2,815 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
The free rigid body dynamics: generalized versus classic
In this paper we analyze the normal forms of a general quadratic Hamiltonian
system defined on the dual of the Lie algebra of real -
skew - symmetric matrices, where is an arbitrary real symmetric
matrix. A consequence of the main results is that any first-order autonomous
three-dimensional differential equation possessing two independent quadratic
constants of motion which admits a positive/negative definite linear
combination, is affinely equivalent to the classical "relaxed" free rigid body
dynamics with linear controls.Comment: 12 page
Euler buckling instability and enhanced current blockade in suspended single-electron transistors
Single-electron transistors embedded in a suspended nanobeam or carbon
nanotube may exhibit effects originating from the coupling of the electronic
degrees of freedom to the mechanical oscillations of the suspended structure.
Here, we investigate theoretically the consequences of a capacitive
electromechanical interaction when the supporting beam is brought close to the
Euler buckling instability by a lateral compressive strain. Our central result
is that the low-bias current blockade, originating from the electromechanical
coupling for the classical resonator, is strongly enhanced near the Euler
instability. We predict that the bias voltage below which transport is blocked
increases by orders of magnitude for typical parameters. This mechanism may
make the otherwise elusive classical current blockade experimentally
observable.Comment: 15 pages, 10 figures, 1 table; published versio
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
A constrained random-force model for weakly bending semiflexible polymers
The random-force (Larkin) model of a directed elastic string subject to
quenched random forces in the transverse directions has been a paradigm in the
statistical physics of disordered systems. In this brief note, we investigate a
modified version of the above model where the total transverse force along the
polymer contour and the related total torque, in each realization of disorder,
vanish. We discuss the merits of adding these constraints and show that they
leave the qualitative behavior in the strong stretching regime unchanged, but
they reduce the effects of the random force by significant numerical
prefactors. We also show that a transverse random force effectively makes the
filament softer to compression by inducing undulations. We calculate the
related linear compression coefficient in both the usual and the constrained
random force model.Comment: 4 pages, 1 figure, accepted for publication in PR
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
Reconstructing Generalized Exponential Laws by Self-Similar Exponential Approximants
We apply the technique of self-similar exponential approximants based on
successive truncations of continued exponentials to reconstruct functional laws
of the quasi-exponential class from the knowledge of only a few terms of their
power series. Comparison with the standard Pad\'e approximants shows that, in
general, the self-similar exponential approximants provide significantly better
reconstructions.Comment: Revtex file, 21 pages, 21 figure
Discontinuous Euler instability in nanoelectromechanical systems
We investigate nanoelectromechanical systems near mechanical instabilities.
We show that quite generally, the interaction between the electronic and the
vibronic degrees of freedom can be accounted for essentially exactly when the
instability is continuous. We apply our general framework to the Euler buckling
instability and find that the interaction between electronic and vibronic
degrees of freedom qualitatively affects the mechanical instability, turning it
into a discontinuous one in close analogy with tricritical points in the Landau
theory of phase transitions.Comment: 4+ pages, 3 figures, published versio
On the completability of incomplete orthogonal Latin rectangles
We address the problem of completability for 2-row orthogonal Latin rectangles (OLR2). Our approach is to identify all pairs of incomplete 2-row Latin rectangles that are not com- pletable to an OLR2 and are minimal with respect to this property; i.e., we characterize all circuits of the independence system associated with OLR2. Since there can be no poly- time algorithm generating the clutter of circuits of an arbitrary independence system, our work adds to the few independence systems for which that clutter is fully described. The result has a direct polyhedral implication; it gives rise to inequalities that are valid for the polytope associated with orthogonal Latin squares and thus planar multi-dimensional assign- ment. A complexity result is also at hand: completing a set of (n - 1) incomplete MOLR2 is NP-complete
Heavy-quark contribution to the proton's magnetic moment
We study the contribution to the proton's magnetic moment from a heavy quark
sea in quantum chromodynamics. The heavy quark is integrated out perturbatively
to obtain an effective dimension-6 magnetic moment operator composed of three
gluon fields. The leading contribution to the matrix element in the proton
comes from a quadratically divergent term associated with a light-quark tensor
operator. With an approximate knowledge of the proton's tensor charge, we
conclude that a heavy sea-quark contribution to the proton's magnetic moment is
positive in the asymptotic limit. We comment on the implication of this result
for the physical strange quark.Comment: 4 pages, 2 figure
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