Herbert Spohn

Energy transport in stochastically perturbed lattice dynamics (2008)

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε−1 the local spectral density (Wigner function) evolves...

Kinetics of the Bose-Einstein Condensation (2008)

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε−1 the local spectral density (Wigner function) evolves...

Kramers degeneracy theorem in nonrelativistic QED (2008)

We study the bosonic Boltzmann-Nordheim kinetic equation, which describes the kinetic regime of weakly interacting bosons with s-wave scattering only. We consider a spatially homogeneous fluid with...

Loss, Michael, Miyao, Tadahiro, Spohn, Herbert

Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed total momentum is also investigated.

Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids (2008)

Lukkarinen, Jani, Spohn, Herbert

The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle...

On Scattering of Solitons for Maxwell Equation Coupled to a Particle (2008)

Imaykin, Valery, Komech, Alexander, Spohn, Herbert

We establish a long time soliton asymptotics for a nonlinear system of Maxwell equation coupled to a charged particle. The coupled system has a six dimensional manifold of soliton solutions. We show...

Spectral Analysis of the Semi-relativistic Pauli-Fierz Hamiltonian (2008)

Miyao, Tadahiro, Spohn, Herbert

We consider a charged particle, spin 1/2, with relativistic kinetic energy and minimally coupled to the quantized Maxwell field. Since the total momentum is conserved, the Hamiltonian admits a fiber...

Wigner functions and stochastically perturbed lattice dynamics (2008)

Wigner functions and stochastically perturbed lattice dynamics (2008)

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε−1 the Wigner function evolves according to a linear...

Energy transport in stochastically perturbed lattice dynamics (2008)

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε−1 the Wigner function evolves according to a linear...

Motions of electrons in adiabatically perturbed periodic structures (2007)

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε−1 the local spectral density (Wigner function) evolves...

The time-dependent Born-Oppenheimer approximation (2007)

We study the motion of electrons in a periodic background potential (usually resulting from a crystalline solid). For small velocities one would use either the non-magnetic or the magnetic Bloch...

Notes on coherent backscattering from a random potential (2007)

We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the...

Kinetic Equations for Quantum Many-Particle Systems (2007)

We consider the quantum scattering from a random potential of strength $\lambda^{1/2}$ and with a support on the scale of the mean free path, which is of order $\lambda^{-1}$. On the basis of...

Energy Current Correlations For Weakly Anharmonic Lattices (2007)

The current status of the derivation of kinetic equations from quantum many-particle dynamics is reviewed.

On the Boltzmann Equation for Weakly Nonlinear Wave Equations (2007)

We discuss energy current correlations in thermal equilibrium and point out the linkage to the fluctuating Peierls equation.

Scaling limit for a class of gradient fields with non-convex potentials (2007)

We explain how the kinetic theory of L. Boltzmann is applied to weakly nonlinear wave equations.

Biskup, Marek, Spohn, Herbert

We consider gradient fields $(\phi_x\colon x\in\Z^d)$ whose law takes the Gibbs-Boltzmann form $Z^{-1}\exp\{-\sum_{< x,y>}V(\phi_y-\phi_x)\}$ where the sum runs over nearest neighbors. We assume that...

Anomalous energy transport in the FPU-beta chain (2007)

Lukkarinen, Jani, Spohn, Herbert

We consider the energy current correlation function for the FPU-beta lattice. For small non-linearity one can rely on kinetic theory. The issue reduces then to a spectral analysis of the linearized...

Polymer pinning in a random medium as influence percolation (2006)

Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia

In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...

Polymer pinning in a random medium as influence percolation (2006)

Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia

In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...

Collisional invariants for the phonon Boltzmann equation (2006)

On the Integrated Form of the BBGKY Hierarchy for Hard Spheres (2006)

For the phonon Boltzmann equation with only pair collisions we characterize the set of all collisional invariants under some mild conditions on the dispersion relation.

Domino tilings and the six-vertex model at its free fermion point (2006)

In my book ``Large Scale Dynamics of Interacting Particles'' [S] I refer to an unpublished note from early 1985 on the BBGKY hierarchy for hard spheres. My main point there was to provide a direct...

Lowest energy states in nonrelativistic QED: atoms and ions in motion (2006)

At the free-fermion point, the six-vertex model with domain wall boundary conditions (DWBC) can be related to the Aztec diamond, a domino tiling problem. We study the mapping on the level of complete...

Loss, Michael, Miyao, Tadahiro, Spohn, Herbert

Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and $N$ electrons coupled to the radiation field. Since the total momentum $P$ is conserved, the...

Energy Transport in Weakly Anharmonic Chains (2006)

Aoki, Kenichiro, Lukkarinen, Jani, Spohn, Herbert

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for...

Polymer pinning in a random medium as influence percolation (2006)

Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia

In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...

Polymer pinning in a random medium as influence percolation (2006)

Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia

In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...

Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals (2005)

Polymer pinning in a random medium as influence percolation (2005)

Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently...

Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia

In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...

Polymer pinning in a random medium as influence percolation (2005)

Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia

In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...

A Remark on the Strict Positivity of the Entropy Production (2005)

Aschbacher, Walter H., Spohn, Herbert

We establish an algebraic criterion which ensures the strict positivity of the entropy production in quantum models consisting of a small system coupled to thermal reservoirs at different...

Constrained Brownian motion: Fluctuations away from circular and parabolic barriers (2005)

Kinetic Limit for Wave Propagation in a Random Medium (2005)

Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(±T)=0 conditioned to stay above the semicircle $c_{T}(t)=\sqrt{T^{2}-t^{2}}$ . In the limit of large T, the...

Lukkarinen, Jani, Spohn, Herbert

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The dispersion relation...

The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics (2005)

A determinantal formula for the GOE Tracy-Widom distribution (2005)

For low density gases the validity of the Boltzmann transport equation is well established. The central object is the one-particle distribution function, $f$, which in the Boltzmann-Grad limit...

KPZ equation in one dimension and line ensembles (2005)

Investigating the long time asymptotics of the totally asymmetric simple exclusion process, Sasamoto obtains rather indirectly a formula for the GOE Tracy-Widom distribution. We establish that his...

Towards a microscopic derivation of the large phonon Boltzmann equation (2005)

For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one...

Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process (2005)

We outline the kinetic limit for weakly nonlinear wave equations

Gibbs measures on Brownian paths: Theory and applications (2004)

The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli \rho measure as initial conditions, 0

Betz, Volker, Lorinczi, Jozsef, Spohn, Herbert

We review our investigations on Gibbs measures relative to Brownian motion, in particular the existence of such measures and their path properties, uniqueness, resp. non-uniqueness. For the case when...

Binding energy for hydrogen-like atoms in the Nelson model without cutoffs (2003)

Hainzl, Christian, Hirokawa, Masao, Spohn, Herbert

In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge $Ze$, $Z > 0$, fixed at the origin and an electron of...

Stochastic Growth in One Dimension and Gaussian Multi-Matrix Models (2003)

Ferrari, Patrik L., Praehofer, Michael, Spohn, Herbert

We discuss the space-time determinantal random field which arises for the PNG model in one dimension and resembles the one for Dyson's Brownian motion. The information of interest for growth...

Mass renormalization in nonrelativistic QED (2003)

Hiroshima, Fumio, Spohn, Herbert

In nonrelativistic QED the charge of an electron equals its bare value, whereas the self-energy and the mass have to be renormalized. In our contribution we study perturbative mass renormalization,...

Constrained Brownian motion: Fluctuations away from circular and parabolic barriers (2003)

A central limit theorem for Gibbs measures relative to Brownian motion (2003)

Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(\pm T)=0 conditioned to stay above the semicircle c_T(t)=\sqrtT^2-t^2. In the limit of large T, the fluctuation...

Betz, Volker, Spohn, Herbert

We study a Gibbs measure over Brownian motion with a pair potential which depends only on the increments. Assuming a particular form of this pair potential, we establish that in the infinite volume...

Stationary measures and hydrodynamics of zero range processes with several species of particles (2003)

Grosskinsky, Stefan, Spohn, Herbert

We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the...

Fluctuations of an Atomic Ledge Bordering a Crystalline Facet (2003)

Ferrari, Patrik L., Praehofer, Michael, Spohn, Herbert

When a high symmetry facet joins the rounded part of a crystal, the step line density vanishes as sqrt(r) with r denoting the distance from the facet edge. This means that the ledge bordering the...

Condensation in the zero range process: stationary and dynamical properties (2003)

Grosskinsky, Stefan, Schuetz, Gunter M., Spohn, Herbert

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which...

Space-adiabatic perturbation theory (2003)

Panti, Gianluca, Spohn, Herbert, Teufel, Stefan

We study approximate solutions to the time-dependent Schrodinger equation $i\epsi\partial_t\psi_t(x)/\partial t = H(x,-i\epsi\nabla_x)\,\psi_t(x)$ with the Hamiltonian given as the Weyl quantization...

Effective dynamics for Bloch electrons: Peierls substitution and beyond (2003)

Space-adiabatic perturbation theory (2003)

We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\phi(\epsi x)$, and vector potential $A(\epsi x)$, with $x \in...

Exact scaling functions for one-dimensional stationary KPZ growth (2002)

We study approximate solutions to the Schr\"odinger equation $i\epsi\partial\psi_t(x)/\partial t = H(x,-i\epsi\nabla_x) \psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol...

Step Uctuations for a Faceted Crystal (2002)

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence...

Patrik L. Ferrari, Herbert Spohn

A statistical mechanics model for a faceted crystal is the 3D Ising model at zero temperature. It is assumed that in one octant all sites are occupied by atoms, the remaining ones being empty....

Step fluctuations for a faceted crystal (2002)

Effective dynamics for Bloch electrons: Peierls substitution and beyond (2002)

A statistical mechanics model for a faceted crystal is the 3D Ising model at zero temperature. It is assumed that in one octant all sites are occupied by atoms, the remaining ones being empty....

Gianluca Panati, Herbert Spohn, Stefan Teufel

We reconsider the longstanding problem of an electron moving in a crystal under the influence of weak external electromagnetic fields. More precisely we analyze the dynamics generated by the...

Effective dynamics for Bloch electrons: Peierls substitution and beyond (2002)

Ground state for point particles interacting through a massless scalar Bose field (2002)

We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\phi(\epsi x)$, and vector potential $A(\epsi x)$, with $x \in...

Hirokawa, Masao, Hiroshima, Fumio, Spohn, Herbert

We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is...

Last Branching in Directed Last Passage Percolation (2002)

Patrik L. Ferrari, Herbert Spohn

The 1+1 dimensional directed polymers in a Poissonean random environment is studied. For two polymers of maximal length with the same origin and distinct end points we establish that the point of...

Last Branching in Directed Last Passage Percolation (2002)

Space-adiabatic Decoupling to All Orders (2002)

The 1+1 dimensional directed polymers in a Poissonean random environment is studied. For two polymers of maximal length with the same origin and distinct end points we establish that the point of...

Space-Adiabatic Perturbation Theory (2002)

A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schroedinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the...

Gianluca Panati, Herbert Spohn, Stefan Teufel

We study approximate solutions to the Schrödinger equation i"@ t (x)=@t = H(x; i"r x ) t (x) with the Hamiltonian H the Weyl quantization of the symbol H(q; p) taking values in the space of bounded...

Space-Adiabatic Perturbation Theory (2002)

Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory (2001)

We study approximate solutions to the Schr\"odinger equation $i\epsi\partial\psi_t(x)/\partial t = H(x,-i\epsi\nabla_x) \psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol...

Herbert Spohn, Stefan Teufel

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the...

Infrared regular representation of the three dimensional massless Nelson model (2001)

Lorinczi, Jozsef, Minlos, Robert A., Spohn, Herbert

We prove that in the Euclidean representation of the three dimensional massless Nelson model the t = 0 projection of the interacting measure is absolutely continuous with respect to a Gaussian...

Equilibrium Fluctuations for $\nabla_{\varphi}$ Interface Model (2001)

Giacomin, Giambattista, Olla, Stefano, Spohn, Herbert

We study the large scale space–time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove...

Equilibriumflucl Ations For (2001)

Stefano Olla, Herbert Spohn

this paper we will study small (central limit type) fluctuations. Such fluctuations should relax according to the linearized version of (1.4) and, according to (1.3) should be perturbed by white...

Ground state properties of the Nelson Hamiltonian - A Gibbs measure-based approach (2001)

Betz, Volker, Hiroshima, Fumio, Lorinczi, Jozsef, Minlos, Robert A., Spohn, Herbert

We study properties of the ground state of the Nelson model through functional integration. We obtain bounds on the average and the variance of the Bose field both in position and momentum space, on...

Scale Invariance of the PNG Droplet and the Airy Process (2001)

Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory (2001)

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy...

Spohn, Herbert, Teufel, Stefan

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the...

Porous silicon formation and electropolishing (2001)

Rauscher, Markus, Spohn, Herbert

Electrochemical etching of silicon in hydrofluoride containing electrolytes leads to pore formation for low and to electropolishing for high applied current. The transition between pore formation and...

Post-Coulombian Dynamics at Order 1.5 (2001)

Kunze, Markus, Spohn, Herbert

We study the dynamics of N charges interacting with the Maxwell field. If their initial velocities are small compared to the velocity of light, c, then in lowest order their motion is governed by the...

Current Fluctuations for the Totally Asymmetric Simple Exclusion Process (2001)

Herbert Spohn

The time-integrated current of the TASEP has non-Gaussian fluctuations of order t^{1/3} . The recently discovered connection to random matrices and the Painlevé II Riemann-Hilbert problem...

Equilibrium Fluctuations For ... Interface Model (2001)

Giambattista Giacomin, Stefano Olla, Herbert Spohn

. We study the large scale space{time uctuations of an interface which is modeled by a massless scalar eld with reversible Langevin dynamics. For a strictly convex interaction potential we prove that...

The infrared behaviour in Nelson's model of a quantum particle coupled to a massless scalar field (2000)

Lorinczi, Jozsef, Minlos, Robert A., Spohn, Herbert

We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian and the Hamiltonian obtained from Euclidean quantization are not...

Semi-Classical Motion of Dressed Electrons (2000)

Stefan Teufel, Herbert Spohn

We consider an electron coupled to the quantized radiation field and subject to a slowly varying electrostatic potential. We establish that over sufficiently long times radiation effects are...

Semi-classical motion of dressed electrons (2000)

Teufel, Stefan, Spohn, Herbert

We consider an electron coupled to the quantized radiation field and subject to a slowly varying electrostatic potential. We establish that over sufficiently long times radiation effects are...

Semiclassical Limit For The Schrödinger Equation With A Short Scale Periodic Potential (2000)

Frank H Overmann, Herbert Spohn, Stefan Teufel

We consider the dynamics generated by the Schrödinger operator H = Gamma 1 2 Delta + V (x) +W ("x), where V is a lattice periodic potential and W an external potential which varies slowly on the...

Slow Motion of Charges Interacting Through the Maxwell Field (2000)

Markus Kunze, Herbert Spohn

We study the Abraham model for N charges interacting with the Maxwell field. On the scale of the charge diameter, R ' , the charges are a distance " Gamma1 R ' apart and have a velocity p "c with " a...

Slow Motion of Charges Interacting Through the Maxwell Field (2000)

Kunze, Markus, Spohn, Herbert

We study the Abraham model for $N$ charges interacting with the Maxwell field. On the scale of the charge diameter, $R_{\phi}$, the charges are a distance $\eps^{-1}R_{\phi}$ apart and have a...

Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices (1999)

The critical manifold of the Lorentz-Dirac equation (1999)

We develop a scaling theory for KPZ growth in one dimension by a detailed study of the polynuclear growth (PNG) model. In particular, we identify three universal distributions for shape fluctuations...

Semiclassical limit of the Dirac equation and spin precession (1999)

We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena. The physical...

Statistical Self-Similarity of One-Dimensional Growth Processes (1999)

We study the Dirac equation with slowly varying external potentials. Using matrix-valued Wigner functions we prove that the electron follows with high precision the classical orbit and that the spin...

Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory (1999)

For one-dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times. We argue that for...

Dynamics of charged particles and their radiation field (1999)

Through a Euclidean path integral we establish that the density fluctuations of a Fermi fluid in one dimension are related to vicinal surfaces and to the stochastic dynamics of particles interacting...