413,422 research outputs found

    QCD at a Finite Density of Static Quarks

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    Recently, cluster methods have been used to solve a variety of sign problems including those that arise in the presence of fermions. In all cases an analytic partial re-summation over a class of configurations in the path integral was necessary. Here the new ideas are illustrated using the example of QCD at a finite density of static quarks. In this limit the sign problem simplifies since the fermionic part decouples. Furthermore, the problem can be solved completely when the gauge dynamics is replaced by a Potts model. On the other hand in QCD with light quarks the solution will require a partial re-summation over both fermionic and gauge degrees of freedom. The new approach points to unexplored directions in the search for a solution to this more challenging sign problem.Comment: Lattice 2000 (Plenary

    A fast, high-order numerical method for the simulation of single-excitation states in quantum optics

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    We consider the numerical solution of a nonlocal partial differential equation which models the process of collective spontaneous emission in a two-level atomic system containing a single photon. We reformulate the problem as an integro-differential equation for the atomic degrees of freedom, and describe an efficient solver for the case of a Gaussian atomic density. The problem of history dependence arising from the integral formulation is addressed using sum-of-exponentials history compression. We demonstrate the solver on two systems of physical interest: in the first, an initially-excited atom decays into a photon by spontaneous emission, and in the second, a photon pulse is used to an excite an atom, which then decays

    Unconstrained Hamiltonian formulation of General Relativity with thermo-elastic sources

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    A new formulation of the Hamiltonian dynamics of the gravitational field interacting with(non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the ``gravity + matter''-system (two gravitational and four thermo-mechanical ones), together with their conjugate momenta, in the Riemannian metric q_{ij} and its conjugate ADM momentum P^{ij}. These variables are not subject to constraints. We prove that the Hamiltonian of this system is equal to the total matter entropy. It generates uniquely the dynamics once expressed as a function of the canonical variables. Any function U obtained in this way must fulfil a system of three, first order, partial differential equations of the Hamilton-Jacobi type in the variables (q_{ij},P^{ij}). These equations are universal and do not depend upon the properties of the material: its equation of state enters only as a boundary condition. The well posedness of this problem is proved. Finally, we prove that for vanishing matter density, the value of U goes to infinity almost everywhere and remains bounded only on the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on constraints and infinity elsewhere) can be obtained as the limit of a ``deep potential well'' corresponding to non-vanishing matter. This unconstrained description of Hamiltonian General Relativity can be useful in numerical calculations as well as in the canonical approach to Quantum Gravity.Comment: 29 pages, TeX forma

    -Generic Computability, Turing Reducibility and Asymptotic Density

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    Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has density 1 and which agrees with the characteristic function of A on its domain. A set A is coarsely computable if there is a computable set C such that the symmetric difference of A and C has density 0. We prove that there is a c.e. set which is generically computable but not coarsely computable and vice versa. We show that every nonzero Turing degree contains a set which is not coarsely computable. We prove that there is a c.e. set of density 1 which has no computable subset of density 1. As a corollary, there is a generically computable set A such that no generic algorithm for A has computable domain. We define a general notion of generic reducibility in the spirt of Turing reducibility and show that there is a natural order-preserving embedding of the Turing degrees into the generic degrees which is not surjective

    Partial traces in decoherence and in interpretation: What do reduced states refer to?

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    The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearly stating the problem, our argument is developed in three stages. First, we consider the phenomenon of environment-induced decoherence as an example of the case in which the subsystems interact with each other; we show that decoherence does not solve the measurement problem precisely because the reduced state of the measuring apparatus is not its quantum state. Second, the non-interacting case is illustrated in the context of no-collapse interpretations, in which we show that certain well-known experimental results cannot be accounted for due to the fact that the reduced states of the measured system and the measuring apparatus are conceived as their quantum states. Finally, we prove that reduced states are a kind of coarse-grained states, and for this reason they cancel the correlations of the subsystem with other subsystems with which it interacts or is entangled.Comment: 26 page
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