This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.

The core of the material on large scale dynamics of interacting particles grew out of courses I taught at the Katholieke Universiteit Leuven, Rutgers Universi ty, and the Ludwig-Maximilians-Universitat Munchen and out of lectures I gave at the workshop "Hydrodynamical Behavior of Microscopic Systems" at the Universita dell'Aquila. I had the good luck of being helped through difficult ground by many friends. Amongst them I am deeply indebted to Joel L. Lebowitz. He got me started. Relatively little would have been achieved without his never-ending curiosity and insistence on clarity. Furthermore, I gratefully acknowledge the cooperation of Michael Aizenman, Henk van Beijeren, Carlo Boldrighini, Jean Bricmont, Paola Calderoni, Brian Davies, Anna DeMasi, Roland Dobrushin, Detlef Durr, Gregory Eyink, Mark Fannes, Pablo Ferrari, Alberto Frigerio, Joseph Fritz, Antonio Galves, Shelly Goldstein, Vittorio Gorini, Reinhard Illner, Claude Kipnis, Joachim Krug, Oscar Lanford, Reinhard Lang, Joel Lebowitz, Christian Maes, Stefano Olla, George Papanicolaou, Errico Presutti, Mario Pulvirenti, Fraydoun Rezakhanlou, Hermann Rost, Yasha Sinai, Yuri Suhov, Domo Szasz, Ragu Varadhan, Andre Verbeure, David Wick, and Horng-Tzer Yau. The list is somewhat lengthy, perhaps, but besides thanks I want to make clear that what I will describe is the outcome of a common scientific enterprise. I thank Henk van Beijeren and Detlef Durr for careful reading of and com ments on a previous version. Paola Calderoni and Detlef Durr supplied me with the proof in Part I, Chapter 8. 4 which is most appreciated. Munchen, May 1991 Herbert Spohn Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ."

Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincare (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas.

Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincare (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas.

This book provides a self-contained and systematic introduction to classical electron theory and its quantization, non-relativistic quantum electrodynamics. The first half of the book covers the classical theory. It discusses the well-defined Abraham model of extended charges in interaction with the electromagnetic field, and gives a study of the effective dynamics of charges under the condition that, on the scale given by the size of the charge distribution, they are far apart and the applied potentials vary slowly. The second half covers the quantum theory, leading to a coherent presentation of non-relativistic quantum electrodynamics. Topics discussed include non-perturbative properties of the basic Hamiltonian, the structure of resonances, the relaxation to the ground state through emission of photons, the non-perturbative derivation of the g-factor of the electron and the stability of matter. First released in 2004, this title has been reissued as an Open Access publication on Cambridge Core.

This book provides a self-contained and systematic introduction to classical electron theory and its quantization, non-relativistic quantum electrodynamics. The first half of the book covers the classical theory. It discusses the well-defined Abraham model of extended charges in interaction with the electromagnetic field, and gives a study of the effective dynamics of charges under the condition that, on the scale given by the size of the charge distribution, they are far apart and the applied potentials vary slowly. The second half covers the quantum theory, leading to a coherent presentation of non-relativistic quantum electrodynamics. Topics discussed include non-perturbative properties of the basic Hamiltonian, the structure of resonances, the relaxation to the ground state through emission of photons, the non-perturbative derivation of the g-factor of the electron and the stability of matter. First released in 2004, this title has been reissued as an Open Access publication on Cambridge Core.

Herbert Spohn's poetry is rooted in his life experiences. In his collection of free verse, Spohn illuminates elements of the human condition, such as romantic love, identity, aging, death, and childhood in post-World War I Germany.

Spohn, an emigre from Nazi Germany and decorated World War II veteran, relies on both his personal and professional backgrounds to share his unique reflections on life. With a style that is at times warm and lyrical, analytical and searing, and sensual and thought-provoking, Spohn encourages others to look inward and rediscover emotions about such relatable subjects as falling in love, the betrayal of an aging body, and the pain of loss.

Who We Are is a poignant and sophisticated collection of poetry that shares one man's reflections as he looks back on an imperfect, yet fulfilling, life.

Words float at random

arrayed in patterns on the surface.

Meanings they seem to yield

seduce us readily into belief.

When they disaggregate

we do not know we are betrayed.

Misled by ineluctable formations,

we walk in truth until we fall.

Words can lead us into regions

where our pain resides.

Yet they can lift us into ecstasy,

and bring us healing love.

A retired therapist shares hard-fought wisdom and a little whimsy in this collection of original poetry. The subjects of aging, depression and interpersonal relationships are explored in depth in these poems, with the message that none of them is easy. Not even the satisfactions of posterity are a salve to the poet-"I take no comfort that in dying / I live on in the memory of others," Spohn writes in an untitled poem. The book is separated thematically, so that "Aging" gets its own section, alongside chapters with headings like "Love, Loss and Longing," and "Depression," among others. The poems are brutally direct, and the language largely eschews ornament...The lines are broken into free-verse fragments that hew closely to the rhythms of prose. "Love no longer walks beside you. / In that moment you are truly alone," he writes in one poem. "All that your passing left me / Is a question. / Why?" he writes forlornly in another. He does not transform his experience, but merely transcribes it. This is why the more whimsical and imaginative chapters provide some relief, especially a chapter in which ordinary objects are imbued, with some light alchemy, with the attitudes of grumpy old people. Here a chair complains of a hutch and a lamp that "I am an alien in their midst," and a saltshaker's "ardent feelings for a vase nearby / Cooled when her mums began to fade." We all age, it's true. Yet small personifications, like this empathetic saltshaker's love for a vase of flowers, differentiate our suffering and make it the subject of worthwhile poetry. A predominantly dark collection of verse. -Kirkus Discoveries

In many of the thought-provoking stories in "Broken Glass," author Herbert Spohn delves into the situations that people face that make them question their sense of self and how they cope with such challenges.

In the title story, "Broken Glass," a homeless man seeks to recover the image of his wife who was horribly disfigured and killed in an automobile accident. In "Becoming an American," an immigrant youth gains both citizenship and maturity in World War II. A produce department manager tells how he learned to cope with blindness in "Diary of a Blind Man." In "Drunks," a recovering alcoholic faces a grave threat to his sobriety. Searching for the source of a death threat, a workaholic therapist finds something he lost in "David Shore Ph.D." And "Emalyne" features a troubled young woman who takes her father, a renowned judge, to court on charges of molestation.

Other stories tell of a daughter realizing too late that her father loved her, a boy acutely sensitive to other people's feelings, and a middle-aged man obsessed with a search for a long-lost love. Each of the tales in "Broken Glass" relays important life lessons and a profound ending that will leave you wanting more.