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 $\mathfrak{o}(K)$ of real $K$ - skew - symmetric matrices, where $K$ is an arbitrary $3\times 3$ 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