase transition in multidimensional voting models on continua
• p-species integrable reaction-diffusion processes
• Lattice Kinetics of Diffusion-Limited Coalescence and Annihilation with Sources
• Multi-species extension of the solvable partially asymmetric reaction- diffusion processes
• Reaction-diffusion on the fully-connected lattice: $A+A\to A$
• Particle Statistics and Population Dynamics
• Coarsening dynamics of adsorption processes with diffusional relaxation
• Diffusion with restrictions
• Representation-theoretic derivation of the Temperley-Lieb-Martin algebras
• Scaling approach to related disordered stochastic and free-fermion models
• Collective Diffusion and a Random Energy Landscape
• Solvable multi-species reaction-diffusion processes, including the extended drop-push model
• Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations
• Asymmetric exclusion model with several kinds of impurities
• Perturbative calculation of one-point functions of one-dimensional single-species reaction-diffusion systems
• Competition between homogeneous and local processes in a diffusive many-body system
• Autonomous models solvable through the full interval method
• Tagged particle dynamics in one dimensional $A+A\to kA$ models with the particles biased to diffuse towards their nearest neighbour
• Corrections to reaction-diffusion dynamics above the upper critical dimension
• $A+A\to \varnothing$ reaction for particles with a dynamic bias to move away from their nearest neighbour in one dimension
• Stochastic Model and Equivalent Ferromagnetic Spin Chain with Alternation
• A two-species d-dimensional diffusive model and its mapping onto a growth model
• The spectrum and the phase transition of models solvable through the full interval method
• Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
• Critical values for a non-attractive lattice gas model
• Contact process with aperiodic temporal disorder
• Integrable Stochastic Ladder Models
• Analytical results for a coagulation/decoagulation model on an inhomogeneous lattice
• Novel approach of exploring ASEP-like models through the Yang Baxter Equation
• Time Series Path Integral Expansions for Stochastic Processes
• New Integrable Models from Fusion
• Phase transition in annihilation-limited processes
• The spectral gap and the dynamical critical exponent of an exact solvable probabilistic cellular automaton
• Two-species diffusion-annihilation process on the fully-connected lattice: probability distributions and extreme value statistics
• Avalanches in the Raise and Peel model in the presence of a wall
• Intermediate time scale in the first product formation time distribution of Michaelis-Menten kinetics with inhibitors
• Restoring detailed balance in non-Hermitian Markov processes
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain
• Scale-invariant universal crossing probability in one-dimensional diffusion-limited coalescence
• Many-body methods in agent-based epidemic models