[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657527-105":59,"doc-detail-657527-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","diagram-technique-for-nonequilibrium-processes","DIAGRAM TECHNIQUE FOR NONEQUILIBRIUM PROCESSES","","Develops a diagram technique analogous to Feynman’s method for calculating Green’s functions in statistical systems driven by an external field that can deviate arbitrarily from thermodynamic equilibrium. Introduces two Green’s functions for each particle type to capture the nonequilibrium distribution. Shows that one resulting equation is essentially analogous to the Boltzmann kinetic equation, generalizing the equilibrium nonequilibrium treatment. Formulates the density matrix and operator representations and derives the structure needed for the kinetic-type equation.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/diagram-technique-for-nonequilibrium-processes/657527/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/diagram-technique-for-nonequilibrium-processes/657527.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main goal of the diagram technique developed in the paper?","Question",{"text":112,"@type":113},"To calculate Green’s functions for particles in nonequilibrium statistical systems under an external field, using a diagram method analogous to Feynman’s technique in field theory.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why does the method require two Green’s functions for each particle type?",{"text":117,"@type":113},"Because describing such nonequilibrium systems needs additional information beyond what a single Green’s function provides; introducing two functions allows the approach to reproduce the particle distribution dynamics.",{"name":119,"@type":110,"acceptedAnswer":120},"How is one of the derived equations related to the usual kinetic equation?",{"text":121,"@type":113},"One of the equations for the Green’s functions is found to be essentially analogous to the Boltzmann kinetic equation, acting as the kinetic equation that governs the particle distribution.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657527,1792981968,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068","# DIAGRAM TECHNIQUE FOR NONEQUILIBRIUM PROCESSES\n\nL.V.KELDYSH  \nP.N.Lebedev Physics Institute,Academy of Sciences,U.S.S.R.  \nSubmitted to JETP editor April 23,1964  \nJ.Exptl.Theoret.Phys.(U.S.S.R.)47,1515-1527(October,1964)  \nA graph technique analogous to the usual Feynman technique in field theory is developed forcalculating Green's functions for particles in a statistical system which under the action of anexternal field deviates to any arbitrary extent from the state of thermodynamic equilibrium.It is found that in order to describe such a system it is necessary to introduce two Green’sfunctions for each type of particles.The equation for one of these functions is a generaliza-tion of the usual Boltzmann kinetic equation.  \nTHE use of quantum field theory methods hasturned out to be very effective for the formulationand for the solution of problems in statistical phys-ics.A number of prescriptions has been given forthe description of thermodynamic characteristicsof equilibrium systems[1-6]and of the ground stateof a many-body system[7-9].In the papers of Kon-stantinov and Perel’[10],DzyaloshinskiY[11]andMills[12]a technique has been developed for thecalculation of time dependent quantities (kineticcoefficients)in systems in thermodynamic equili-brium.In carrying out this program the deviationof the system from the Gibbs equilibrium distribu-tion was assumed to be small,i.e.,the externalfield was taken to be sufficiently small.The pres-ent paper is devoted to the application of analogousmethods to the description of essentially nonequili-brium systems,for example,such systems as thesystem of electrons in a strong electric field.Inthe simplest cases in order to describe such sys-tems Boltzmann's kinetic equation or the systemof coupled equations proposed by Bogolyubov[13]are used.  \nence that the number of Green's functions appear-ing in it is increased.In the course of the discus-sion there appears automatically a function whichdescribes the distribution of the particles in thesystem,and the equation for this function plays therole of the kinetic equation.  \nFollowing the method of Konstantinov and Perel'we shall define the density matrixp for thesystem by the usual equation  \nidp/ot =[Hi,p]-=H;(t)p(t)一p(t)H;(t)  (1)  \nwith the boundary condition  \np(t=-∞)=po=exp{V。—H₀(—∞))/kT},(2)  \nwhere H=H₀+Hi is the Hamiltonian of the system  \n(3)  \n×ψo(rt)dr+HT.  \nThe first term in H₀is the energy of noninteractingelectrons in an external electromagnetic field{A(rt),重(rt)},the second is the Hamiltonian of theheat bath in contact with the system under consid-eration,∈(p)is the dispersion law for the elec-trons,业ois the initial free energy.  \nWe shall obtain below a system of equations forthe Green's functions of the particles in the system,and we shall show that one of these equations isessentially analogous to the kinetic equation.Theappearance of such an equation-an additional onein comparison with systems in thermodynamicequilibrium—in the problem under consideration isquite natural,since we must have an equation whichdescribes the distribution of particles in the sys-tem.In the equilibrium case this is given by theGibbs canonical distribution.Our diagram tech-nique will be close to Mills'technique for equili-brium systems.This technique has the advantagethat it is completely analogous to the usual Feyn-man technique in field theory,with the only differ-  operatorψ₀(rt)is defined by the relation  \nare defined in theThe field operators ψo andfollowing manner:let φp(rt)be the complete sys-tem of functions determined by the equation  \nand by the boundary condition at t→-∞  \n(5)φp(rt)→exp{i(pr—ept)},  \nwhere we consider the external field to be switchedoff at t→-∞,i.e.,(A,)→0.Then the field  \n1019DIAGRAM TE CHNIQUE FOR NONEQUILIBRIUM PROCESSES  \n\u003CL₀(t)>=Tr{p(t)L₀(t)},  \n(6)  \n(14)  \nwhere the subscript zero on the operator Lo showsthat this operator is taken in the interaction repre-sentation,i.e.,its time dependence is determinedby the","cbCaii0aLNZcTKSD","https://ap.wps.com/l/cbCaii0aLNZcTKSD","pdf",1129547,"English","# DIAGRAM TECHNIQUE FOR NONEQUILIBRIUM PROCESSES\n## Introduction and motivation\n## Density matrix and operator representations\n## Green's functions system and kinetic-type equation","[{\"question\":\"What is the main goal of the diagram technique developed in the paper?\",\"answer\":\"To calculate Green’s functions for particles in nonequilibrium statistical systems under an external field, using a diagram method analogous to Feynman’s technique in field theory.\"},{\"question\":\"Why does the method require two Green’s functions for each particle type?\",\"answer\":\"Because describing such nonequilibrium systems needs additional information beyond what a single Green’s function provides; introducing two functions allows the approach to reproduce the particle distribution dynamics.\"},{\"question\":\"How is one of the derived equations related to the usual kinetic equation?\",\"answer\":\"One of the equations for the Green’s functions is found to be essentially analogous to the Boltzmann kinetic equation, acting as the kinetic equation that governs the particle distribution.\"}]","DIAGRAM TECHNIQUE FOR NONEQUILIBRIUM PROCESSES | PDF",23]