413,422 research outputs found
QCD at a Finite Density of Static Quarks
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
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
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
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?
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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