Athermal State Research Articles

Quantum batteries at the verge of a phase transition

Starting from the observation that the reduced state of a system strongly coupled to a bath is, in general, an athermal state, we introduce and study a cyclic battery–charger quantum device that is in thermal equilibrium, or in a ground state, during the charge storing stage. The cycle has four stages: the equilibrium storage stage is interrupted by disconnecting the battery from the charger, then work is extracted from the battery, and then the battery is reconnected with the charger; finally, the system is brought back to equilibrium. At no point during the cycle are the battery–charger correlations artificially erased. We study the case where the battery and charger together comprise a spin-1/2 Ising chain, and show that the main characteristics—the extracted energy and the thermodynamic efficiency—can be enhanced by operating the cycle close to the quantum phase transition point. When the battery is just a single spin, we find that the output work and efficiency show a scaling behavior at criticality and derive the corresponding critical exponents. Due to always present correlations between the battery and the charger, operations that are equivalent from the perspective of the battery can entail different energetic costs for switching the battery–charger coupling. This happens only when the coupling term does not commute with the battery’s bare Hamiltonian, and we use this purely quantum leverage to further optimize the performance of the device.

Charging assisted by thermalization

A system in thermal equilibrium with a bath will generally be in an athermal state, if the system-bath coupling is strong. In some cases, it will be possible to extract work from that athermal state, after disconnecting the system from the bath. We use this observation to devise a battery charging and storing unit, simply consisting of a system, acting as the battery, and a bath. The charging cycle---connect, let thermalize, disconnect, extract work---requires very little external control and the charged state of the battery, being a part of global thermal equilibrium, can be maintained indefinitely and for free. The efficiency, defined as the ratio of the extractable work stored in the battery and the total work spent on connecting and disconnecting, is always $\leq 1$, which is a manifestation of the second law of thermodynamics. Moreover, coupling, being a resource for the device, is also a source of dissipation: the entropy production per charging cycle is always significant, strongly limiting the efficiency in all coupling strength regimes. We show that our general results also hold for generic microcanonical baths. We illustrate our theory on the Caldeira-Leggett model with a harmonic oscillator (the battery) coupled to a harmonic bath, for which we derive general asymptotic formulas in both weak and ultrastrong coupling regimes, for arbitrary Ohmic spectral densities. We show that the efficiency can be increased by connecting several copies of the battery to the bath. Finally, as a side result, we derive a general formula for Gaussian ergotropy, that is, the maximal work extractable by Gaussian unitary operations from Gaussian states of multipartite continuous-variable systems.

The heat is on

Model magnetic systems known as artificial spin ices have almost always been found in frozen, athermal states. But an artificial spin ice that is designed to be thermally active has now been imaged as it explores its frustrated energy landscape.

Charge transfer and coherence dynamics of a tunnelling system coupled to an harmonicoscillator

We study the transition probability and coherence of a two-site system, interacting with anoscillator. Both properties depend on the initial preparation. The oscillator is prepared in athermal state and, even though it cannot be considered as an extended bath,it produces decoherence because of the large number of states involved in thedynamics. In the case in which the oscillator is initially displaced, a coherentdynamics of charge entangled with oscillator modes takes place. Coherency is,however, degraded as far as the oscillator mass increases, producing an increasinglylarge recoherence time. Calculations are carried on by exact diagonalization andcompared with two semiclassical approximations. The role of the quantum effectsare highlighted in the long time dynamics, where semiclassical approaches giverise to a dissipative behaviour. Moreover, we find that the oscillator dynamicshas to be taken into account, even in a semiclassical approximation, in orderto reproduce a thermally activated enhancement of the transition probability.

Lattice Monte Carlo simulation of dilute ionic surfactants

We made progress towards developing a model for ionic surfactants that allows us to predict their micellization properties quantitatively. The strength of the model lies in its simplicity and generality, and it could be used to study different surfactants. The aggregation of surfactants in binary mixtures of water and an ionic surfactant was studied by Metropolis Monte Carlo simulation (MCS) in the canonical ensemble (NVT) on a 3-D lattice model. The lattice theory was changed in order to investigate the aggregation of ionic surfactant systems using the simulation technique. In the model contributions of both the short-range and long-range forces were considered. We determined the monomer concentration and plotted it against the total surfactant concentration. We observed two distinct regions of different slopes in the curve. At low concentrations, the curve follows a higher slope that corresponds to the single surfactant molecules in solution, there is a break in the curve, and a second straight line with a lower slope continues at higher concentrations. Thermodynamically this indicates that above a certain concentration surfactant molecules in the system will begin to form aggregates and that the concentration of free surfactants will remain roughly constant around the critical micelle concentration (CMC). It would also be of great interest to perform a systematic study on the effects of the various parameters on the micellization properties. The systems were quenched to low temperatures from the athermal state, and relaxed for an adequately long time. To avoid metastable states, the simulations for each condition were started at athermal conditions and the interaction energy was increased in small steps, after equilibrium was attained at each step, until the desired interaction energy was reached. It was found that the CMC decreased with an increase in surfactant chain length and increased with an enhancement in solvent dipole moment. It was also found that the CMC decreased as the counter-ion radius decreased.

Low-temperature ordering effects in diblock copolymer melts from lattice simulation

A lattice simulation of a model diblock copolymer melt is presented. In a series of simulation experiments an 8-8 diblock melt is quenched from an athermal state to 47 lower temperatures. A set of simulation boxes, 30 x 32 x 30, 40 x 32 x 60, 50 x 32 x 30, and 60 x 32 x 30, is used in order to explore the size effects. Energy, specific heat, copolymer end-to-end distance, lamellar spacing, and the degree of interfacial ordering are reported. For all sizes considered, the low-temperature interfacial ordering is noticeable.

Lamellar ordering in computer-simulated block copolymer melts by a variety of thermal treatments

A lattice computer simulation of a symmetric A–B–A triblock copolymer melt is reported. This melt is quenched, in simulation, from an athermal state to 39 different temperatures using cooperative motion algorithm. Energy, specific heat, copolymer end-to-end distance, bridging fraction, lamellar spacing, concentration profiles, and microstructure visualizations are reported. The quenching simulation results are compared with those obtained by alternative thermal treatments, that is by slow heating and slow cooling. Quenches yield data consistent with theory and experiment, whereas slow cooling and slow heating results do not capture the expected behavior for the lamellar spacing and the bridging fraction. Finally, at very low temperatures, below the conventional order–disorder transition temperature, an additional ordering is recorded, from a conventional lamellar phase to a lamellar structure showing copolymer junction points condensed into a two-dimensional plane.

Ionized physical vapor deposition of Cu on 300 mm wafers: A modeling study

A two-dimensional model has been used to understand the physics and process engineering issues associated with a conceptual 300 mm Cu internal-coil ionized physical vapor deposition reactor. It has been found that inductive coupling from the coil is the primary source of plasma production. Since the coil is in direct contact with the plasma, a significant fraction of the coil power is deposited in the gas capacitively as well. This results in sputtering of the Cu coil, which tends to improve Cu flux uniformity at the outer edges of the wafer. Since the Cu ionization threshold is much lower than Ar, Cu+ density is comparable to Ar+ density even though ground state Cu density is much smaller than Ar. Significant fraction of the neutral Cu flux to the wafer is in the metastable or athermal state. The effects of several actuators, reactor dimensions, and buffer gas on important plasma and process quantities have also been investigated. Electron density in the reactor and Cu ionization fraction increases with increasing total coil power because of enhanced ionization. Total coil power however does not affect the Cu density appreciably, except near the coil where enhanced coil sputtering increases the Cu density. Decrease in dc target voltage with increasing coil power decreases Cu+ loss to the target and results in an increase in total Cu flux to the wafer. Electron and Cu density in the reactor increase with increasing dc target power. This is due to enhancement in target sputtering and consequent ionization of the sputtered Cu. While this increases the total Cu flux to the wafer, ionization fraction is not affected much. It is demonstrated that uniformity of Cu flux to the wafer and ionization fraction can be controlled by means of the terminating capacitor at the coil. Decreasing the terminating capacitance increases the coil voltage, enhances coil sputtering and enhances Cu flux toward the outer edges of the wafer. This, however, decreases the amount of power that is transferred to the plasma inductively, reducing the ionization efficiency. Increasing the coil–wafer distance results in fewer sputtered Cu atoms being ionized as the target–coil distance becomes smaller than the mean free path for thermalization of hot sputtered Cu atoms. Also, one can control the ionization fraction of Cu flux to the wafer by replacing Ar by Ne or Xe, without significantly impacting the total Cu flux.

Entropy-driven phase separation and configurational correlations on a lattice: some rigorous results.

We prove that if there is a phase separation in a fully packed (FP) athermal system, it must be between pure components only. We then rigorously demonstrate that no phase separation in an athermal FP state of hard particle mixtures on a lattice is possible merely due to size disparity or nonadditivity, if the configurations are weakly correlated, i.e., are quasirandom. We consider a mixture of linear polymers at all packing fractions and argue that no phase separation is possible in an athermal state. The last result also applies to a mixture of flexible particles and hard dimers. Our results contradict many recent numerical results.

Simulations of excluded volume effects due to chain thickness and solvent quality on the chain vector distributions and mean coil dimensions

AbstractLattice simulations of chains in good, theta and poor solvents were performed with an explicit incorporation of the excluded volume (chain thickness) into the model. The scaling power law for chain dimensions was found to apply in the theta and athermal states and to fail in the region below the theta state where collapsed chains with voids inside a globule occur. The solvent‐induced globule‐to‐coil transition is transparently manifested by changes in the chain vector distribution functions. In the region of small and medium chain elongations, the simulation data can be fitted in the theta solvent by a Gaussian distribution function and in the athermal solvent by a function due to Oono et al. The stored elastic energy of the chains with fixed ends was calculated as a function of the chain‐end displacement for fully flexible molecules in all three types of solvent and for poly(methylene).