1,987 research outputs found
A proof of Jarzynski's non-equilibrium work theorem for dynamical systems that conserve the canonical distribution
We present a derivation of the Jarzynski identity and the Crooks fluctuation
theorem for systems governed by deterministic dynamics that conserves the
canonical distribution such as Hamiltonian dynamics, Nose-Hoover dynamics,
Nose-Hoover chains and Gaussian isokinetic dynamics. The proof is based on a
relation between the heat absorbed by the system during the non-equilibrium
process and the Jacobian of the phase flow generated by the dynamics.Comment: 12 page
Photon-Photon Interaction in a Photon Gas
Using the effective Lagrangian for the low energy photon-photon interaction
the lowest order photon self energy at finite temperature and in
non-equilibrium is calculated within the real time formalism. The Debye mass,
the dispersion relation, the dielectric tensor, and the velocity of light
following from the photon self energy are discussed. As an application we
consider the interaction of photons with the cosmic microwave background
radiation.Comment: REVTEX, 7 pages, 1 PostSrcipt figur
Piezoelectric-based apparatus for strain tuning
We report the design and construction of piezoelectric-based apparatus for
applying continuously tuneable compressive and tensile strains to test samples.
It can be used across a wide temperature range, including cryogenic
temperatures. The achievable strain is large, so far up to 0.23% at cryogenic
temperatures. The apparatus is compact and compatible with a wide variety of
experimental probes. In addition, we present a method for mounting
high-aspect-ratio samples in order to achieve high strain homogeneity.Comment: 8 pages, 8 figure
Viking navigation
A comprehensive description of the navigation of the Viking spacecraft throughout their flight from Earth launch to Mars landing is given. The flight path design, actual inflight control, and postflight reconstruction are discussed in detail. The preflight analyses upon which the operational strategies and performance predictions were based are discussed. The inflight results are then discussed and compared with the preflight predictions and, finally, the results of any postflight analyses are presented
Supergoop Dynamics
We initiate a systematic study of the dynamics of multi-particle systems with
supersymmetric Van der Waals and electron-monopole type interactions. The
static interaction allows a complex continuum of ground state configurations,
while the Lorentz interaction tends to counteract this configurational fluidity
by magnetic trapping, thus producing an exotic low temperature phase of matter
aptly named supergoop. Such systems arise naturally in gauge
theories as monopole-dyon mixtures, and in string theory as collections of
particles or black holes obtained by wrapping D-branes on internal space
cycles. After discussing the general system and its relation to quiver quantum
mechanics, we focus on the case of three particles. We give an exhaustive
enumeration of the classical and quantum ground states of a probe in an
arbitrary background with two fixed centers. We uncover a hidden conserved
charge and show that the dynamics of the probe is classically integrable. In
contrast, the dynamics of one heavy and two light particles moving on a line
shows a nontrivial transition to chaos, which we exhibit by studying the
Poincar\'e sections. Finally we explore the complex dynamics of a probe
particle in a background with a large number of centers, observing hints of
ergodicity breaking. We conclude by discussing possible implications in a
holographic context.Comment: 35 pages,11 figures. v2: updated references to include a previous
proof of classical integrability, exchanged a figure for a prettier versio
Renormalization of Multiple -Zeta Values
In this paper we shall define the renormalization of the multiple -zeta
values (MZV) which are special values of multiple -zeta functions
when the arguments are all positive integers or all
non-positive integers. This generalizes the work of Guo and Zhang
(math.NT/0606076v3) on the renormalization of Euler-Zagier multiple zeta
values. We show that our renormalization process produces the same values if
the MZVs are well-defined originally and that these renormalizations of
MZV satisfy the -stuffle relations if we use shifted-renormalizations for
all divergent (i.e., ). Moreover, when \qup
our renormalizations agree with those of Guo and Zhang.Comment: 22 pages. This is a substantial revision of the first version. I
provide a new and complete proof of the fact that our renormalizations
satisfy the q-stuffle relations using the shifting principle of MqZV
Energy-momentum tensor in thermal strong-field QED with unstable vacuum
The mean value of the one-loop energy-momentum tensor in thermal QED with
electric-like background that creates particles from vacuum is calculated. The
problem differes essentially from calculations of effective actions (similar to
that of Heisenberg--Euler) in backgrounds that do not violate the stability of
vacuum. The role of a constant electric background in the violation of both the
stability of vacuum and the thermal character of particle distribution is
investigated. Restrictions on the electric field and its duration under which
one can neglect the back-reaction of created particles are established.Comment: 7 pages, Talk presented at Workshop "Quantum Field Theory under the
Influence of External Conditions", Leipzig, September 17-21, 2007;
introduction extended, version accepted for publication in J.Phys.
Thirty-two Goldbach Variations
We give thirty-two diverse proofs of a small mathematical gem--the
fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also
discuss various generalizations for multiple harmonic (Euler) sums and some of
their many connections, thereby illustrating both the wide variety of
techniques fruitfully used to study such sums and the attraction of their
study.Comment: v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory
material added and material on inequalities, Hilbert matrix and Witten zeta
functions. Errors in the second section on Complex Line Integrals are
corrected. To appear in International Journal of Number Theory. Title change
Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque
New exact analytic solutions are introduced for the rotational motion of a
rigid body having two equal principal moments of inertia and subjected to an
external torque which is constant in magnitude. In particular, the solutions
are obtained for the following cases: (1) Torque parallel to the symmetry axis
and arbitrary initial angular velocity; (2) Torque perpendicular to the
symmetry axis and such that the torque is rotating at a constant rate about the
symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial
angular velocity perpendicular to the symmetry axis, with the torque being
fixed with the body. In addition to the solutions for these three forced cases,
an original solution is introduced for the case of torque-free motion, which is
simpler than the classical solution as regards its derivation and uses the
rotation matrix in order to describe the body orientation. This paper builds
upon the recently discovered exact solution for the motion of a rigid body with
a spherical ellipsoid of inertia. In particular, by following Hestenes' theory,
the rotational motion of an axially symmetric rigid body is seen at any instant
in time as the combination of the motion of a "virtual" spherical body with
respect to the inertial frame and the motion of the axially symmetric body with
respect to this "virtual" body. The kinematic solutions are presented in terms
of the rotation matrix. The newly found exact analytic solutions are valid for
any motion time length and rotation amplitude. The present paper adds further
elements to the small set of special cases for which an exact solution of the
rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The
following typos present in the Journal version are HERE corrected: 1)
Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3)
Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6
Radiative Corrections to the Casimir Energy
The lowest radiative correction to the Casimir energy density between two
parallel plates is calculated using effective field theory. Since the
correlators of the electromagnetic field diverge near the plates, the
regularized energy density is also divergent. However, the regularized integral
of the energy density is finite and varies with the plate separation L as
1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but
more transparent theory of a massless scalar field in 1+1 dimensions confined
to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late
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