Abstract: In this talk I will discuss the importance of a fundamental physical theory to be grounded on a clear primitive ontology. I will address questions like the following: What is a clear primitive ontology? What is its role in the theory? What are the consequences for a theory without a clear primitive ontology?
Abstract: We introduce new methods to analyze existence and uniqueness of solutions of relatively general nonlinear systems of evolution PDEs in Rn. We will illustrate the methods to show existence of local solutions to the 3d Navier-Stokes equation and show how the methods can provide computer-assisted proofs of global existence for special initial data.
Abstract: I will present a recent result (in collaboration with I. Merola, E. Presutti and Y. Vignaud) on a continuum version of the Potts model, where particles are points in Rd, d >= 2, with a spin which may take S >= 3 possible values. Particles with different spins repel each other via a Kac pair potential of range gamma-1, gamma>0. We prove that given any beta, for any gamma sufficiently small there is a value of the chemical potential for which there are S+1 extremal DLR measures. The proof uses the Pirogov-Sinai theory and it is based on proving a finite size, Dobrushin-Sholsman condition in a suitably defined restricted ensemble, while the Dobrushin uniqueness condition does not hold.
Abstract: Viewing quantum mechanics as a generalisation of a classical stochastic process (rather than of a classical deterministic Hamiltonian system) affords a different perspective on foundational questions. It fits more naturally with a fully space-time approach and deals fundamentally with "events which can happen" (rather than "events which can be measured"). It will be argued that if the related concepts of "preclusion" and "typicality" are sufficient to exhaust the meaning of probability in classical stochastic processes, the preclusion "axiom" can formally be extended to a quantum theory in which a quantum measure takes the place of a classical probability measure. An interpretation of quantum measure theory, based on preclusion, will be presented. In this interpretation, logical "rules of inference" are impelled to be dynamical rather than fixed and immutable.
Abstract: I shall describe the impact of his scientific work and the lesson we learn from it.
Abstract: Kipnis and myself have shown that a second class particle in the rarefaction fan of TASEP converges to a uniform random variable in law. Now put a second class particle at site 1, a third class particle at site 0, first class particles at all negative sites and holes at the remaining (positive) sites. We show that the probability the third class particle is eventually to the right of the second class particle is 2/3. This is related with the flux of first class particles through the second class particle. Joint work with Patricia Goncalves and James Martin.
Abstract: It is shown how the atomistic constitution of matter and radiation can be understood as originating from continuum theories of matter and radiation by 'quantization'. Among other examples, it is explained how the Newtonian mechanics of point particles can be derived from a quantization of Vlasov dynamics. It is argued that the puzzling features of ordinary quantum mechanics arise from the combination of quantum theory and atomism. Conclusions from this observation will be left to the audience.
Abstract: We present numerical results on the one dimensional Kipnis-Marchioro-Pressutti lattice model for heat conductivity. We focus on the fluctuating behavior of the heat current and the thermal profile. We compare the results with the Bodineau-Derrida theory. We also present some preliminary results on the heat conductivity behavior of a two dimensional system of hard disks. Non linear profiles appear when a large temperature gradient is applied but macroscopic local equilibrium and Fourier law still hold. However, the behavior of fluctuations differs from the one corresponding to a true local equilibrium behavior.
Abstract: We briefly review the debate which has characterized, since its inception, our best theory: quantum mechanics. After focussing on the crucial problem of the theory, i.e., the macro-objectification problem, we analyze critically the proposal to solve the problem by resorting to decoherence. We then stress the necessity of making precise the primitive ontology of any theoretical framework for the description of natural processes and we focus our attention on the two "exact" available proposals to overcome the difficulties: Bohmian Mechanics and the Dynamical Reduction Theory. In particular we point out some recent serious misunderstanding and unappropriate criticism which have been raised against these two approaches and we take this opportunity to stress the unsatisfactory status of most of the recent debate on foundational issues.
Abstract: Often, the most revealing testing ground for a theory is one that pushes the theory to the limits of its applicability. For quantum mechanics and general relativity, it has long been recognized that spacetime singularities provide such an arena. It is thus of great interest to investigate how string theory, an approach that is meant to go beyond general relativity and quantum mechanics, addresses spacetime singularities. In this talk, I'll describe a variety of mathematical singularities and explain the physical resolutions emerging from string theory. I will also emphasize those singularities whose resolution still remains beyond reach.
Abstract: A well known result of Carter-Robinson and Hawking provides a proof of uniqueness of Kerr in the class of real analytic, stationary, solutions of the Einstein vacuum equations. The proof of the result hinges heavily on analyticity, an assumption which is not all justifiable. I will present a completely different attempt to prove the result which does not require analyticity. The program, developed in collaboration with A. Ionescu, depends on a geometric version of Carleman estimates for nonlinear wave equations.
Abstract: I compare the typicality account of probability in Goldstein-Dürr-Zanghì with an account based on David Lewis' Humean account of chance.
Abstract: We present a thermodynamic interpretation of large deviation rate functions for the dynamical fluctuations of densities and currents in nonequilibrium systems. Results include a fluctuation-based understanding of the (non)validity of minimum and maximum entropy production principles and the identification of a canonical structure in the joint density-current fluctuations that couples the time-symmetric and the time-antisymmetric sector when beyond the close-to-equilibrium regime. (Joint work with Karel Netocny.)
Abstract: At the beginning of the 20th century, it was sometimes said that physics must abandon the requirement that the microscopic world be anschaulich, i.e. visualizable. Even if we accept this advice, we would still like for the physical account of the world to be comprehensible. The notion of comprehensibility is best grasped through examples. It seems to have two distinct aspects: First, the relation between at least some part of the mathematical representation used in the physics and the physical state it represents ought to be straightforward, in the way that using R3 as a representation of three-dimensional Euclidean space is straightforward. Second, the relation between at least some part of the physical ontology and our common-sense picture of the world ought to be reasonably transparent. I will discuss how Bohmian mechanics satisfies both of these desiderata, and how several other approaches fail in at least one.
Abstract: The fundamental metaphysical issue of realism vs idealism played an important role in the creation of the Copenhagen approach to quantum theory. In particular, the founding fathers seem to have conceived of experimental measurements on the model of an idealist analysis of conscious awareness. We discuss the connection between metaphysics and the measurement problem, focusing in particular on what a (non-naive) realist metaphysics has to say about the nature and solution of the problem.
Abstract: One of the most clear-cut reasons for believing that quantum mechanics, in the context of general relativity, must be subject to fundamental change comes from considerations of black holes and cosmology. Some new insights into this issue, relating the so-called "black-hole information paradox" to the second law of thermodynamics will be presented in this talk.
Abstract: There are problems in ergodic theory which require the behavior of ergodic sums for non-integrable functions. I shall discuss the cases when the ergodic sums do not converge to a limit but have a limiting distribution. (Joint results with C. Ulchigrai)
Abstract: I report on joint work with Jani Lukkarinen. We consider the weakly nonlinear Schrödinger equation on the lattice Z3 starting in thermal equilibrium. We prove that in the kinetic limit the psi-psi correlation has a specific decay related to the linearized Boltzmann equation. (So far) the result holds for short kinetic times.
Abstract: I will present an overview of some recent work on the extension of the de Broglie-Bohm pilot-wave theory (Bohmian mechanics) to quantum field theory. In the de Broglie-Bohm theory quantum systems are not only described by their wavefunction (or quantum state), as in standard quantum theory, but also by some additional variables, called "hidden variables" or "beables". Within the context of non-relativistic quantum mechanics it is very natural to introduce particle positions as beables. Within the context of quantum field theory, a number of approaches seem possible. I will discuss an approach with particle positions as beables and an approach with fields as beables. In addition I will present a surprisingly minimalist approach, which amounts to introducing beables only for the electromagnetic field degrees of freedom.
Abstract: We consider the Schrödinger equation on a Riemannian manifold with the assumption that the potential localizes finite-energy states close to a certain submanifold. This situation typically occurs for the motion of nuclei in electronic-potential surfaces and for quantum wave guides. Mathematically the limit of strong localization is modeled by scaling the potential like epsilon-1 in the direction normal to the submanifold for epsilon << 1. States with bounded energy are effectively confined to an epsilon-tube around the submanifold by such a potential. We show that the dynamics of such states can be described by an effective Schroedinger equation on the submanifold and derive an asymptotic expansion of the corresponding effective Hamiltonian. This is joint work with Jakob Wachsmuth.
Abstract: I partly review old results due to Goldstein et al. and Ghirardi et al., and partly report recent results due to Ghirardi et al. and myself together with Goldstein, Zanghì, and Allori. The question I'm addressing is simple: Given a theory like Bohmian mechanics or GRW, what do you have to do to derive the prediction for the outcome of an experiment? It is easy to make mistakes about this, mainly because it is hard to avoid quantum ways of thinking. But those quantum ways are out of place here: after all, these theories are not ordinary quantum mechanics. The main new result is a GRW formalism analogous to the quantum formalism, summarizing the predictions of the GRW theory including deviations from quantum mechanics.
Abstract: The Schrödinger equation may be solved by propagating ensembles of quantum trajectories. The development of this approach will be reviewed, equations of motion for the quantum trajectories will be described, and alternative moving grids will be introduced. In addition to this ensemble approach, individual approximate quantum trajectories may be propagated using the derivative propagation method. In either approach, various "moving frames" defined by the instantaneous trajectory locations may be defined. Bohmian motions define a Lagrangian grid, with grid point velocity the same as the local velocity of the probability fluid. However, it is advantageous to employ more general moving grids with "post-Bohmian" trajectories moving at arbitrary velocities along constrained paths, which can enhance the trajectory stability. An alternative to "real space" trajectory dynamics is based upon solving the complex-valued quantum Hamilton-Jacobi equation on complex configuration space, yielding "un-real" trajectories useful for describing barrier tunneling, including deep tunneling, and reactive scattering. Animations will be used to illustrate interesting dynamical features of the trajectory flows.