Deformed Jarzynski Equality

The well-known Jarzynski equality, often written in the form $e^{-\beta\Delta F}=\langle e^{-\beta W}\rangle$, provides a non-equilibrium means to measure the free energy difference $\Delta F$ of a system at the same inverse temperature $\beta$ based on an ensemble average of non-equilibrium work $W$. The accuracy of Jarzynski's measurement scheme was known to be determined by the variance of exponential work, denoted as ${\rm var}\left(e^{-\beta W}\right)$. However, it was recently found that ${\rm var}\left(e^{-\beta W}\right)$ can systematically diverge in both classical and quantum cases. Such divergence will necessarily pose a challenge in the applications of Jarzynski equality because it may dramatically reduce the efficiency in determining $\Delta F$. In this work, we present a deformed Jarzynski equality for both classical and quantum non-equilibrium statistics, in efforts to reuse experimental data that already suffers from a diverging ${\rm var}\left(e^{-\beta W}\right)$. The main feature of our deformed Jarzynski equality is that it connects free energies at different temperatures and it may still work efficiently subject to a diverging ${\rm var}\left(e^{-\beta W}\right)$. The conditions for applying our deformed Jarzynski equality may be met in experimental and computational situations. If so, then there is no need to redesign experimental or simulation methods. Furthermore, using the deformed Jarzynski equality, we exemplify the distinct behaviors of classical and quantum work fluctuations for the case of a time-dependent driven harmonic oscillator dynamics and provide insights into the essential performance differences between classical and quantum Jarzynski equalities.Comment: 24 pages, 1 figure, accepted version to appear in Entropy (Special Issue on "Quantum Thermodynamics"

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one dimensional diffusion. The validity of this approximation, being based on the assumption of an instantaneous equilibration of the particle distribution in the cross-section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.Comment: 20 pages, 7 figure

Comment on "Coherent Ratchets in Driven Bose-Einstein Condensates"

C. E. Creffield and F. Sols (Phys. Rev. Lett. 103, 200601 (2009)) recently reported finite, directed time-averaged ratchet current, for a noninteracting quantum particle in a periodic potential even when time-reversal symmetry holds. As we explain in this Comment, this result is incorrect, that is, time-reversal symmetry implies a vanishing current.Comment: revised versio

Clinical prediction models

Objective!#!The aim of this study was to evaluate the validity of a semiautomated volumetric approach (5DCNS+) for the detailed assessment of the fetal brain in a clinical setting.!##!Methods!#!Stored 3D volumes of > 1100 consecutive 2nd and 3rd trimester pregnancies (range 15-36 gestational weeks) were analyzed using a workflow-based volumetric approach 5DCNS+, enabling semiautomated reconstruction of diagnostic planes of the fetal central nervous system (CNS). All 3D data sets were examined for plane accuracy, the need for manual adjustment, and fetal-maternal characteristics affecting successful plane reconstruction. We also examined the potential of these standardized views to give additional information on proper gyration and sulci formation with advancing gestation.!##!Results!#!Based on our data, we were able to show that gestational age with an OR of 1.085 (95% CI 1.041-1.132) and maternal BMI with an OR of 1.022 (95% CI 1.041-1.054) only had a slight impact on the number of manual adjustments needed to reconstruct the complete volume, while maternal age and fetal position during acquisition (p = 0.260) did not have a significant effect. For the vast majority (958/1019; 94%) of volumes, using 5DCNS+ resulted in proper reconstruction of all nine diagnostic planes. In less than 1% (89/9171 planes) of volumes, the program failed to give sufficient information. 5DCNS+ was able to show the onset and changing appearance of CNS folding in a detailed and timely manner (lateral/parietooccipital sulcus formation seen in < 65% at 16-17 gestational weeks vs. 94.6% at 19 weeks).!##!Conclusions!#!The 5DCNS+ method provides a reliable algorithm to produce detailed, 3D volume-based assessments of fetal CNS integrity through a standardized reconstruction of the orthogonal diagnostic planes. The method further gives valid and reproducible information regarding ongoing cortical development retrieved from these volume sets that might aid in earlier in utero recognition of subtle structural CNS anomalies

Dynamics of magnetization coupled to a thermal bath of elastic modes

We study the dynamics of magnetization coupled to a thermal bath of elastic modes using a system plus reservoir approach with realistic magnetoelastic coupling. After integrating out the elastic modes we obtain a self-contained equation for the dynamics of the magnetization. We find explicit expressions for the memory friction kernel and hence, {\em via} the Fluctuation-Dissipation Theorem, for the spectral density of the magnetization thermal fluctuations. For magnetic samples in which the single domain approximation is valid, we derive an equation for the dynamics of the uniform mode. Finally we apply this equation to study the dynamics of the uniform magnetization mode in insulating ferromagnetic thin films. As experimental consequences we find that the fluctuation correlation time is of the order of the ratio between the film thickness, $h$, and the speed of sound in the magnet and that the line-width of the ferromagnetic resonance peak should scale as $B_1^2h$ where $B_1$ is the magnetoelastic coupling constant.Comment: Revised version as appeared in print. 12 pages 9 figure

Viscosity Dependence of the Folding Rates of Proteins

The viscosity dependence of the folding rates for four sequences (the native state of three sequences is a beta-sheet, while the fourth forms an alpha-helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation we show that the folding rates increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and have a maximum at intermediate values. The Kramers theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn \alpha-helix topology is about 500 nanoseconds, whereas the time scale for forming a beta-sheet topology is about 10 microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical Review Letter

Star clusters dynamics in a laboratory: electrons in an ultracold plasma

Electrons in a spherical ultracold quasineutral plasma at temperature in the Kelvin range can be created by laser excitation of an ultra-cold laser cooled atomic cloud. The dynamical behavior of the electrons is similar to the one described by conventional models of stars clusters dynamics. The single mass component, the spherical symmetry and no stars evolution are here accurate assumptions. The analog of binary stars formations in the cluster case is three-body recombination in Rydberg atoms in the plasma case with the same Heggie's law: soft binaries get softer and hard binaries get harder. We demonstrate that the evolution of such an ultracold plasma is dominated by Fokker-Planck kinetics equations formally identical to the ones controlling the evolution of a stars cluster. The Virial theorem leads to a link between the plasma temperature and the ions and electrons numbers. The Fokker-Planck equation is approximate using gaseous and fluid models. We found that the electrons are in a Kramers-Michie-King's type quasi-equilibrium distribution as stars in clusters. Knowing the electron distribution and using forced fast electron extraction we are able to determine the plasma temperature knowing the trapping potential depth.Comment: Submitted to MNRA

Exciton- and Light-induced Current in Molecular Nanojunctions

We consider exciton- and light-induced current in molecular nanojunctions. Using a model comprising a two two-level sites bridge connecting free electron reservoirs we show that the exciton coupling between the sites of the molecular bridge can markedly effect the source-drain current through a molecular junction. In some cases when excited and unexcited states of the sites are coupled differently to the leads, the contribution from electron-hole excitations can exceed the Landauer elastic current and dominate the observed conduction. We have proposed an optical control method using chirped pulses for enhancing charge transfer in unbiased junctions where the bridging molecule is characterized by a strong charge-transfer transition.Comment: 8 pages, 2 figures,submitted to the Canadian J. Phy

Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivation

We derive the thermal conductivities of one-dimensional harmonic and anharmonic lattices with self-consistent heat baths (BRV lattice) from the Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we obtain the same result as previous works. However, our approach is heuristic and reveals phonon picture explicitly within the heat transport process. The results for harmonic and anharmonic lattices are compared with numerical calculations from Green-Kubo formula. The consistency between derivation and simulation strongly supports that effective (renormalized) phonons are energy carriers in anharmonic lattices although there exist some other excitations such as solitons and breathers.Comment: 4 pages, 3 figures. accepted for publication in JPS