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Herbert Spohn

Publications and source records attributed to Herbert Spohn.

152 records · Page 9Linked to original sources
arXiv1999

Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory

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 through long range forces with inverse distance decay. In the surface picture one easily obtains the Haldane relation and identifies the scaling exponents governing the low energy, Luttinger liquid behavior. For the stochastic particle model we develop a hydrodynamic fluctuation theory, through which in some cases the large distance Gaussian fluctuations are proved nonperturbatively.

cond-mat.stat-mech↗
arXiv1999

Large deviations for ideal quantum systems

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.

math-ph↗
arXiv1999

Radiation Reaction and Center Manifolds

We study the effective dynamics of a mechanical particle coupled to a wave field and subject to the slowly varying potential $V(\eps q)$ with $\eps$ small. To lowest order in $\eps$ the motion of the particle is governed by an effective Hamiltonian. In the next order one obtains ``dissipative'' terms which describe the radiation reaction. We establish that this dissipative dynamics has a center manifold which is repulsive in the normal direction and which is global, in the sense that for given data and sufficiently small $\eps$ the solution stays on the center manifold forever. We prove that the solution of the full system is well approximated by the effective dissipative dynamics on its center manifold.

math-ph↗
arXiv1998

A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics

We extend the work of Kurchan on the Gallavotti-Cohen fluctuation theorem, which yields a symmetry property of the large deviation function, to general Markov processes. These include jump processes describing the evolution of stochastic lattice gases driven in the bulk or through particle reservoirs, general diffusive processes in physical and/or velocity space, as well as Hamiltonian systems with stochastic boundary conditions. For dynamics satisfying local detailed balance we establish a link between the action functional of the fluctuation theorem and the entropy production. This gives, in the linear regime, an alternative derivation of the Green-Kubo formula and the Onsager reciprocity relations. In the nonlinear regime consequences of the new symmetry are harder to come by and the large derivation functional difficult to compute. For the asymmetric simple exclusion process the latter is determined explicitly using the Bethe ansatz in the limit of large N.

cond-mat.stat-mech↗
arXiv1998

A Note on the Eigenvalue Density of Random Matrices

The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a consequence of a more general theorem, proven here, in the statistical mechanics of unstable interactions. Our result establishes the eigenvalue density of some ensembles of random matrices which were not covered by previous theorems.

math-ph↗
arXiv1997

Magneto-Transport in the Two-Dimensional Lorentz Gas

We consider the two-dimensional Lorentz gas with Poisson distributed hard disk scatterers and a constant magnetic field perpendicular to the plane of motion. The velocity autocorrelation is computed numerically over the full range of densities and magnetic fields with particular attention to the percolation threshold between hopping transport and pure edge currents. The Ohmic and Hall conductance are compared with mode-coupling theory and a recent generalized kinetic equation valid for low densities and small fields. We argue that the long time tail as $t^{-2}$ persists for non-zero magnetic field.

cond-mat↗