Demonstration of Jarzynski's Equality in Open Quantum Systems Using a Step-Wise Pulling Protocol

We present a generalization of Jarzynski's Equality, applicable to quantum systems, relating discretized mechanical work and free-energy changes. The theory is based on a step-wise pulling protocol. We find that work distribution functions can be constructed from fluctuations of a reaction coordinate along a reaction pathway in the step-wise pulling protocol. We also propose two sets of equations to determine the two possible optimal pathways that provide the most significant contributions to free-energy changes. We find that the transitions along these most optimal pathways, satisfying both sets of equations, follow the principle of detailed balance. We then test the theory by explicitly computing the free-energy changes for a one-dimensional quantum harmonic oscillator. This approach suggests a feasible way of measuring the fluctuations to experimentally test Jarzynski's Equality in many-body systems, such as Bose-Einstein condensates.Comment: 9 pages, 5 figure

Analytically solvable model of an electronic Mach-Zehnder interferometer

We consider a class of models of non-equilibrium electronic Mach-Zehnder interferometers built on integer quantum Hall edges states. The models are characterized by the electron-electron interaction being restricted to the inner part of the interferometer and transmission coefficients of the quantum quantum point contacts, defining the interferometer, which may take arbitrary values from zero to one. We establish an exact solution of these models in terms of single-particle quantities --- determinants and resolvents of Fredholm integral operators. In the general situation, the results can be obtained numerically. In the case of strong charging interaction, the operators acquire the block Toeplitz form. Analyzing the corresponding Riemann-Hilbert problem, we reduce the result to certain singular single-channel determinants (which are a generalization of Toeplitz determinants with Fisher-Hartwig singularities), and obtain an analytic result for the interference current (and, in particular, for the visibility of Aharonov-Bohm oscillations). Our results, which are in good agreement with experimental observations, show an intimate connection between the observed "lobe" structure in the visibility of Aharonov-Bohm oscillations and multiple branches in the asymptotics of singular integral determinants.Comment: 29 pages, 10 figure

Interaction Quench in Nonequilibrium Luttinger Liquids

We study the relaxation dynamics of a nonequilibrium Luttinger liquid after a sudden interaction switch-on ("quench"), focussing on a double-step initial momentum distribution function. In the framework of the non-equilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasi-particle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.Comment: 11 pages, 5 figure

Influence of Coulomb interaction on the Aharonov-Bohm effect in an electronic Fabry-Perot interferometer

We study the role of Coulomb interaction in an electronic Fabry-Perot interferometer (FPI) realized with chiral edge states in the integer quantum Hall regime in the limit of weak backscattering. Assuming that a compressible Coulomb island in a bulk region of the FPI is formed, we develop a capacitance model which explains the plethora of experimental data on the flux and gate periodicity of conductance oscillations. It is also shown that a suppression of finite-bias visibility stems from a combination of weak Coulomb blockade and a nonequilibrium dephasing by the quantum shot noise

Noncanonical Amino Acids in the Interrogation of Cellular Protein Synthesis

Proteins in living cells can be made receptive to bioorthogonal chemistries through metabolic labeling with appropriately designed noncanonical amino acids (ncAAs). In the simplest approach to metabolic labeling, an amino acid analog replaces one of the natural amino acids specified by the protein’s gene (or genes) of interest. Through manipulation of experimental conditions, the extent of the replacement can be adjusted. This approach, often termed residue-specific incorporation, allows the ncAA to be incorporated in controlled proportions into positions normally occupied by the natural amino acid residue. For a protein to be labeled in this way with an ncAA, it must fulfill just two requirements: (i) the corresponding natural amino acid must be encoded within the sequence of the protein at the genetic level, and (ii) the protein must be expressed while the ncAA is in the cell. Because this approach permits labeling of proteins throughout the cell, it has enabled us to develop strategies to track cellular protein synthesis by tagging proteins with reactive ncAAs. In procedures similar to isotopic labeling, translationally active ncAAs are incorporated into proteins during a “pulse” in which newly synthesized proteins are tagged. The set of tagged proteins can be distinguished from those made before the pulse by bioorthogonally ligating the ncAA side chain to probes that permit detection, isolation, and visualization of the labeled proteins. Noncanonical amino acids with side chains containing azide, alkyne, or alkene groups have been especially useful in experiments of this kind. They have been incorporated into proteins in the form of methionine analogs that are substrates for the natural translational machinery. The selectivity of the method can be enhanced through the use of mutant aminoacyl tRNA synthetases (aaRSs) that permit incorporation of ncAAs not used by the endogenous biomachinery. Through expression of mutant aaRSs, proteins can be tagged with other useful ncAAs, including analogs that contain ketones or aryl halides. High-throughput screening strategies can identify aaRS variants that activate a wide range of ncAAs. Controlled expression of mutant synthetases has been combined with ncAA tagging to permit cell-selective metabolic labeling of proteins. Expression of a mutant synthetase in a portion of cells within a complex cellular mixture restricts labeling to that subset of cells. Proteins synthesized in cells not expressing the synthetase are neither labeled nor detected. In multicellular environments, this approach permits the identification of the cellular origins of labeled proteins. In this Account, we summarize the tools and strategies that have been developed for interrogating cellular protein synthesis through residue-specific tagging with ncAAs. We describe the chemical and genetic components of ncAA-tagging strategies and discuss how these methods are being used in chemical biology

Joint Resource Optimization for Multicell Networks with Wireless Energy Harvesting Relays

This paper first considers a multicell network deployment where the base station (BS) of each cell communicates with its cell-edge user with the assistance of an amplify-and-forward (AF) relay node. Equipped with a power splitter and a wireless energy harvester, the self-sustaining relay scavenges radio frequency (RF) energy from the received signals to process and forward the information. Our aim is to develop a resource allocation scheme that jointly optimizes (i) BS transmit powers, (ii) received power splitting factors for energy harvesting and information processing at the relays, and (iii) relay transmit powers. In the face of strong intercell interference and limited radio resources, we formulate three highly-nonconvex problems with the objectives of sum-rate maximization, max-min throughput fairness and sum-power minimization. To solve such challenging problems, we propose to apply the successive convex approximation (SCA) approach and devise iterative algorithms based on geometric programming and difference-of-convex-functions programming. The proposed algorithms transform the nonconvex problems into a sequence of convex problems, each of which is solved very efficiently by the interior-point method. We prove that our algorithms converge to the locally optimal solutions that satisfy the Karush-Kuhn-Tucker conditions of the original nonconvex problems. We then extend our results to the case of decode-and-forward (DF) relaying with variable timeslot durations. We show that our resource allocation solutions in this case offer better throughput than that of the AF counterpart with equal timeslot durations, albeit at a higher computational complexity. Numerical results confirm that the proposed joint optimization solutions substantially improve the network performance, compared with cases where the radio resource parameters are individually optimized

Fabrication and characterization of large arrays of mesoscopic gold rings on large-aspect-ratio cantilevers

We have fabricated large arrays of mesoscopic metal rings on ultrasensitive cantilevers. The arrays are defined by electron beam lithography and contain up to $10^5$ rings. The rings have a circumference of 1 $\mu$m, and are made of ultrapure (6N) Au that is deposited onto a silicon-on-insulator wafer without an adhesion layer. Subsequent processing of the SOI wafer results in each array being supported at the end of a free-standing cantilever. To accommodate the large arrays while maintaining a low spring constant, the cantilevers are nearly 1 mm in both lateral dimensions and 100 nm thick. The extreme aspect ratio of the cantilevers, the large array size, and the absence of a sticking layer are intended to enable measurements of the rings' average persistent current $\langle I \rangle$ in the presence of relatively small magnetic fields. We describe the motivation for these measurements, the fabrication of the devices, and the characterization of the cantilevers' mechanical properties. We also discuss the devices' expected performance in measurements of $\langle I \rangle$.Comment: 5 pages, 5 figure

Off-fault tensile cracks: A link between geological fault observations, lab experiments, and dynamic rupture models

We examine the local nature of the dynamic stress field in the vicinity of the tip of a semi-infinite sub-Rayleigh (slower than the Rayleigh wave speed, c_R) mode II crack with a velocity-weakening cohesive zone. We constrain the model using results from dynamic photoelastic experiments, in which shear ruptures were nucleated spontaneously in Homalite-100 plates along a bonded, precut, and inclined interface subject to a far-field uniaxial prestress. During the experiments, tensile cracks grew periodically along one side of the shear rupture interface at a roughly constant angle relative to the shear rupture interface. The occurrence and inclination of the tensile cracks are explained by our analytical model. With slight modifications, the model can be scaled to natural faults, providing diagnostic criteria for interpreting velocity, directivity, and static prestress state associated with past earthquakes on exhumed faults. Indirectly, this method also allows one to constrain the velocity-weakening nature of natural ruptures, providing an important link between field geology, laboratory experiments, and seismology