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Quantum Phases and Phase Transitions in Disordered Low-Dimensional Systems: Thin Film Superconductors, Bilayer Two-Dimensional Electron Systems, and One-Dimensional Optical Lattices
Get PDFThe study of various quantum phases and the phase transitions between them in low-dimensional disordered systems has been a central theme of recent developments of condensed matter physics. Examples include disordered thin film superconductors, whose critical temperature and density of states can be affected by a normal metallic layer deposited on top of them; amorphous thin films exhibiting superconductor-insulator transitions (SIT) tuned by disorder or magnetic field; and bilayer two-dimensional electron systems at total filling factor ν=1, which exhibit interlayer coherent quantum Hall state at small layer separation and have a phase transition tuned by layer separation, parallel magnetic field, density imbalance, or temperature. Although a lot of theoretical and experimental investigations have been done, many properties of these phases and natures of the phase transitions in these systems are still being debated. Here in this thesis, we report our progress towards a better understanding of these systems. For disordered thin film superconductors, we first propose that the experimentally observed lower-than-theory gap-Tc ratio in bilayer superconducting-normal-metal films is due to inhomogeneous couplings. Next, for films demonstrating superconductor-insulator transitions, we propose a new type of experiment, namely the drag resistance measurement, as a method capable of pointing to the correct theory among major candidates such as the quantum vortex picture and the percolation picture. For bilayer two-dimensional electron systems, we propose that a first-order phase transition scenario and the resulting Clausius-Clapeyron equations can describe various transitions observed in experiments quite well. Finally, in one-dimensional optical lattices, we show that one can engineer the long-sought-after random hopping model with only off-diagonal disorder by fast-modulating an Anderson insulator
Pulselike Ruptures on Strong Velocity-Weakening Frictional Interfaces: Dynamics and Implications
Get PDFSeismic inversion and computational models have shown that earthquake ruptures may propagate in one of two basic modes; the cracklike mode and the slip pulse mode. In this work we use analytical and numerical techniques to study the dynamics and implications of pulselike ruptures propagating on strong velocity-weakening frictional interfaces using both discrete and continuum models of fracture.
Results of the study of the discrete spring block slider model suggest that strong velocity-weakening friction might yield to the propagation of unsteady slip pulses and chaotic dynamics. The prestress in most of these systems evolves into very heterogeneous spatial distributions characterized, in general, by non-Gaussian statistics and power-law spectral properties. It is also shown that the combined effect of slip pulse propagation and strong velocity-weakening friction could yield to size effects in strength with the strength decreasing as a power law with increasing rupture length.
By examining the energy budget of slip pulses in the discrete model, we show that it is possible to derive a nonlinear differential equation that could predict the final slip distribution in an event, given the prestress existing before that event and some information about friction and pulse dynamics. The equation is successful in replicating many of the macroscopic slip features, including the slip distribution and total rupture length, can also match many long-time statistics regarding the prestress evolution and the event size distribution.
Results from the continuum study suggest that the absence of steady pulses in previous studies could be attributed to the details of the nucleation procedure. We show that steady pulses could exist on strong velocity-weakening friction and uniform prestress if both the prestress and nucleation procedures are correctly tuned. We find that steady pulses are unstable to perturbations in the form of a step in the prestress and could arrest quickly in regions of low prestress. Steady pulses are also found to adapt well to local fluctuations in the prestress, leading to heterogeneous slip distributions. This result might have important implications for the problem of slip complexity in real earthquakes.</p
Imaging with Second-Harmonic Generation Nanoparticles
Get PDFSecond-harmonic generation nanoparticles show promise as imaging probes due to their coherent and stable signal with a broad flexibility in the choice of excitation wavelength. In this thesis, we developed and demonstrated barium titanate nanoparticles as second-harmonic radiation imaging probes. We studied the absolute second-harmonic generation efficiency of the nanoparticles on single-particle level. The polarization dependent second-harmonic signal of single nanoparticles was studied in detail. From the measured polar response, we were able to find the orientation of the nanoparticle. We developed a biochemical interface for using the second-harmonic nanoprobes as biomarkers, including in vitro cellular imaging and in vivo live animal imaging. The nanoparticles were surface functionalized with primary amine groups for stable colloidal dispersion. We achieved specific labeling of the second-harmonic nanoprobes via immunostaining where the antibodies were covalently conjugated onto the nanoparticles. We observed no toxicity of the functionalized nanoparticles to biological cells. The coherent second-harmonic signal radiated from the nanoparticles offers opportunities for new imaging techniques. Using interferometric detection, namely harmonic holography, both amplitude and phase of the second-harmonic field can be captured. Through digital beam propagation, three-dimensional field distribution, reflecting three-dimensional distribution of the nanoparticles, can be reconstructed. We achieved a scan-free three-dimensional imaging of nanoparticles in biological cells with sub-micron spatial resolution by using the harmonic holographic microscope. We further exploited the coherent second-harmonic signal for imaging through scattering media by performing optical phase conjugation of the second-harmonic signal. We demonstrated an all-digital optical phase conjugation of the second-harmonic signal originated from a nanoparticle by combining harmonic holography and dynamic computer generated holography using a spatial light modulator. The phase-conjugated second-harmonic scattered field retraced the scattering trajectory and formed a clean focus on the nanoparticle placed inside a scattering medium. The nanoparticle acted as a beacon of light; it helped us find the tailored wavefront for concentrating light at the nanoparticle inside the scattering medium. We also demonstrated imaging through a thin scattering medium by raster-scanning the phase-conjugated focus in the vicinity of the beacon nanoparticle, in which a clear image of a target placed behind a ground glass diffuser was obtained
Properties of the Subduction System in Mexico
Get PDFThis thesis presents seismic imaging results of the structure of the Mexican subduction zone using receiver function (RF) based on teleseismic P-to-S converted waves, in order to gain insight into the physical and chemical factors associated with internal geodynamic processes. More specifically, this thesis investigates (1) the nature of tectonic processes involved in the buildup and subsequent modification of continental and oceanic lithosphere, and (2) the determination of mineralogy/petrology and fluidphase
reactions in the subducting Cocos oceanic crust.
Utilizing the data acquired from two dense broadband seismic lines in Mexico, the geometries and seismic properties of the interface of the subducting Cocos plate beneath Mexico are determined from the RFs. The RF image for central Mexico shows that the subducting oceanic crust dips shallowly north at 15 degrees for a distance of 80 km from Acapulco at the Pacific coast, and then horizontally underplates the continental crust for approximately 200 km to the Trans-Mexican Volcanic Belt (TMVB). Modeling of the RF conversion amplitudes and timings of the underplated features reveals a thin very-low velocity zone between the plate and the continental crust that appears to absorb nearly all of the strain between the upper plate and the slab. The migrated image of the RFs shows that the slab dips steeply into the mantle at an angle of about 75 degrees beneath the TMVB.
The RF results for southern Mexico in the Isthmus of Tehuantepec show an image of the Cocos slab down to about 100 km depth. The same cross-section image also reveals a slab-like south-dipping structure interpreted to be subducted from the Gulf of Mexico. This anomalous slab with the opposite dip direction of the Cocos slab appears to cut off the Cocos slab at 150 km depth. There is no tectonic explanation for the south-dipping slab under the current paradigm of Caribbean plate reconstructions. We present in this thesis the case for a new reconstruction of the Gulf of Mexico and propose that the slab may be due to the collision of the Yucatan Block into Mexico in the Miocene, and may also be responsible for the Cocos plate truncation imaged from previous tomography studies. This hypothesis explains the Chiapas Fold and Thrust Belt to the south of the Yucatan Block and may explain the unusual volcanic arc configuration in southern Mexico.
We formulate and apply a new inversion technique based on the plane wave conversion to obtain the seismic parameters (S wave velocity, Vs, and density) of the oceanic crust. We use such parameters to infer mineralogical properties of subducting oceanic crust. From this effort, we provide tighter constraints on physical properties of the subducting Cocos oceanic crust, and explain the difference in the slab geometries betweeen central and southern Mexico from the mineral physics point of view. Anomalously low Vs (2.4−3.4 km/s) in the upper part of the flat oceanic crust in central Mexico points to elevated Poisson’s and Vp/Vs ratios of the oceanic crust. This directly relates to the presence of water and hydrous minerals or high pore pressure; the mechanically weak hydrous layer may explain current subduction geometry at very shallow depth of about 45 km without strong coupling between the plates.
Using Vp/Vs as a function of Vs in a range of likely pressure and temperature for candidate hydrous phases, we identify the major hydrous mineral phases present in the upper (3−5 km thickness) and lower parts (3−5 km thickness) of the subducted oceanic crust of central and southern Mexico. In central Mexico, the upper oceanic crust in the flat slab region is enriched with hydrous minerals such as talc over the normal oceanic crustal compositions such as MORB-like gabbro. Petrologically, the generation of talc during subduction of the oceanic crust is nearly impossible. One possible mechanism to produce such a low-velocity anomaly at the upper oceanic crust is that lower crustal rocks are hydrated with 15-20 percent of free water to reduce the seismic velocities significantly. We thus propose that the thin low-velocity, talc-rich layer in the upper oceanic crust is then generated from the mantle wedge side during the slab flattening process coupled with trench rollback. The talc-rich rocks at the slab interface can be formed in the mantle by the addition of silica transported by rising fluids via the dehydration reaction from the subducting oceanic crust and by mechanical mixing of mantle and siliceous rocks. The evolution of the thin low-strength zone, which decouples the horizontal slab from the continental crust, originating from the mantle wedge side rather than the trench side, has important implications for the dynamics of the subduction system, including the flattening process of the slab, as well as the geochemistry of the mantle wedge and arc in central Mexico. After passing through the flat segment, the major compositions of the steeply subducting oceanic crust underneath the TMVB are zoisite and lawsonite from 60 to 100 km in depth. The eclogitization occurs at the depth of about 100 km. The dominant mineral phase in the upper oceanic crust of southern Mexico from 45 to 120 km depth is amphibole on top of unaltered gabbroic oceanic crust.</p
Mechanistic Investigations into the Palladium-Catalyzed Decarboxylative Allylic Alkylation of Ketone Enolates Using the PHOX Ligand Architecture
Get PDFPalladium-catalyzed asymmetric allylic alkylation has become a large and important field for chemical synthesis. Many methodologies in this field offer mild conditions under which challenging and important molecular features can be reliably synthesized, including chiral all-carbon quaternary stereocenters. As a result, palladium- catalyzed asymmetric allylic alkylation has found significant use in total synthesis, and growing use in industry. While the general process of palladium-catalyzed asymmetric allylic alkylation has been studied for decades, there have been a number of recent modifications and developments, such as asymmetric versions of decarboxylative allylic alkylation procedures that are not yet well understood. The development of future implementations and improvements to palladium-catalyzed asymmetric allylic alkylation and related methodologies is expected to be facilitated by a better understanding of these more recent developments, and thus further mechanistic investigation is warranted.
Reported herein is a set of investigations into the palladium-catalyzed decarboxylative asymmetric allylic alkylation of ketone enolates using the PHOX ligand architecture. By monitoring the reaction via 31P NMR, a series of previously unidentified key intermediates is discovered. Two representatives of these key intermediates are isolated and characterized. The solution behavior of these species under reaction-like conditions is studied along with a few novel and related complexes. The role of these intermediates and their impact on the behavior of the reaction and product formation is discussed. Previously confounding experimentally observed behavior for this methodology is rationalized via the properties elucidated for these discovered intermediates.</p
Emerging Paradigms in Quantum Error Correction and Quantum Cryptography
Get PDFWe study two novel paradigms in quantum error correction and quantum cryptography — approximate quantum error correction and noisy-storage cryptography — which explore alternate approaches for dealing with quantum noise. Approximate quantum error correction seeks to relax the constraint of perfect error correction and construct codes that might be better adapted to correct for specific noise models. Noisy-storage cryptography relies on the power of quantum noise to execute two-party cryptographic tasks securely.
Motivated by examples of approximately correcting codes, which make use of fewer physical resources than perfect codes and still obtain comparable levels of fidelity, we study the problem of finding and characterizing such codes in general. We construct for the first time a universal, near-optimal recovery map for approximate quantum error correction (AQEC), with optimality defined in terms of worst-case fidelity. Using the analytical form of this recovery, we also obtain easily verifiable conditions for AQEC. This in turn leads to a simple algorithm for identifying good approximate codes, without having to perform a difficult optimization over all recovery maps for every possible encoding.
Noisy-storage cryptography envisions a setting where two-party cryptographic protocols can be securely implemented based solely on the assumption that the quantum storage device possessed by either party is noisy and bounded. Here, we construct two-party protocols (using higher-dimensional states) that are secure even when a dishonest player can store all but a small fraction of the information transmitted during the protocol, in his noiseless quantum memory. We also show that when his memory is noisy, security can be extended to a larger class of noisy quantum memories. Our result demonstrates that the physical limits of the quantum noisy-storage model are indeed achievable, albeit asymptotically.
We also describe our investigations on obtaining strong entropic uncertainty relations using symmetric complementary bases. Uncertainty relations are an important and useful resource in analyzing the security of quantum cryptographic protocols, in addition to being of interest from a foundational standpoint. We present a novel construction of sets of symmetric, complementary bases in dimension d = 2n, which are cyclically permuted under the action of a unitary transformation. We also obtain new lower bounds for uncertainty relations in terms of the min-entropy, which are tight for specific instances of our construction.</p
Network Coding for Error Correction
Get PDFIn this thesis, network error correction is considered from both theoretical and practical viewpoints. Theoretical parameters such as network structure and type of connection (multicast vs. nonmulticast) have a profound effect on network error correction capability. This work is also dictated by the practical network issues that arise in wireless ad-hoc networks, networks with limited computational power (e.g., sensor networks) and real-time data streaming systems (e.g., video/audio conferencing or media streaming).
Firstly, multicast network scenarios with probabilistic error and erasure occurrence are considered. In particular, it is shown that in networks with both random packet erasures and errors, increasing the relative occurrence of erasures compared to errors favors network coding over forwarding at network nodes, and vice versa. Also, fountain-like error-correcting codes, for which redundancy is incrementally added until decoding succeeds, are constructed. These codes are appropriate for use in scenarios where the upper bound on the number of errors is unknown a priori.
Secondly, network error correction in multisource multicast and nonmulticast network scenarios is discussed. Capacity regions for multisource multicast network error correction with both known and unknown topologies (coherent and noncoherent network coding) are derived. Several approaches to lower- and upper-bounding error-correction capacity regions of general nonmulticast networks are given. For 3-layer two-sink and nested-demand nonmulticast network topologies some of the given lower and upper bounds match. For these network topologies, code constructions that employ only intrasession coding are designed. These designs can be applied to streaming erasure correction code constructions.</p
Geophysical Investigations of Near-Surface Structure on the Earth and Mars
Get PDFI use remote sensing and active seismic methods to investigate near-surface structure on the Earth and Mars. These studies provide insight into styles of crustal deformation acting on continental margins in regions of extension, as well as paleoclimates that shaped the polar ice caps on Mars. I map the overall structure of the ice-rich Planum Boreum deposit at the north pole of Mars using 178 orbits of Mars Advanced Radar for Subsurface and Ionosphere Sounding data, and find no deflection of the lithosphere beneath the ice load. Bright, laterally extensive subsurface reflectors in the radargrams define the surface underlying Planum Boreum, as well as the interface between the two main units, the stratigraphically older Basal Unit and the stratigraphically younger North Polar Layered Deposits. The volumes of these units, and the overall edifice, are determined to the greatest accuracy possible to date. On Earth, I use a GPS campaign network in the state of Jalisco to investigate tectonic motion and interseismic deformation in the area. The consistent magnitude and direction of station velocities on the Jalisco Block suggest that it is moving rigidly with respect to North America. We constrain extension across the bounding fault zones of the block to values that are slow compared to relative rates of motion at nearby plate boundaries. I study another continental rift zone, in the Ross Sea, Antarctica, with refraction seismic data collected during research cruise NBP0701. I construct velocity models from 71 sonobuoys that detect deep structure in the oceanic crust of the Adare Basin and the crust of the Northern Basin, which lies to the south on the continental shelf. We demonstrate the importance of using multi-channel seismic data to correct for ocean currents and changes in ship navigation, the finite-difference modeling techniques necessary for accurately determining 1D velocity profiles for each sonobuoy, and for tying true velocities to the multi-channel seismic images of subsurface structure. We construct 2D velocity profiles using widely spaced sonobuoys in the Adare Basin, and using overlapping sonobuoys along some lines in both basins, and across the shelf break, to investigate crustal structure in the region. Detection of the Moho at 5.5 km below the seafloor by one sonobuoy suggests relatively thin oceanic crust in the Adare Basin, and flat velocity contours across the margin suggest continuity in crustal structure between the two basins
Constraining Anthropogenic and Biogenic Emissions using Chemical Ionization Mass Spectrometry
Get PDFNumerous gas-phase anthropogenic and biogenic compounds are emitted into the atmosphere. These gases undergo oxidation to form other gas-phase species and particulate matter. Whether directly or indirectly, primary pollutants, secondary gas-phase products, and particulate matter all pose health and environmental risks. In this work, ambient measurements conducted using chemical ionization mass spectrometry are used as a tool for investigating regional air quality.
Ambient measurements of peroxynitric acid (HO₂NO₂) were conducted in Mexico City. A method of inferring the rate of ozone production, PO3, is developed based on observations of HO₂NO₂, NO, and NO₂. Comparison of this observationally based PO3 to a highly constrained photochemical box model indicates that regulations aimed at reducing ozone levels in Mexico City by reducing NOx concentrations may be effective at higher NOx levels than predicted using accepted photochemistry.
Measurements of SO₂ and particulate sulfate were conducted over the Los Angeles basin in 2008 and are compared to measurements made in 2002. A large decrease in SO₂ concentration and a change in spatial distribution are observed. Nevertheless, only a modest reduction in sulfate concentration is observed at ground sites within the basin. Possible explanations for these trends are investigated.
Two techniques, single and triple quadrupole chemical ionization mass spectrometry, were used to quantify ambient concentrations of biogenic oxidation products, hydroxyacetone and glycolaldehyde. The use of these techniques demonstrates the advantage of triple quadrupole mass spectrometry for separation of mass analogues, provided the collision-induced daughter ions are sufficiently distinct. Enhancement ratios of hydroxyacetone and glycolaldehyde in Californian biomass burning plumes are presented as are concentrations of these compounds at a rural ground site downwind of Sacramento.</p
Individual Particle Motion in Colloids: Microviscosity, Microdiffusivity, and Normal Stresses
Get PDFColloidal dispersions play an important role in nearly every aspect of life, from paint to biofuels to nano-therapeutics. In the study of these so-called complex fluids, a connection is sought between macroscopic material properties and the micromechanics of the suspended particles. Such properties include viscosity, diffusivity, and the osmotic pressure, for example. But many such systems are themselves only microns in size overall; recent years have thus seen a dramatic growth in demand for exploring microscale systems at a much smaller length scale than can be probed with conventional macroscopic techniques. Microrheology is one approach to such microscale interrogation, in which a Brownian “probe” particle is driven through a complex fluid, and its motion tracked in order to infer the mechanical properties of the embedding material. With no external forcing the probe and background particles form an equilibrium microstructure that fluctuates thermally with the solvent. Probe motion through the dispersion distorts the microstructure; the character of this deformation, and hence its influence on probe motion, depends on the strength with which the probe is forced, F ext , compared to thermal forces, kT/b, defining a P´eclet number, P e = F ext /(kT /b), where kT is the thermal energy and b the bath-particle size. Both the mean and the fluctuating motion of the probe are of interest. Recent studies showed that the reduction in mean probe speed gives the effective material viscosity. But the velocity of the probe also fluctuates due to collisions with the suspended particles, causing the probe to undergo a random walk process. It is shown that the long-time mean-square fluctuational motion of the probe is diffusive and the effective diffusivity of the forced probe is determined for the full range of P´eclet number. At small Pe Brownian motion dominates and the diffusive behavior of the probe characteristic of passive microrheology is recovered, but with an incremental flow-induced “micro-diffusivity” that scales as Dmicro ∼ Da P e 2 φb , where viii φb is the volume fraction of bath particles and Da is the self-diffusivity of an isolated probe. At the other extreme of high P´eclet number the fuctuational motion is still diffusive, and the diffusivity becomes primarily force-induced , scaling as (F ext /η)φb , where η is the viscosity of the solvent. The force-induced “microdiffusivity” is anisotropic, with diffusion longitudinal to the direction of forcing larger in both limits compared to transverse diffusion, but more strongly so in the high-P e limit.
Previous work in microrheology defined a scalar viscosity; however, a tensorial expression for the suspension stress in microrheology was still lacking. The notion that diffusive flux is driven by gradients in particle-phase stress leads to the idea that the microdiffusivity can be related directly to the suspension stress. In consequence, the anisotropy of the diffusion tensor may reflect the presence of normal stress differences in non-linear microrheology. While the particle-phase stress tensor can be determined as the second moment of the deformed microstructure, in this study a connection is made between diffusion and stress gradients, and an analytical expression for particle-phase stress as a function of the microdiffusivity and microviscosity is obtained. The two approaches agree, suggesting that normal stresses and normal stress differences can be measured in active microrheological experiments if both the mean and mean-square motion of the probe are monitored. Owing to the axisymmetry of the motion about a spherical probe, the second normal stress difference is zero, while the first normal stress difference is linear in P e for P e ≫ 1 and vanishes as P e 3 for P e ≪ 1. An additional important outcome is that the analytical expression obtained for stress-induced migration can be viewed as a generalized non-equilibrium Stokes-Einstein relation.
Studies of steady-state dispersion behavior reveal the hydrodynamic and microstructural mechanisms that underlie non-Newtonian behaviors (e.g. shear-thinning, shear-thickening, and normal stress differences). But an understanding of how the microstructures evolve from the equilibrium state, and how non-equilibrium properties develop in time is much less well understood. Transient suspension behavior in the near-equilibrium, linear response regime has been studied via its connection to low-amplitude oscillatory probe forcing and the complex modulus; at very weak forcing, the microstructural response that drives viscosity is indistinguishable from equilibrium fluctuations. But important information about the basic physical aspects of structural development and relaxation ix in a medium are captured by start-up and cessation of the imposed deformation in the non-linear regime, where the structure is driven far from equilibrium. Here we study the evolution of stress and microstructure in a colloidal dispersion by tracking transient probe motion during start-up and cessation of a strong flow. For large P e, steady state is reached when a boundary layer (in which advection balances diffusion) forms at particle contact on the timescale of the flow, a/U , where a is the probe size and U its speed. On the other hand, relaxation following cessation occurs over several timescales corresponding to distinct physical processes. For very short times, the timescale for relaxation is set by the diffusion over the boundary-layer thickness. Nearly all stress relaxation occurs during this process, owing to the dependence of the bath-particle drag on the contact value of the microstructure. At longer times the collective diffusion of the bath particles acts to close the wake. In this long-time limit as structural isotropy is restored, the majority of the microstructural relaxation occurs with very little change in suspension stress. Theoretical results are presented and compared with Brownian dynamics simulation. Two regimes of probe motion are studied: an externally applied constant force and an imposed constant velocity. The microstructural evolution is qualitatively different for the two regimes, with a longer transient phase and a thinner boundary layer and longer wake at steady state in the latter case. The work is also compared to analogous results for sheared suspensions undergoing start-up and cessation.
The study moves next to investigations of dual-probe microrheology. Motivated by the phenomenon of equilibrium depletion interactions, we study the interaction between a pair of probe particles translating with equal velocity through a dispersion with their line of centers transverse to the external forcing. The character of the microstructure surrounding the probes is determined both by the distance R by which the two probes are separated and by the strength of the external forcing, P e = U a/Db , where U is the constant probe velocity and Db the diffusivity of the bath particles. Osmotic pressure gradients develop as the microstructure is deformed, giving rise to an interactive force between the probes. This force is studied for a range of P e and R. For all separations R > 2a, the probes attract when P e is small. As the strength of the forcing increases, a qualitative change in the interactive force occurs: the probes repel each other. The probe separation R at which the x attraction-to-repulsion transition occurs decreases as P e increases, because the entropic depletion attraction becomes weak compared to the force-induced osmotic repulsion. The non-equilibrium interactive force is strictly repulsive for two separated probes.
But non-linear microrheology provides far more than a microscale technique for interrogating complex fluids. In 1906, Einstein published the famous thought experiment in which he proposed that if a liquid were indeed composed of atoms, then the motion of a small particle suspended in the fluid would move with the same random trajectories as the solvent atoms. Combining the theories of kinetics, diffusion, and thermodynamics, he showed that the diffusive motion of a small particle is indeed evidence of the existence of the atom. Perrin confirmed the theory with measurement in 1909. This is a profound conclusion, drawn by simply watching a particle move in a liquid. Here, we follow this example and watch a particle move in a complex fluid—but now for a system that is not at equilibrium. In equilibrium systems, the relationship between fluctuation and dissipation is fundamental to our understanding of colloid physics. By studying fluctuations away from equilibrium, we have discovered an analogous non-equilibrium relation between fluctuation and dissipation—and that the balance between the two is stored in the material stress. A final connection can be made between this stress and energy storage.</p