The inclusion process: duality and correlation inequalities

We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other -- a process which we call here the symmetric inclusion process (SIP) -- or repel each other -- a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction, -- the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.Comment: This is a new version: correlation inequalities for the Brownian energy process are added, and the part of the asymmetric inclusion process is removed

Comment on ``Collapse of Coherent Quasiparticle States in θ\theta-(BEDT-TTF)2_2I3_3 Observed by Optical Spectroscopy''

Recently, Takenaka et al. reported that the resistivity rho(T) of theta-(BEDT-TTF)_2I_3 (theta-ET) exceeds the Ioffe-Regel resistivity by a factor of 50 at large temperatures T (``bad metal''). This was ascribed to strong correlation. We argue that the optical conductivity sigma(omega) implies that correlation is not very strong, and that correlation gives no general strong suppression of sigma(omega). The large rho(T) is primarily due to a downturn in sigma(omega) at small omega, earlier emphasized by Takenaka et al. as the explanation for bad metal behavior of high-T_c cuprates. We argue, however, that for cuprates strong correlation is the main effect. The data of Takenaka et al. puts theta-ET in a new class of bad metals.Comment: 1 page, 1figur

Dualitiy, bosonic particle systems and some exactly solvable models of non-equilibrium

We study stochastic models of non-equilibrium which are exactly solvable with the technique of duality and self-duality. The models include a new class of particle systems which are bosonic, i.e., models where there is an attractive interaction between the particles and as a consequence condensation phenomena can occur. Our models belong to the class of interacting particle systems, or systems of interacting diffusions. Via the technique of duality, we connect models of interacting diffusions (e.g. Brownian Momentum Process) to simpler interacting particle systems (e.g. Symmetric Inclusion Process), both in equilibrium and non-equilibrium settings. Part of the thesis is devoted to develop a general formalism for duality.UBL - phd migration 201

Electronic thermal conductivity at high temperatures: Violation of the Wiedemann-Franz law in narrow band metals

We study the electronic part of the thermal conductivity kappa of metals. We present two methods for calculating kappa, a quantum Monte-Carlo (QMC) method and a method where the phonons but not the electrons are treated semiclassically (SC). We compare the two methods for a model of alkali-doped C60, A3C60, and show that they agree well. We then mainly use the SC method, which is simpler and easier to interpret. We perform SC calculations for Nb for large temperatures T and find that kappa increases with T as kappa(T)=a+bT, where a and b are constants, consistent with a saturation of the mean free path, l, and in good agreement with experiment. In contrast, we find that for A3C60, kappa(T) decreases with T for very large T. We discuss the reason for this qualitatively in the limit of large T. We give a quantum-mechanical explanation of the saturation of l for Nb and derive the Wiedemann-Franz law in the limit of T much smaller than W, where W is the band width. In contrast, due to the small W of A3C60, the assumption T much smaller than W can be violated. We show that this leads to kappa(T) \sim T^{-3/2} for very large T and a strong violation of the Wiedemann-Franz law.Comment: 8 pages, 4 figure

Mapping out of equilibrium into equilibrium in one-dimensional transport models

Systems with conserved currents driven by reservoirs at the boundaries offer an opportunity for a general analytic study that is unparalleled in more general out of equilibrium systems. The evolution of coarse-grained variables is governed by stochastic {\em hydrodynamic} equations in the limit of small noise.} As such it is amenable to a treatment formally equal to the semiclassical limit of quantum mechanics, which reduces the problem of finding the full distribution functions to the solution of a set of Hamiltonian equations. It is in general not possible to solve such equations explicitly, but for an interesting set of problems (driven Symmetric Exclusion Process and Kipnis-Marchioro-Presutti model) it can be done by a sequence of remarkable changes of variables. We show that at the bottom of this `miracle' is the surprising fact that these models can be taken through a non-local transformation into isolated systems satisfying detailed balance, with probability distribution given by the Gibbs-Boltzmann measure. This procedure can in fact also be used to obtain an elegant solution of the much simpler problem of non-interacting particles diffusing in a one-dimensional potential, again using a transformation that maps the driven problem into an undriven one

Abundance of nanoclusters in a molecular beam : the magic numbers for Lennard-Jones potential

We review the theory behind abundance of experimentally observed nanoclusters produced in beams, aiming to understand their magic number behavior. It is shown how use of statistical physics, with certain assumptions, reduces the calculation of equilibrium abundance to that of partition functions of single clusters. Methods to practically calculate these partition functions are introduced. The formalism is general and potential independent, but is only applicable to equilibrium or close-to-equilibrium scenarios and the interactions for which the partition functions can be accurately calculated. As an illustration, we compute the abundance of Lennard-Jones clusters at low temperatures, which reveals their experimentally observed magic number behavior. This shows that purely energetic and thermodynamic reasons can cause the magic numbers. We then briefly review kinetic approach to the problem and comment on the interplay between chemical, mechanical and thermodynamic stability of the clusters in more generality. Keywords: Nanoclusters synthesis; Magic numbers; Nucleatio

Duality and hidden symmetries in interacting particle systems

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the "hidden" symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing

Dynamics of condensation in the symmetric inclusion process

The inclusion process is a stochastic lattice gas, which is a natural bosonic counterpart of the well-studied exclusion process and has strong connections to models of heat conduction and applications in population genetics. Like the zero-range process, due to attractive interaction between the particles, the inclusion process can exhibit a condensation transition. In this paper we present first rigorous results on the dynamics of the condensate formation for this class of models. We study the symmetric inclusion process on a finite set S with total number of particles N in the regime of strong interaction, i.e. with independent diffusion rate m=mN¿0. For the case NmN¿8 we show that on the time scale 1/mN condensates emerge from general homogeneous initial conditions, and we precisely characterize their limiting dynamics. In the simplest case of two sites or a fully connected underlying random walk kernel, there is a single condensate hopping over S as a continuous-time random walk. In the non fully connected case several condensates can coexist and exchange mass via intermediate sites in an interesting coarsening process, which consists of a mixture of a diffusive motion and a jump process, until a single condensate is formed. Our result is based on a general two-scale form of the generator, with a fast-scale neutral Wright-Fisher diffusion and a slow-scale deterministic motion. The motion of the condensates is described in terms of the generator of the deterministic motion and the harmonic projection corresponding to the absorbing states of the Wright Fisher diffusion